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How to Cross Multiply

September 23, 2023 by admin Category: How To

You are viewing the article How to Cross Multiply  at Tnhelearning.edu.vn you can quickly access the necessary information in the table of contents of the article below.

Cross multiplication is a mathematical method commonly used to compare two ratios or solve for an unknown variable in a proportion. It is a useful technique that allows us to simplify equations and find solutions efficiently. By understanding how to cross multiply, we can navigate various mathematical problems involving proportions and ratios. In this guide, we will delve into the concept of cross multiplication, exploring its basic principles and providing step-by-step instructions on how to effectively use it. Whether you’re a student struggling with math problems or simply curious about improving your mathematical skills, mastering the art of cross multiplication will undoubtedly prove invaluable.

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This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.

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This article has been viewed 38,553 times.

Cross multiplication is a way of solving equations where the variable is in two equal fractions. The variable represents an unknown value, and the cross-multiplication reduces the rule of triangles to a simple equation, allowing you to solve problems to find the variable. The cross-multiplication method is especially useful if you want to calculate proportions. Here’s how to do it:

Table of Contents

  • Steps
    • For an equation with one variable
    • With an equation with the same two variables
  • Advice

Steps

For an equation with one variable

Image titled Cross Multiply Step 1

Image titled Cross Multiply Step 1

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Multiply the numerator of the fraction on the left by the denominator of the fraction on the right. For example, we have the equation 2/x = 10/13. Proceed to multiply 2 by 13. We have 2 * 13 = 26. [1] X Research Source
Image titled Cross Multiply Step 2

Image titled Cross Multiply Step 2

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Multiply the numerator of the fraction on the right by the denominator of the fraction on the left. Performing multiplication with variables, we multiply x by 10. x * 10 = 10x. You can cross multiply either way first, as long as both the numerator and denominator of the two fractions are multiplied diagonally. [2] X Research Source
Image titled Cross Multiply Step 3

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Image titled Cross Multiply Step 3

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Put the two results in the equation. 26 would be equivalent to 10x. We have 26 = 10x. The order of the two sides does not matter; since they are equal, you can swap both sides of the equation at the same time without affecting anything. [3] X Research Sources

  • So, to solve the equation 2/x = 10/13 and find x, we have 2 * 13 = x * 10, which is equivalent to 26 = 10x.
Image titled Cross Multiply Step 4

Image titled Cross Multiply Step 4

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Find x. With 26 = 10x, you can divide both 26 and 10 by the common denominator of both numbers. Since both are even, both are divisible by 2; 26/2 = 13 and 10/2 = 5. The remaining equation will be 13 = 5x. So, you need to divide both sides of the equation by 5 to find x. We have 13/5 = 5/5, which is equivalent to 13/5 = x. If you want the answer in decimal form, you can divide both sides by 10 to get 26/10 = 10/10, deducing x = 2.6. [4] X Research Sources

With an equation with the same two variables

Image titled Cross Multiply Step 5

Image titled Cross Multiply Step 5

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Multiply the numerator of the fraction on the left by the denominator of the fraction on the right. [5] X Research Source Example: the problem asks to find x in the equation: (x + 3)/2 = (x + 1)/4 . To start, you take (x + 3) * 4 = 4(x +3) = 4x + 12.
Image titled Cross Multiply Step 6

Image titled Cross Multiply Step 6

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Multiply the numerator of the fraction on the right by the denominator of the fraction on the left. [6] X Research Sources Doing the same as before, we have (x +1) x 2 = 2(x +1) = 2x + 2.
Image titled Cross Multiply Step 7

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Image titled Cross Multiply Step 7

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Set both sides equal and combine the same terms. Now we have 4x + 12 = 2x + 2. Let’s put the terms containing x on one side and the term unchanged on the other side of the equation.

  • Combine 4x and 2x by moving 2x to the left side and changing the sign of the term. When you move 2x to the left, the right side is left with only 2 . On the left side, we have 4x – 2x = 2x, so 2x is left.
  • Do the same with 12 and 2 by bringing 12 from the left side to the right side and changing the sign of the term. The left side will be 2-12 = -10.
  • The other equation is 2x = -10.
  • Image titled Cross Multiply Step 8

    Image titled Cross Multiply Step 8

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    Find x. Now you just need to divide both sides of the equation by 2 . 2x/2 = -10/2 => x = -5. After cross multiplication, we find x = -5. You can double check by substituting x = -5 and trying to see if both sides of the equation are equal. After substituting -5 back into the original equation, we get -1 = -1.
  • Advice

    • You can check your work by substituting the answers you found in the original equation. If after simplifying the remaining equation is valid, such as 1 = 1, then you have calculated correctly. If the equation after simplifying is not valid, for example 0 = 1 then you are doing it wrong. For example, if we put 2.6 into the first equation, we get 2/(2,6) = 10/13. Multiplying the left side by 5/5 we get 10/13 = 10/13, this equation is valid because after simplifying it will become 1 = 1. So 2.6 is the correct result.
    • Note that when you put another number (e.g. 5) into the same equation, you get 2/5 = 10/13. Even if you multiply the left side by 5/5 again, the result will be 10/25 = 10/13 and obviously not. If this is the case, it means that you are wrong while performing the cross multiplication.
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    X

    This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.

    The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.

    This article has been viewed 38,553 times.

    Cross multiplication is a way of solving equations where the variable is in two equal fractions. The variable represents an unknown value, and the cross-multiplication reduces the rule of triangles to a simple equation, allowing you to solve problems to find the variable. The cross-multiplication method is especially useful if you want to calculate proportions. Here’s how to do it:

    In conclusion, cross multiplication is a valuable technique that enables individuals to solve proportion problems efficiently. By multiplying the numerator of one fraction with the denominator of another and vice versa, cross multiplication allows for the comparison and determination of equivalent ratios. This method can be particularly helpful when dealing with proportions involving unknown variables or when simplifying complex fractions. Through practice and understanding of the concept, anyone can master the art of cross multiplication and confidently solve proportion problems in various contexts.

    Thank you for reading this post How to Cross Multiply at Tnhelearning.edu.vn You can comment, see more related articles below and hope to help you with interesting information.

    Related Search:

    1. Steps to cross multiply in mathematics
    2. Examples of cross multiplying fractions
    3. Cross multiplication technique for solving equations
    4. How to use cross multiplication for comparing ratios
    5. Understanding the concept of proportionality and cross multiplication
    6. Cross multiplication method for finding the unknown variable
    7. Cross multiplying to solve word problems involving proportions
    8. When to use cross multiplication in geometry
    9. Benefits and limitations of using cross multiplication
    10. Common mistakes to avoid when applying cross multiplication

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