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Sat / act prep online guides and tips, the 5 best homework help websites (free and paid).

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Listen: we know homework isn’t fun, but it is a good way to reinforce the ideas and concepts you’ve learned in class. But what if you’re really struggling with your homework assignments?

If you’ve looked online for a little extra help with your take-home assignments, you’ve probably stumbled across websites claiming to provide the homework help and answers students need to succeed . But can homework help sites really make a difference? And if so, which are the best homework help websites you can use? 

Below, we answer these questions and more about homework help websites–free and paid. We’ll go over: 

• The basics of homework help websites
• The cost of homework help websites 
• The five best homework websites out there 
• The pros and cons of using these websites for homework help 
• The line between “learning” and “cheating” when using online homework help 
• Tips for getting the most out of a homework help website

So let’s get started! 

The Basics About Homework Help Websites–Free and Paid

Homework help websites are designed to help you complete your homework assignments, plain and simple. 

What Makes a Homework Help Site Worth Using

Most of the best sites allow users to ask questions and then provide an answer (or multiple possible answers) and explanation in seconds. In some instances, you can even send a photo of a particular assignment or problem instead of typing the whole thing out! 

Homework help sites also offer more than just help answering homework questions. Common services provided are Q&A with experts, educational videos, lectures, practice tests and quizzes, learning modules, math solving tools, and proofreading help. Homework help sites can also provide textbook solutions (i.e. answers to problems in tons of different textbooks your school might be using), one-on-one tutoring, and peer-to-peer platforms that allow you to discuss subjects you’re learning about with your fellow students. 

And best of all, nearly all of them offer their services 24/7, including tutoring! 

What You Should Should Look Out For

When it comes to homework help, there are lots–and we mean lots –of scam sites out there willing to prey on desperate students. Before you sign up for any service, make sure you read reviews to ensure you’re working with a legitimate company. 

A word to the wise: the more a company advertises help that veers into the territory of cheating, the more likely it is to be a scam. The best homework help websites are going to help you learn the concepts you’ll need to successfully complete your homework on your own. (We’ll go over the difference between “homework help” and “cheating” a little later!) 

You don't need a golden piggy bank to use homework help websites. Some provide low or no cost help for students like you!

How Expensive Are the Best Homework Help Websites?

First of all, just because a homework help site costs money doesn’t mean it’s a good service. Likewise, just because a homework help website is free doesn’t mean the help isn’t high quality. To find the best websites, you have to take a close look at the quality and types of information they provide! 

When it comes to paid homework help services, the prices vary pretty widely depending on the amount of services you want to subscribe to. Subscriptions can cost anywhere from $2 to $150 dollars per month, with the most expensive services offering several hours of one-on-one tutoring with a subject expert per month.

The 5 Best Homework Help Websites 

So, what is the best homework help website you can use? The answer is that it depends on what you need help with. 

The best homework help websites are the ones that are reliable and help you learn the material. They don’t just provide answers to homework questions–they actually help you learn the material. 

That’s why we’ve broken down our favorite websites into categories based on who they’re best for . For instance, the best website for people struggling with math might not work for someone who needs a little extra help with science, and vice versa. 

Keep reading to find the best homework help website for you! 

Best Free Homework Help Site: Khan Academy

• Price: Free!
• Best for: Practicing tough material 

Not only is Khan Academy free, but it’s full of information and can be personalized to suit your needs. When you set up your account , you choose which courses you need to study, and Khan Academy sets up a personal dashboard of instructional videos, practice exercises, and quizzes –with both correct and incorrect answer explanations–so you can learn at your own pace. 

As an added bonus, it covers more course topics than many other homework help sites, including several AP classes.

Runner Up: Brainly.com offers a free service that allows you to type in questions and get answers and explanations from experts. The downside is that you’re limited to two answers per question and have to watch ads. 

Best Paid Homework Help Site: Chegg

• Price: $14.95 to $19.95 per month
• Best for: 24/7 homework assistance  

This service has three main parts . The first is Chegg Study, which includes textbook solutions, Q&A with subject experts, flashcards, video explanations, a math solver, and writing help. The resources are thorough, and reviewers state that Chegg answers homework questions quickly and accurately no matter when you submit them.  

Chegg also offers textbook rentals for students who need access to textbooks outside of their classroom. Finally, Chegg offers Internship and Career Advice for students who are preparing to graduate and may need a little extra help with the transition out of high school. 

Another great feature Chegg provides is a selection of free articles geared towards helping with general life skills, like coping with stress and saving money. Chegg’s learning modules are comprehensive, and they feature solutions to the problems in tons of different textbooks in a wide variety of subjects. 

Runner Up: Bartleby offers basically the same services as Chegg for $14.99 per month. The reason it didn’t rank as the best is based on customer reviews that say user questions aren’t answered quite as quickly on this site as on Chegg. Otherwise, this is also a solid choice!

Best Site for Math Homework Help: Photomath

• Price: Free (or $59.99 per year for premium services) 
• Best for: Explaining solutions to math problems

This site allows you to t ake a picture of a math problem, and instantly pulls up a step-by-step solution, as well as a detailed explanation of the concept. Photomath also includes animated videos that break down mathematical concepts to help you better understand and remember them. 

The basic service is free, but for an additional fee you can get extra study tools and learn additional strategies for solving common math problems.

Runner Up: KhanAcademy offers in-depth tutorials that cover complex math topics for free, but you won’t get the same tailored help (and answers!) that Photomath offers. 

Best Site for English Homework Help: Princeton Review Academic Tutoring

• Price: $40 to $153 per month, depending on how many hours of tutoring you want 
• Best for: Comprehensive and personalized reading and writing help 

While sites like Grammarly and Sparknotes help you by either proofreading what you write via an algorithm or providing book summaries, Princeton Review’s tutors provide in-depth help with vocabulary, literature, essay writing and development, proofreading, and reading comprehension. And unlike other services, you’ll have the chance to work with a real person to get help. 

The best part is that you can get on-demand English (and ESL) tutoring from experts 24/7. That means you can get help whenever you need it, even if you’re pulling an all-nighter! 

This is by far the most expensive homework site on this list, so you’ll need to really think about what you need out of a homework help website before you commit. One added benefit is that the subscription covers over 80 other subjects, including AP classes, which can make it a good value if you need lots of help!  

Best Site for STEM Homework Help: Studypool

• Best for: Science homework help
• Price: Varies; you’ll pay for each question you submit

When it comes to science homework help, there aren’t a ton of great resources out there. The best of the bunch is Studypool, and while it has great reviews, there are some downsides as well. 

Let’s start with the good stuff. Studypool offers an interesting twist on the homework help formula. After you create a free account, you can submit your homework help questions, and tutors will submit bids to answer your questions. You’ll be able to select the tutor–and price point–that works for you, then you’ll pay to have your homework question answered. You can also pay a small fee to access notes, lectures, and other documents that top tutors have uploaded. 

The downside to Studypool is that the pricing is not transparent . There’s no way to plan for how much your homework help will cost, especially if you have lots of questions! Additionally, it’s not clear how tutors are selected, so you’ll need to be cautious when you choose who you’d like to answer your homework questions.  

What Are the Pros and Cons of Using Homework Help Sites?

Homework help websites can be a great resource if you’re struggling in a subject, or even if you just want to make sure that you’re really learning and understanding topics and ideas that you’re interested in. But, there are some possible drawbacks if you don’t use these sites responsibly. 

We’ll go over the good–and the not-so-good–aspects of getting online homework help below. 

3 Pros of Using Homework Help Websites 

First, let’s take a look at the benefits. 

#1: Better Grades Beyond Homework

This is a big one! Getting outside help with your studies can improve your understanding of concepts that you’re learning, which translates into better grades when you take tests or write essays. 

Remember: homework is designed to help reinforce the concepts you learned in class. If you just get easy answers without learning the material behind the problems, you may not have the tools you need to be successful on your class exams…or even standardized tests you’ll need to take for college. 

#2: Convenience

One of the main reasons that online homework help is appealing is because it’s flexible and convenient. You don’t have to go to a specific tutoring center while they’re open or stay after school to speak with your teacher. Instead, you can access helpful resources wherever you can access the internet, whenever you need them.

This is especially true if you tend to study at off hours because of your extracurriculars, work schedule, or family obligations. Sites that offer 24/7 tutoring can give you the extra help you need if you can’t access the free resources that are available at your school. 

#3: Variety

Not everyone learns the same way. Maybe you’re more of a visual learner, but your teacher mostly does lectures. Or maybe you learn best by listening and taking notes, but you’re expected to learn something just from reading the textbook . 

One of the best things about online homework help is that it comes in a variety of forms. The best homework help sites offer resources for all types of learners, including videos, practice activities, and even one-on-one discussions with real-life experts. 

This variety can also be a good thing if you just don’t really resonate with the way a concept is being explained (looking at you, math textbooks!).

Not so fast. There are cons to homework help websites, too. Get to know them below!

3 Cons of Using Homework Help Websites 

Now, let’s take a look at the drawbacks of online homework help. 

#1: Unreliable Info

This can be a real problem. In addition to all the really good homework help sites, there are a whole lot of disreputable or unreliable sites out there. The fact of the matter is that some homework help sites don’t necessarily hire people who are experts in the subjects they’re talking about. In those cases, you may not be getting the accurate, up-to-date, and thorough information you need.

Additionally, even the great sites may not be able to answer all of your homework questions. This is especially true if the site uses an algorithm or chatbot to help students…or if you’re enrolled in an advanced or college-level course. In these cases, working with your teacher or school-provided tutors are probably your best option. 

#2: No Clarification

This depends on the service you use, of course. But the majority of them provide free or low-cost help through pre-recorded videos. Watching videos or reading info online can definitely help you with your homework… but you can’t ask questions or get immediate feedback if you need it .

#3: Potential For Scamming 

Like we mentioned earlier, there are a lot of homework help websites out there, and lots of them are scams. The review comments we read covered everything from outdated or wrong information, to misleading claims about the help provided, to not allowing people to cancel their service after signing up. 

No matter which site you choose to use, make sure you research and read reviews before you sign up–especially if it’s a paid service! 

When Does “Help” Become “Cheating”?

Admittedly, whether using homework help websites constitutes cheating is a bit of a grey area. For instance, is it “help” when a friend reads your essay for history class and corrects your grammar, or is it “cheating”? The truth is, not everyone agrees on when “help” crosses the line into “cheating .” When in doubt, it can be a good idea to check with your teacher to see what they think about a particular type of help you want to get. 

That said, a general rule of thumb to keep in mind is to make sure that the assignment you turn in for credit is authentically yours . It needs to demonstrate your own thoughts and your own current abilities. Remember: the point of every homework assignment is to 1) help you learn something, and 2) show what you’ve learned. 

So if a service answers questions or writes essays for you, there’s a good chance using it constitutes cheating. 

Here’s an example that might help clarify the difference for you. Brainstorming essay ideas with others or looking online for inspiration is “help” as long as you write the essay yourself. Having someone read it and give you feedback about what you need to change is also help, provided you’re the one that makes the changes later. 

But copying all or part of an essay you find online or having someone write (or rewrite) the whole thing for you would be “cheating.” The same is true for other subjects. Ultimately, if you’re not generating your own work or your own answers, it’s probably cheating.

5 Tips for Finding the Best Homework Help Websites for You

Now that you know some of our favorite homework help websites, free and paid, you can start doing some additional research on your own to decide which services might work best for you! Here are some top tips for choosing a homework help website. 

Tip 1: Decide How You Learn Best 

Before you decide which site or sites you’re going to use for homework help, y ou should figure out what kind of learning style works for you the most. Are you a visual learner? Then choose a site that uses lots of videos to help explain concepts. If you know you learn best by actually doing tasks, choose a site that provides lots of practice exercises.

Tip 2: Determine Which Subjects You Need Help With

Just because a homework help site is good overall doesn’t mean that it’s equally good for every subject. If you only need help in math, choose a site that specializes in that area. But if history is where you’re struggling, a site that specializes in math won’t be much help. So make sure to choose a site that you know provides high-quality help in the areas you need it most. 

Tip 3: Decide How Much One-On-One Help You Need 

This is really about cost-effectiveness. If you learn well on your own by reading and watching videos, a free site like Khan Academy is a good choice. But if you need actual tutoring, or to be able to ask questions and get personalized answers from experts, a paid site that provides that kind of service may be a better option.

Tip 4: Set a Budget

If you decide you want to go with a paid homework help website, set a budget first . The prices for sites vary wildly, and the cost to use them can add up quick. 

Tip 5: Read the Reviews

Finally, it’s always a good idea to read actual reviews written by the people using these homework sites. You’ll learn the good, the bad, and the ugly of what the users’ experiences have been. This is especially true if you intend to subscribe to a paid service. You’ll want to make sure that users think it’s worth the price overall!

What’s Next?

If you want to get good grades on your homework, it’s a good idea to learn how to tackle it strategically. Our expert tips will help you get the most out of each assignment…and boost your grades in the process.

Doing well on homework assignments is just one part of getting good grades. We’ll teach you everything you need to know about getting great grades in high school in this article.

Of course, test grades can make or break your GPA, too. Here are 17 expert tips that’ll help you get the most out of your study prep before you take an exam.

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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What is WeBWork?

Introduction

WeBWorK is an open-source online homework system for math and science courses. WeBWorK is supported by the MAA and the NSF and comes with a National Problem Library (NPL) of over 20,000 homework problems. Problems in the NPL target most lower division undergraduate math courses and some advanced courses. Supported courses include college algebra, discrete mathematics, probability and statistics, single and multivariable calculus, differential equations, linear algebra and complex analysis.

WeBWorK is used successfully at over 700 colleges and universities from large research institutions to small teaching colleges. WeBWorK has been developed and maintained by mathematicians since 1994 always with the goal of providing the mathematical community with the most robust, flexible, and mathematically capable online homework system possible.

WeBWorK is open-source and freely available for download. There is no cost to departments or institutions who wish to host their own WeBWorK server, and the WeBWorK community has always provided prompt technical and pedagogical support through active and friendly discussion forums and mailing lists.

Additionally, the MAA will host WeBWorK courses on a limited basis for departments or institutions who are not in a position to host their own WeBWorK installation.

Learn more...

Video Tutorials for WeBWork

Video 1:   Import assignments and export the sets

Explains how to import homework sets into a WeBWorK course, how to assign the sets to the students and how to export the sets.

Video 2:  Change due dates, add  and drop students

Explains how to add students, change due dates for individual students and drop students."

Video 3:  Creating tests in WeBWork

Explains how to create a test using problems from the Open Problem Library, how to choose the correct settings for the test and how to assign it to the students. Possible pitfalls to avoid are also covered.

Video 4: Monitor student progress

Shows the test from the students’ prospective and shows how the instructor can monitor the students’ progress and check their activity.

Video 5: Test special cases

Explains how to handle special accommodations and what the instructor can do if the student is disconnected.

Video 6: Reduced Scoring

The Reduced Scoring feature in WeBWork allows to set a period after the due date and before the close date during which all additional work done by the student counts at a reduced rate. This feature can be effective in eliminating student requests for time extensions. This video explains how to enable and configure the Reduced Scoring feature.

Video 7: Show me Another

The show me Another feature allows students to see an alternative version of their assigned problem. This video shows how to enable the feature and gives best practice suggestions.

How to use Respondus Lockdown Browser for WeBWorK tests

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Everyday Math Grade 5 Answers Unit 7 Multiplication of Mixed Numbers; Geometry; Graphs

Everyday mathematics 5th grade answer key unit 7 multiplication of mixed numbers; geometry; graphs, everyday mathematics grade 5 home link 7.1 answers.

Mixed-Number Multiplication

For Problems 1 and 2:

• Use the rectangle to make an area model. Label the sides. The model in Problem 1 has been started for you.
• Find and list the partial products. Label the partial products in the area model.
• Add the partial products to find your answer. You may need to rename fractions with a common denominator .

Answer: 20 x 15/8.

Explanation: In the above-given question, given that, the length of the large rectangle = 4. the length of the small rectangle = 3/8. the width of the larger rectangle = 5. the width of the smaller rectangle = 5. area = l x w. where l = length, and w = width. area = 3/8 x 5. area = 15/8. area = 5 x 4. area = 20. area = 20(15/8).

Question 2. 2\(\frac{3}{5}\) ∗ 3\(\frac{1}{3}\) = ? Partial products: 2\(\frac{3}{5}\) ∗ 3\(\frac{1}{3}\) = _________ Area Model:

Answer: 8(10/15).

Question 3. Write a number story that matches Problem 1.

Explanation: In the above-given question, given that, the length of the large rectangle = 4. the length of the small rectangle = 3/8. the width of the larger rectangle = 5. the width of the smaller rectangle = 5. area = l x w. where l = length, and w = width. area = 3/8 x 5. area = 15/8. area = 5 x 4. area = 20.

Practice Solve. Question 4. \(\frac{2}{3}\) + \(\frac{5}{8}\) = _________

Answer: 2/3 + 5/8 = 31/24.

Explanation: In the above-given question, given that, \(\frac{2}{3}\) + \(\frac{5}{8}\). 8 x 3 = 24. 24 + 2 = 26. 26 + 5 = 31. 2/3 + 5/8 = 31/24.

Question 5. \(\frac{1}{16}\) + \(\frac{3}{4}\) = ___________

Answer: 1/16 + 3/4 = 13/16.

Explanation: In the above-given question, given that, \(\frac{1}{16}\) + \(\frac{3}{4}\). 4 x 4 = 16. 4 x 3 = 12. 12 + 1 = 13. 1/16 + 3/4 = 13/16.

Everyday Math Grade 5 Home Link 7.2 Answer Key

More Mixed-Number Multiplication

Solve Problems 1 and 2 using the method in the example below. Show your work. Example: 2\(\frac{1}{5}\) ∗ 1\(\frac{3}{4}\)

• Rename any mixed or whole numbers as fractions: 2\(\frac{1}{5}\) = \(\frac{11}{5}\); 1\(\frac{3}{4}\) = \(\frac{7}{4}\)
• Rewrite the problem using the fractions as factors: \(\frac{11}{5}\) * \(\frac{7}{4}\)
• Multiply using a fraction multiplication algorithm: \(\frac{(11 * 7)}{(5 * 4)}=\frac{77}{20}\), or 3\(\frac{17}{20}\)

Question 1. 1\(\frac{3}{5}\) ∗ 6 = ? 1\(\frac{3}{5}\) ∗ 6 = __________

Answer: 48/5.

Explanation: In the above-given question, given that, 1\(\frac{3}{5}\) ∗ 6. 1\(\frac{3}{5}\) = \(\frac{8}{5}\). 8/5 x 6. 6 x 8 = 48. 48/5.

Question 2. 4\(\frac{1}{2}\) ∗ 1\(\frac{5}{6}\) = ? 4\(\frac{1}{2}\) ∗ 1\(\frac{5}{6}\) = __________

Answer: 99/12.

Explanation: In the above-given question, given that, 4\(\frac{1}{2}\) ∗ 1\(\frac{5}{6}\). \(\frac{9}{2}\) ∗ \(\frac{11}{6}\). latex]\frac{(11 * 9)}{(6 * 2)}=\frac{99}{12}[/latex] 99/12.

Solve Problems 3 and 4 using the method of your choice. Question 3. What is the area of a table that is 1\(\frac{1}{4}\) m long and 2\(\frac{1}{3}\) m wide? Write a number model with a letter for the unknown. Then solve. Show your work. Number model: _________________ The area of the table is _________________ m 2 .

Answer: The area of the table is 35/12 sq m.

Explanation: In the above-given question, given that, 1\(\frac{1}{4}\) ∗ 2\(\frac{1}{3}\). \(\frac{5}{4}\) ∗ \(\frac{7}{3}\). latex]\frac{(5 * 7)}{(6 * 2)}=\frac{35}{12}[/latex] 5 x 7 = 35. 4 x 3 = 12. 35/12. so the area of the table is 35/12 sq m.

Question 4. Write a number story that can be solved by multiplying 2\(\frac{3}{4}\) and \(\frac{1}{2}\). Then solve the problem. Show your work on the back of this page. Number story:

Answer: 11/8.

Explanation: In the above-given question, given that, 2\(\frac{3}{4}\) ∗ \(\frac{1}{2}\). \(\frac{11}{4}\) ∗ \(\frac{1}{2}\). latex]\frac{(11 * 1)}{(4 * 2)}=\frac{11}{8}[/latex]

Practice Question 5. \(\frac{11}{12}\) – \(\frac{3}{4}\) = ________

Answer: \(\frac{11}{12}\) – \(\frac{3}{4}\) = 2/12.

Explanation: In the above-given question, given that, \(\frac{11}{12}\) – \(\frac{3}{4}\). 14 – 2/12. 2/12 = 1/6.

Question 6. \(\frac{7}{8}\) – \(\frac{1}{6}\) = _________

Answer: \(\frac{7}{8}\) – \(\frac{1}{6}\) = 17/24.

Explanation: In the above-given question, given that, \(\frac{7}{8}\) – \(\frac{1}{6}\). lcm of 6 and 8 = 24. 7 x 3 = 21. 1 x 4 = 4. 21 – 4 = 17. 17/24.

Everyday Mathematics Grade 5 Home Link 7.3 Answers

Solving More Area Problems

Solve. Sho w your work. Write a number model to summarize each solution. Question 1. The cover of Martina’s book measures 7\(\frac{1}{4}\) inches by 9 inches. What is the area of the book cover? Area: ____________ Number Model: ____________

Answer: The area of the book cover = 65(1/4) sq in.

Explanation: In the above-given question, given that, The cover of Martina’s book measures 7(1/4) inches by 9 inches. 7(1/4) = 7 x 4 = 28. 28 + 1 = 29. 29 x 9 = 261. 261/4. so the area of the book cover = 261/4 sq in.

Question 2. The hallway floor in Ryan’s school is covered with square tiles that are \(\frac{1}{2}\) foot by \(\frac{1}{2}\) foot. Ryan counted and found that the hallway is 15 tiles wide and 60 tiles long. a. How many tiles cover the hallway floor? b. What is the area of the hallway floor? Area: ____________ Number Model: ____________

Answer: a.The number of tiles cover the hallway floor = 900 tiles. b. The area of the hallway floor = 225 sq ft.

Explanation: In the above-given question, given that, The hallway floor in Ryan’s school is covered with square tiles that are 1/2 foot by 1/2. Ryan counted and found that the hallway is 15 tiles wide and 60 tiles long. 60 x 15. 60 x 15 = 900. so no of tiles = 900 tiles. area = 15 x 15. area = 225 sq ft.

Question 3. An artist made a stained-glass window that is 3\(\frac{1}{2}\) feet by 2 \(\frac{3}{4}\) feet. a. What is the area of the window? Area: ____________ Number Model: ____________

Answer: The area of the window = 77/8 sq ft.

Explanation: In the above-given question, given that, An artist made a stained-glass window that is 3(1/2) feet by 2(3/4). 3 x 2 = 6. 6 + 1/2 = 7/2. 4 x 2 = 8. 8 + 3/4 = 11/4. 7/2 x 11/4. 11 x 7 = 77. 4 x 2 = 8. 77/8. so the area of the window = 77/8 sq ft.

b. The artist’s design used squares of colored glass that measure \(\frac{1}{4}\) foot by \(\frac{1}{4}\) foot. How many colored squares did the artist use? Area: ____________ Number Model: ____________

Answer: The number of colored squares did the artist use = 154 tiles.

Explanation: In the above-given question, given that, The artist’s design used squares of colored glass that measure 1/4 foot by 1/4. 4 x 4 = 16. 16 x 9 = 144. 144 + 10 = 154. so the number of colored squares did the artist use = 154 tiles.

Practice Question 4. 3\(\frac{1}{8}\) + 4\(\frac{2}{3}\) = _________

Answer: 3\(\frac{1}{8}\) + 4\(\frac{2}{3}\) = 187.

Explanation: In the above-given question, given that, 3\(\frac{1}{8}\) + 4\(\frac{2}{3}\). 3(1/8) + 4(2/3). 3 x 8 = 24. 24 + 1/8 = 25/8. 4 x 3 = 12. 12 + 2/3 = 14/3. lcm of 8 and 3 = 24. 25 x 3 = 75. 14 x 8 = 112. 112 + 75 = 187.

Question 5. 2\(\frac{1}{6}\) + 1\(\frac{5}{8}\) = __________

Answer: 2\(\frac{1}{6}\) + 1\(\frac{5}{8}\) = 62/18.

Explanation: In the above-given question, given that, 2\(\frac{1}{6}\) + 1\(\frac{5}{8}\). 2(1/6) + 1(5/8). 6 x 2 = 12. 12 + 1/6 = 13/6. 8 x 1 = 8. 8 + 5/8 = 13/8. lcm of 6 and 8 = 18. 13 + 3 = 16. 16/18 + 46/18 = 62/18.

Everyday Math Grade 5 Home Link 7.4 Answer Key

Solving Fraction Division Problems

Using Common Denominators to Divide 210 One way to divide fractions is to use common denominators. This method can be used to divide whole numbers by fractions and fractions by whole numbers. Step 1 Rename the dividend and divisor as fractions with a common denominator Step 2 Divide the numerators

Example: \(\frac{1}{3}\) ÷ 4 = \(\frac{1}{3}\) ÷ \(\frac{12}{3}\) 1 ÷ 12 = \(\frac{1}{12}\)

Solve Problems 1–4. Show your work. Use multiplication to check your answer. Question 1. 5 ÷ \(\frac{1}{3}\)= ? Check: _______

Answer: \(\frac{1}{15}\)

Explanation: In the above-given question, given that, 5 ÷ \(\frac{1}{3}\). \(\frac{1}{3}\) ÷ \(\frac{15}{3}\). 1 ÷ 15. \(\frac{1}{15}\).

Question 2. 4 ÷ \(\frac{1}{8}\) = ? Check: _______

Answer: \(\frac{1}{32}\).

Explanation: In the above-given question, given that, 4 ÷ \(\frac{1}{8}\). \(\frac{1}{8}\) ÷ \(\frac{32}{8}\). 1 ÷ 32. \(\frac{1}{32}\).

Question 3. \(\frac{1}{6}\) 4 = ? Check: _______

Answer: \(\frac{1}{24}\).

Explanation: In the above-given question, given that, 4 ÷ \(\frac{1}{6}\). \(\frac{1}{6}\) ÷ \(\frac{24}{6}\). 1 ÷ 24. \(\frac{1}{24}\).

Question 4. \(\frac{1}{5}\) 6 = ? Check: _________

Answer: \(\frac{1}{30}\).

Explanation: In the above-given question, given that, 6 ÷ \(\frac{1}{5}\). \(\frac{1}{5}\) ÷ \(\frac{30}{6}\). 1 ÷ 30. \(\frac{1}{30}\).

Question 5. Write a number story to match Problem 2.

Practice Question 6. 4\(\frac{1}{2}\) – 1\(\frac{3}{4}\) = _________

Answer: 4\(\frac{1}{2}\) – 1\(\frac{3}{4}\) = 11/4.

Explanation: In the above-given question, given that, 4\(\frac{1}{2}\) – 1\(\frac{3}{4}\). 4(1/2) – 1(3/4). 4 x 2 = 8. 8 + 1/2 = 9/2. 1 x 4 = 4. 4 + 3/4 = 7/4. lcm of 2 and 4 is 4. 9 x 2 = 18. 18 – 7 = 11/4.

Question 7. 2\(\frac{7}{8}\) – 1\(\frac{1}{3}\) = __________

Answer: 2\(\frac{7}{8}\) – 1\(\frac{1}{3}\) = 37/24.

Explanation: In the above-given question, given that, 2\(\frac{7}{8}\) – 1\(\frac{1}{3}\). 2(7/8) – 1(1/3). 8 x 2 = 16. 16 + 7/8 = 23/8. 1 x 3 = 3. 3 + 1/3 = 4/3. lcm of 8 and 3 is 24. 23 + 3/8 = 26/8. 4 + 8 = 12/8. 26 + 11 = 37/24.

Everyday Mathematics Grade 5 Home Link 7.5 Answers

Using a Hierarchy

a. Can this shape go in the top category, Pentagons? How do you know?

Answer: Yes.

Explanation: In the above-given question, given that, pentagons are in the above diagrams. so the shape belongs to this category.

b. Can this shape go in the first subcategory, Equilateral pentagons? How do you know?

Answer: No.

Explanation: In the above-given question, given that, Equilateral pentagons are in the second subcategory. so the shape does not belong to the 1st category.

c. Can this shape go into the second subcategory, Equilateral pentagons with at least one right angle? How do you know?

Explanation: In the above-given question, given that, Equilateral pentagons with at least one right angle are in the third subcategory. so the shape does not belong to the second subcategory.

Answer: The shape fits the Equilateral pentagon.

Everyday Math Grade 5 Home Link 7.6 Answer Key

The Quadrilateral Hierarchy

b. All __________ are __________, but not all __________ are __________. c. All __________are __________, but not all __________ are __________

Answer: a.Yes. b. All parallelograms are rhombuses, but not all rectangles are squares.

Explanation: In the above-given question, given that, All quadrilaterals are trapezoids and kites. All trapezoids are parallelograms. All parallelograms are rectangles. All parallelograms are rhombuses. All rhombuses are squares.

Question 2. a. All parallelograms have two pairs of parallel sides. Does this mean that all rectangles have two pairs of parallel sides? Explain how you can tell by looking at the hierarchy.

Explanation: In the above-given question, given that, All parallelograms have two pairs of parallel sides. Yes, it means that all rectangles have two pairs of parallel sides.

b. All trapezoids have at least one pair of parallel sides. Which other shapes have at least one pair of parallel sides? Explain how you can tell by looking at the hierarchy.

Answer: Yes, All trapezoids have at least one pair of parallel sides. Rhombuses have at least one pair of parallel sides. All rectangles are squares.

Explanation: In the above-given question, given that, Yes, All trapezoids have at least one pair of parallel sides. Rhombuses have at least one pair of parallel sides. All rectangles are squares.

Practice Question 3. \(\frac{1}{4}\) ÷ 8 = ________

Answer: \(\frac{1}{4}\) ÷ 8 = 1/32.

Explanation: In the above-given question, given that, \(\frac{1}{4}\) ÷ 8. 1/4 ÷ 8. 8 x 4 = 32. 1/32. \(\frac{1}{4}\) ÷ 8 = 1/32.

Question 4. \(\frac{1}{10}\) ÷ 3 = __________

Answer: \(\frac{1}{10}\) ÷ 3 = 1/30.

Explanation: In the above-given question, given that, \(\frac{1}{10}\) ÷ 3. 1/10 ÷ 3. 10 x 3 = 30. 1/30. \(\frac{1}{10}\) ÷ 3 = 1/30.

Question 5. \(\frac{1}{6}\) ÷ 2 = ___________

Answer: \(\frac{1}{6}\) ÷ 2 = 1/12.

Explanation: In the above-given question, given that, \(\frac{1}{6}\) ÷ 2. 1/6 ÷ 2. 6 x 2 = 12. 1/12. \(\frac{1}{6}\) ÷ 2 = 1/12.

Question 6. \(\frac{1}{5}\) ÷ 12 = _________

Answer: \(\frac{1}{5}\) ÷ 12 = 1/60.

Explanation: In the above-given question, given that, \(\frac{1}{5}\) ÷ 12. 1/5 ÷ 12. 12 x 5 = 60. 1/60. \(\frac{1}{5}\) ÷ 12 = 1/60.

Everyday Mathematics Grade 5 Home Link 7.7 Answers

Property Pandemonium

Answer: The total score = 8.

Practice Divide. Question 2. 9 ÷ \(\frac{1}{3}\) = _______

Answer: 9 ÷ \(\frac{1}{3}\) = 27.

Explanation: In the above-given question, given that, 9 ÷ \(\frac{1}{3}\). 9 x 3 = 27. 9 ÷ \(\frac{1}{3}\) = 27.

Question 3. 4 ÷ \(\frac{1}{5}\) = _________

Answer: 4 ÷ \(\frac{1}{5}\) = 20.

Explanation: In the above-given question, given that, 4 ÷ \(\frac{1}{5}\). 5 x 4 = 20. 4 ÷ \(\frac{1}{5}\) = 20.

Question 4. 2 ÷ \(\frac{1}{10}\) = _________

Answer: 2 ÷ \(\frac{1}{10}\) = 20.

Explanation: In the above-given question, given that, 2 ÷ \(\frac{1}{10}\). 10 x 2 = 20. 2 ÷ \(\frac{1}{10}\) = 20.

Question 5. 12 ÷ \(\frac{1}{4}\) = __________

Answer: 12 ÷ \(\frac{1}{4}\) = 48.

Explanation: In the above-given question, given that, 12 ÷ \(\frac{1}{4}\). 12 x 4 = 48. 12 ÷ \(\frac{1}{4}\) = 48.

Everyday Math Grade 5 Home Link 7.8 Answer Key

Classifying Polygons

Answer: The shapes that have at least 1 right angle = rhombus. The shapes that have exactly 4 right angles = 90 degrees. The shapes that have at least 1 obtuse angle = trapezoid, rhombus, acute angle, diamond shape. The shapes that have exactly all obtuse angles = hexagon, pentagon, octagon, parallelogram.

Question 2. Explain how you decided where to place the hexagon.

Answer: Hexagon is placed in all obtuse angles.

Explanation: In the above-given question, given that, The shape Hexagon has all the sides 120 degrees. so hexagon is placed in all obtuse angles.

Practice Solve. Question 3. 6.8 ∗ 10 3 = ________

Answer: 6.8 x 10 3 = 6800.

Explanation: In the above-given question, given that, Multiply. 6.8 x 10 3. 6.8 x 10 x 10 x 10. 6.8 x 1000. 6800.

Question 4. 12.7 ÷ 10 4 = __________

Answer: 12.7 ÷ 10 4 = 0.00127.

Explanation: In the above-given question, given that, Divide. 12.7 ÷ 10 4. 12.7 ÷ 10 x 10 x 10 x 10. 0.00127.

Question 5. 0.4 ∗ _________ = 4,000

Answer: 0.4 x 10 4. = 4000.

Explanation: In the above-given question, given that, Multiply. 0.4 x 10 4.. 0.4 x 10 x 10 x 10 x 10. 4000.

Question 6. 64.3 ÷ ________ = 0.643

Answer: 64.3 x 10 x 10 = 0.643.

Explanation: In the above-given question, given that, Divide. 64.3 x 10 x 10. 64.3 x 100. 0.643.

Everyday Mathematics Grade 5 Home Link 7.9 Answers

Plotting and Interpreting Line-Plot Data

Answer: The fingers on 4 inches = 1. 4.5 in = 2, 5 in = 4, 5.5 in = 7, 6 in = 4, 6.5 = 3, 7 = 1.

Question 2. Marisela wants to find the total length of all the 6 \(\frac{1}{2}\)inch finger stretches. Write a number model using addition to help her find the total, then solve. Number model: __________ ________ inches

Answer: The total length of all 6-inch finger stretches = 39/2.

Explanation: In the above-given question, given that, Marisela wants to find the total length of all the 6(1/2) inch finger stretches. 6 x 2 = 12. 6 x 5 = 30. 30 + 9/2 = 39/2. so the total length of all 6-inch finger stretches = 39/2.

Question 3. Now Marisela wants to use multiplication to find the total length of all the 5 \(\frac{1}{2}\) inch finger stretches. Write a number model. Then solve. Number model: __________ __________ inches

Answer: The total length of all the 5(1/2) inch finger stretches = 77/2.

Explanation: In the above-given question, given that, Now Marisela wants to use multiplication to find the total length of all the 5(1/2) inch finger stretches. 5 x 2 = 10. 10 + 1/2 = 11/2. 11 x 7/2 = 77/2.

Question 4. Find the total length of all the finger stretches in Marisela’s class. __________ inches

Answer: The total length of all the finger stretches in Marisela’s class = 122.

Explanation: In the above-given question, given that, Now Marisela wants to use multiplication to find the total length of all the 5(1/2) inch finger stretches. 5 x 2 = 10. 10 + 1 = 11. 11 x 12 = 120. 120 + 2 = 122. so the total length of all the finger stretches in Marisela’s class = 122.

Practice Question 5. 4 \(\frac{1}{5}\) ∗ \(\frac{1}{3}\) = ________

Answer: 4 \(\frac{1}{5}\) ∗ \(\frac{1}{3}\) = 21/15.

Explanation: In the above-given question, given that, 4 \(\frac{1}{5}\) ∗ \(\frac{1}{3}\) . 4(1/5) x 1/3. 5 x 4 = 20. 20 + 1/5 = 21/5. 21/5 x 1/3. 5 x 3 = 15. 4(1/5) x 1/3 = 21/15.

Question 6. 2 \(\frac{5}{6}\) ∗ 7 \(\frac{1}{4}\) = ________

Answer: 2 \(\frac{5}{6}\) ∗ 7 \(\frac{1}{4}\) = 493/24.

Explanation: In the above-given question, given that, 2 \(\frac{5}{6}\) ∗ 7 \(\frac{1}{4}\) . 2(5/6) x 7 (1/4). 6 x 2 = 12. 12 + 5/6 = 17/6. 7 x 4 = 28. 28 + 1/4 = 29/4. lcm of 6 and 4 is 24. 17 + 4 = 21. 29 + 6 = 31. 493/24.

Everyday Math Grade 5 Home Link 7.10 Answer Key

Identifying Patterns

Answer: In (x) = 2, 4, 6, 8, and 10. In (Y) = 8, 6, 4, 2, and 0.

b. What rule relates the numbers in the in column to the numbers in the out column? Hint: What happens when you add the numbers in each row?

Answer: Subtract the numbers in from 10 to get out.

Explanation: In the above-given question, given that, when we add the numbers in each row is to subtract the numbers in from 10 to get out.

Answer: The order pairs are (2,8), (6, 4), (8, 2), (10, 0).

Question 2. How does your graph in Problem 1c show the + 2 rule from the in column?

Answer: The graph shows the problem + 2 rule.

Explanation: In the above-given question, given that, in (x) Rule: 0 + 2 = 2. 2 + 2 = 4. 4 + 2 = 6. 6 + 2 = 8. 8 + 2 = 10. in (Y) Rule: 10 – 2 = 8. 8 – 2 = 6. 6 – 2 = 4. 4 – 2 = 2. 2 – 2 = 0.

Practice The digits in each product or quotient are given. Use an estimate to place the decimal point. Write a number sentence to show how you estimated. Question 3. 42.96 ÷ 1.2 = 3 5 8 Number sentence: ___________

Answer: 42.96 ÷ 1.2 = 35.8.

Explanation: In the above-given question, given that, Divide. 42.96 ÷ 1.2. 35.8.

Question 4. 19.2 ∗ 8.8 = 1 6 8 9 6 Number sentence: ___________

Answer: 19.2 ∗ 8.8 = 168.96.

Explanation: In the above-given question, given that, Multiplication. 19.2 x 8.8. 168.96.

Everyday Mathematics Grade 5 Home Link 7.11 Answers

Working with Rules, Tables, and Graphs

Answer: The weight in pounds 1 = $2.50, 3 = $7.50, 6 = $15, 10 = $25.00.

b. Ordered pairs: ___________ ___________ ___________ ___________

Answer: The ordered pairs are (1, 2.50), (3, 7.50), (6, 15.00), (10, 25.00).

Explanation: In the above-given question, given that, Cherry tomatoes cost $2.50 per pound. 2.50 + 2.50 + 2.50 = 7.50. 2.50 x 6 = $15. 2.50 x 10 = $25.00. The ordered pairs are (1, 2.50), (3, 7.50), (6, 15.00), (10, 25.00).

d. Plot a point to show the cost of 8 pounds of cherry tomatoes. What is the cost?

Answer: The cost of 8 pounds of cherry tomatoes = $20.00.

e. Julius has $12.00. Does he have enough money to buy 5 pounds of cherry tomatoes? Explain.

Explanation: In the above-given question, given that, Julius has $12.00. 2.50 x 5 = $12.5. so he does not have enough money.

f. Would you use the graph, the table, or the rule to find out how much 50 pounds of cherry tomatoes would cost? Explain.

Answer: 50 x 2.50 = $125.

Explanation: In the above-given question, given that, 50 x 2.50 = $125.

Practice Multiply. Show your work on the back of this page. Question 2. 29.5 ∗ 62.3 = ___________

Answer: 29.5 x 62.3 = 1837.85.

Explanation: In the above-given question, given that, Multiply. 29.5 x 62.3. 1837.85.

Question 3. 4.1 ∗ 250.8 = ___________

Answer: 4.1 x 250.8 = 1028.28.

Explanation: In the above-given question, given that, Multiply. 4.1 x 250.8. 1028.28.

Everyday Math Grade 5 Home Link 7.12 Answer Key

Interpreting Tables and Graphs

Ami runs 6 yards per second. Derek runs 5 yards per second. Ami challenged Derek to an 80-yard race. She told him he could have a 12-yard head start.

• Complete the tables to show the distances Ami and Derek are from the starting line during the first 5 seconds of the race.
• Write 3 ordered pairs each for Ami and Derek.
• Graph the ordered pairs you wrote and connect them with a line. Extend each line to the 80-yard mark to find out who wins. Label each line.

Question 1. Who wins the race? How do you know?

Answer: Ami wins the race.

Answer: 68 ÷ 0.5 = 136.

Explanation: In the above-given question, given that, Equivalent problems. 680 ÷ 5. 136. 68 ÷ 0.5 = 136.

Answer: 7.92 ÷ 0.22 = 36.

Everyday Mathematics Grade 5 Home Link 7.13 Answers

Analyzing Patterns and Relationships

Answer: In Rule 1: 2, 3, 4, and 5. In Rule 2: 17, 23, 29, and 35.

Question 2. Find a rule that relates the in numbers to the corresponding out numbers. Rule: ______________

Answer: In number x 6 + 5 = out number.

Explanation: In the above-given question, given that, 1 x 6 + 5 = 11. in rule 1 = rule 11. in number x 6 + 5 = out number.

Question 3. Write the numbers in the table as ordered pairs.

Answer: The numbers in ordered pairs are (0,5), (1, 11), (2, 17), (3, 23), (4, 29), (5, 35).

Explanation: In the above-given question, given that, In rule 1 adding 1 to the other number. In rule 2 adding 6 to the other number. In Rule 1: 2, 3, 4, and 5. In Rule 2: 17, 23, 29, and 35.

Question 5. Use the graph to answer the questions below. Use the formula to check your answers. a. When the in number is 8, what is the out number? ___________ b. When y is 64, about how much is x? About __________

Answer: 5a = 53. 5b = 10.

Explanation: In the above-given question, given that, The In number is 8. 8 x 6 + 5 = 53. 48 + 5 = 53. x x 6 + 5 = 5. 4 + 60 = x. x = 64.

Practice Solve. Show your work on the back of this page. Question 6. 3 \(\frac{1}{5}\) ∗ 2 \(\frac{2}{3}\) = ________

Answer: 3 \(\frac{1}{5}\) ∗ 2 \(\frac{2}{3}\) =128/15.

Explanation: In the above-given question, given that, 3 \(\frac{1}{5}\) ∗ 2 \(\frac{2}{3}\). 3(1/5) x 2 (2/3). 3 x 5 = 15. 15 + 1/5 = 16/5. 2 x 3 = 6. 6 + 2/3 = 8/3. lcm of 3 and 5 = 15. 16 x 3 = 48. 8 x 5 = 40. 80 + 48 = 128/15.

Question 7. 8 \(\frac{1}{2}\) ∗ 12 = _________

Answer: 8 \(\frac{1}{2}\) ∗ 12 = 204/2.

Explanation: In the above-given question, given that, 8 x 2 = 16. 16 + 1/2 = 17/2. 17/2 x 12 = 204/2.

Question 8. 9 ∗ 5 \(\frac{1}{7}\) = __________

Answer: 9 ∗ 5 \(\frac{1}{7}\) = 324/7.

Explanation: In the above-given question, given that, 7 x 5 = 35. 35 + 1/7 = 36/7. 36/7 x 9 = 324/7.

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Witness testimony in Trump's hush money trial wraps for the day

From CNN's Kara Scannell, Lauren Del Valle, Jeremy Herb and Sabrina Souza in the courthouse

Prosecutors are walking through a spreadsheet of payments to Cohen

Prosecutor Matthew Colangelo is walking Jeffrey McConney through a report with a spreadsheet of the payments to Michael Cohen.

It shows Trump's trust and then his personal account paid Cohen in 2017.

The first three payments were paid from the revocable trust for $105,000. The final nine payments were paid by Trump's personal account and totaled $315,000, according to the report.

What Jeffrey McConney has said so far

From CNN's Jeremy Herb and Eric Levenson

Jeffrey McConney, the former long-time Trump Organization controller, testified Monday morning about the nuts and bolts of how Michael Cohen was allegedly reimbursed by Donald Trump for the 2016 hush money payments made to Stormy Daniels.

McConney testified that he had a conversation with Allen Weisselberg, the former chief financial officer of the Trump Organization, about a need to “reimburse” Cohen.

McConney then showed jurors 12 checks, each for $35,000, that were paid to Cohen in 2017. Cohen sent invoices for those checks and asked that the payments be listed as part of a “retainer agreement.”

McConney also explained to the jury why Cohen was paid $420,000 in all -- a total that included money set aside to cover taxes on the hush money payment to Daniels -- and how each check was cut, first from Trump's revocable trust and then from his personal account.

McConney is back on the stand

Jeffrey McConney smiled and said something to Eric Trump ask he walked past him in the courtroom.

McConney is now back on the stand and is being questioned by prosecutor Matthew Colangelo.

Prosecutors and Trump are back in the courtroom

Prosecutors have reentered the courtroom following the break. Trump is also back inside the courtroom.

Trump waved and gave a thumbs up as he entered.

Trump leaves with his son and lawyers for the break

Trump was whispering with his attorney Todd Blanche when Jeffrey McConney left the stand. Trump did not appear to look at him

Eric Trump and Alina Habba, who are in the courtroom today, left with Trump and his attorneys for the break.

The court is taking a short break

The court is taking a short morning break.

Jeffrey McConney , the former longtime Trump Organization controller, is expected to continue to testify when the court returns.

McConney says he doesn't recall any payments to Cohen after December 2017

Jeffrey McConney says that he does not recall any additional payments made to Cohen after December 2017.

McConney's voice appears to grow tired as he goes through more of Cohen's monthly invoices

Jeffrey McConney 's voice appears to grow more tired as he repeats himself for each month.

"35,000 dollars," he said with a bit of a sigh, when discussing the August payment to Michael Cohen.

Cohen's July invoice didn't include a number, but it was understood to be for $35,000, McConney says

The July invoice from Michael Cohen did not include an amount — but it was known to be $35,000, Jeffrey McConney says.

"Pursuant to the retainer agreement, kindly remit payment for services rendered for the month of July 2017," the email from Cohen to Allen Weisselberg reads.

Prosecutor Matthew Colangelo asks McConney if there was an understanding of the amount that needed to be paid, even if it wasn't explicit in the email. McConney says yes.

"What was that understanding?" Colangelo asks.

"$35,000," McConney says.

"What was that understanding based on?" Colangelo asks.

It was "based on the prior notes," he took in Weisselberg's office, McConney says.

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Xi Visits Europe, Seeking Strategic Opportunity

The Chinese leader has carefully chosen three countries — France, Serbia and Hungary — that to varying degrees embrace Beijing’s push for a new global order.

By Roger Cohen and Chris Buckley

Reporting from Paris and Taipei, Taiwan

On his first visit to Europe in five years, the Chinese president, Xi Jinping, appears intent on seizing opportunities to loosen the continent’s bonds with the United States and forge a world freed of American dominance.

The Chinese leader has chosen three countries to visit — France, Serbia and Hungary — that all, to a greater or lesser degree, look askance at America’s postwar ordering of the world, see China as a necessary counterweight and are eager to bolster economic ties.

At a time of tensions with much of Europe — over China’s “no limits” embrace of Russia despite the war in Ukraine, its surveillance state and its apparent espionage activities that led to the recent arrest in Germany of four people — Mr. Xi, who arrived in France on Sunday, wants to demonstrate China’s growing influence on the continent and pursue a pragmatic rapprochement.

For Europe, the visit will test its delicate balancing act between China and the United States and will no doubt be seen in Washington as a none-too-subtle effort by Mr. Xi to divide Western allies. Chinese-French relations “have established a model for the international community of peaceful coexistence and win-win cooperation between countries with different social systems,” Mr. Xi said in a statement issued soon after he arrived in Paris.

He has timed his arrival at his second stop, Serbia, to coincide with the 25th anniversary of the deadly NATO bombing of the Chinese Embassy in Belgrade during the Kosovo war. That mistaken strike on May 7, 1999, for which the White House apologized, killed three Chinese journalists and ignited furious protests around the U.S. Embassy in Beijing.

“For Xi, being in Belgrade is a very economical way to ask if the United States is really serious about international law,” said Janka Oertel, the director of the Asia program at the European Council on Foreign Relations in Berlin, “and to say, how about NATO overreach as a problem for other countries?”

The Chinese government has continued to commemorate the Belgrade bombing, using it as an occasion to denounce what it sees as Western hypocrisy and bullying.

“The United States always views itself as the leader — or hegemon — of the world, so China is a competitor or adversary that is challenging its hegemony,” said Tu Xinquan, the dean of a trade institute at the University of International Business and Economics in Beijing. “The European Union does not have a hegemonic mind-set.”

The official doctrine of the 27-member European Union defines China as “a partner for cooperation, an economic competitor and a systemic rival.” If that seems a mouthful, and a perhaps contradictory one, it is because the continent is torn between how to balance economic opportunity in China with national security risk, cybersecurity risk and economic risk to various industries.

In March, China’s foreign minister, Wang Yi, told reporters that Europe’s formula was unworkable. “It’s like driving to a crossing and finding the red, yellow and green lights all on at the same time,” he said. “How can one drive on?”

Now, Mr. Xi would like to ease the lights toward green.

To that end, Mr. Xi’s first and most important stop will be in France, whose president, Emmanuel Macron, has often made the Gaullist point that Europe “must never be a vassal of the United States,” as he did last month at a speech at the Sorbonne . The French leader insists that the survival of the European Union depends on “strategic autonomy” and developing the military resilience to become a “Europe power.” He rejects the notion of “equidistance” between China and the United States — France is one of America’s oldest allies — but wants to keep his options open.

All of this is music to Mr. Xi’s ears.

“Macron is trying to bring a third way in the current global chaos,” said Philippe Le Corre, a prominent French expert on relations with China. “He is trying to walk a fine line between the two main superpowers.”

Just over a year ago, Mr. Macron was lavishly entertained during a visit to China that ended with a Sino-French declaration of a “global strategic partnership.” The French leader echoed the Chinese lexicon of a “multipolar” world, freed of “blocs” and the “Cold War mentality.”

Now, in anticipation of Mr. Xi’s visit, China has praised France as a great power and expressed hopes that their ties “will always be at the forefront of China’s relations with Western countries,” in the words of Lu Shaye , China’s ambassador to France, in People’s Daily.

Mr. Macron, who recently warned that “our Europe is mortal” and will be saved only if it can become “sovereign,” will host a state dinner for Mr. Xi on Monday in Paris before, in a personal touch, ushering him to a favorite childhood haunt in the Pyrenees.

The chemistry between the two men appears to lie essentially in a shared view that the postwar order is moribund and must be replaced by a new architecture that takes account of shifting power. That Mr. Xi is almost certainly the most repressive and authoritarian leader in recent Chinese history, and that China’s military threats to Taiwan have intensified, has not come between the two leaders.

In the past six months, Mr. Macron has visited both India and Brazil in a push to place France at a fulcrum between the BRICS group of developing countries, which includes China, and Western powers. At a time of growing tension between the “Global South” and Western powers, he sees France as a bridge.

From France, Mr. Xi will move on to the warm embrace of Serbia, where China is the second largest trading partner, and Hungary, where its prime minister, Viktor Orban, has backed enormous Chinese investment and used his country’s position as a European Union member to dilute criticism of China. Both countries bridle at American power.

Beyond these two friends of China, there are, however, serious European differences with Beijing, whose economy was roughly the same size, measured in dollars, as the European Union’s when Mr. Xi last visited in 2019. China’s economy is now some 15 percent bigger.

Last fall, the European Union opened an investigation into whether electric vehicles made in China benefited from unfair subsidies, with a decision expected by this summer. That has caused tensions with Beijing and with Germany, whose presence in the Chinese auto market dwarfs that of other European countries. China accounts for at least half of Volkswagen’s annual profits.

German manufacturers, with plants in China, fear that any imposition of European tariffs could affect its own exports from China, as well as cause tit-for-tat retaliation.

The European Union Commission president, Ursula von der Leyen, will join the talks in Paris with Mr. Xi. Chancellor Olaf Scholz of Germany, whose relations with Mr. Macron have been strained, dined with the French president in Paris this past week. All of this is clearly part of an attempt to forge a united European front.

That, however, is always elusive.

Anger toward Russia in Europe runs highest in frontline states with Russia, like Poland and the Baltic States. They are perhaps the most fiercely attached to the alliance with the United States that Mr. Macron wants to offset by building a sovereign Europe. They are also the most wary of China, which has never condemned Russia’s war in Ukraine.

Mr. Macron, like Mr. Scholz during a visit to China last month, believes that Chinese leverage in bringing an end to the war in Ukraine is critical. Only Beijing, in the French analysis, can bring real pressure to bear on President Vladimir V. Putin of Russia, who will be sworn in for a fifth term during Mr. Xi’s European visit.

The issue, as it was last year during Mr. Macron’s visit to Beijing, is that China has shown little or no inclination to do so. Indeed, Mr. Xi is scheduled to host Mr. Putin in China later this month.

“It’s hard to imagine another discussion on Ukraine,” François Godement, a special adviser and resident senior fellow at the Institut Montaigne in Paris, said of the talks between Mr. Macron and Mr. Xi. “Those dice have been rolled.”

Still, there is little doubt that Mr. Macron will try again to enlist Mr. Xi’s support ahead of a Ukraine peace conference in Switzerland in mid-June.

At a deeper level, Mr. Macron appears certain to try to use Mr. Xi’s visit to advance an agenda that guarantees Europe’s relevance in the coming decades. He is wary of a United States that may re-elect former President Donald J. Trump in November, with unpredictable consequences.

Mr. Wang, the Chinese foreign minister, has said , “As long as China and Europe join hands, bloc confrontation will not occur, the world will not fall apart, and a new Cold War will not take place.”

For all of the fundamental differences in governance between China’s one-party state and Western liberal democracy, the leaders of the three European countries Mr. Xi has chosen to visit appear to embrace that Chinese statement.

Reporting was contributed by Olivia Wang from Hong Kong, Keith Bradsher from Beijing, Christopher F. Schuetze and Melissa Eddy from Berlin and Ségolène Le Stradic from Paris.

An earlier version of a picture caption with this article misstated the year of the NATO bombing of the Chinese Embassy in Belgrade. It was 1999, not 1993.

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Roger Cohen is the Paris Bureau chief for The Times, covering France and beyond. He has reported on wars in Lebanon, Bosnia and Ukraine, and between Israel and Gaza, in more than four decades as a journalist. At The Times, he has been a correspondent, foreign editor and columnist. More about Roger Cohen

Chris Buckley , the chief China correspondent for The Times, reports on China and Taiwan from Taipei, focused on politics, social change and security and military issues. More about Chris Buckley