How do you find the proportion of a number?

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You've already met fractions like . A proportion is a pair of fractions that are equal to each other, like . There are many different ways to solve proportion problems that ask you to find the missing number , and you don't need to learn all of them today. If you're learning pre-algebra and are just starting to use proportions, read from the top until you find a method that makes sense to you. If you're taking algebra and are working on more advanced proportions problems, you might need to skip down to later methods.

1. Use the relationship between the top and bottom number of the fraction. If you can multiply or divide the top number to get the bottom number, this method is the easiest.[1]

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1. Use the relationship between the two numbers across the proportion. You can also look from left to right, across the two fractions:

1. 1

   Draw two diagonal lines in an "X" across the proportion. For example, write down this proportion, then draw one line between the purple terms, and another line between the green terms:

2. 2

   Multiply the two numbers connected by a line. One of the lines will connect two numbers (instead of a number and a variable like ). Find the product of these two numbers:

3. 3

   Divide by the last number in the proportion. Take the answer to your multiplication problem and divide it by the number you haven't used yet. (This is the green number in the example.) The result is the value of , the missing number in your proportion.

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1. 1

   Draw a table with two rows. Put the top numbers in your proportion in the top row, and the bottom numbers in the second row. Keep numbers in the same fraction in the same column, and leave a few empty columns between them and to either side.[2] Here's an example for the problem :

   • 	48			128
     	x			8

   • Each column in this table represents a fraction. All of the fractions in this table are equal to each other.

2. 2

   Add equivalent fractions to your table. Start with the fraction where you know both numbers, then multiply or divide each number in that column by the same amount. Write the new fraction into your table, putting it in a column so that the numbers are in order:

3. 3

   Repeat until you notice the pattern. As you find new fractions, make sure to put them in the table so that the numbers are in order. This will help you narrow down options for the value of x.

4. 4

   Check your work. Always check your work with this method. Sometimes the answer won't be a whole number, and you'll have to add fractions to your table or use a different method.

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1. 1

   Rewrite the problem as a proportion. You can write any percentage as a fraction of 100. Use this fact to set up a problem as a proportion (two equal fractions):

2. 2

   Solve by cross-multiplying or any other method. Now that it's set up as a proportion, you can solve the problem by any method. One of the most common methods is cross-multiplication:

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1. 1

   Treat the proportion as an algebraic equation. Proportions are usually introduced in a pre-algebra class. But as you move on to algebra, you'll learn that a proportion is just one kind of algebraic equation. For any algebraic equation, there's one big rule:

   • You can change the left hand side of the equation, as long as you do the same math to the right hand side.

2. 2

3. 3

   Multiply each side by the other denominator. This will get rid of the other fraction. You can do this even if the denominator is the , as shown here:

4. 4

5. 5

   Simplify your answer or leave as-is. You can now plug your result into a calculator (or calculate by hand) and find the value of . Sometimes, the answer won't simplify to a whole number or even an easy decimal. In that case, it's best to leave your answer as a fraction.

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1. 1

   Realize your goal is to get the variable on one side. More difficult proportion problems have an on both sides of the equal sign. This works just like any proportion, but you'll have to use algebra to handle the variable . Your goal is to get every in the equation onto one side, so you can simplify it into one and find the answer.

2. 2

3. 3

   Otherwise, multiply by the entire denominator with . Multiplying by only part of the denominator will not help you get rid of the fraction. Always multiply by the entire denominator:

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Add New Question

• Question

  What are the properties of proportions?

  This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

  wikiHow Staff Editor

  Staff Answer

  There are many properties of proportion, but here are the first 3: 1) If two ratios are equal, this is called a proportion. In other words, in a proportion, a/b = c/d. 2) The quantities a, b, c, and d are the “terms” of the proportion. The first and fourth terms (a and d) are the “extremes.” The second and third (b and c) are the “means.” 3) In a proportion, the product of the extremes equals the product of the means. In other words, if a/b = c/d, then a x d = b x c. This is the “cross product rule.”

• Question

  What is the formula of a proportion?

  This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

  wikiHow Staff Editor

  Staff Answer

  There are many formulae that can apply to proportions, but the basic starting point is a/b = c/d. Going from there, you can get a variety of other formulae, such as a x d = b x c and b^2 = a x c.

• Question

  What is a proportion example?

  This answer was written by one of our trained team of researchers who validated it for accuracy and comprehensiveness.

  wikiHow Staff Editor

  Staff Answer

  Any 2 fractions with different terms that are equal is a proportion. For example, 1/2 = 3/6 or 2/3 = 6/9 are both examples of proportions.

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• It's perfectly fine for your answer to be a fraction or a decimal. Sometimes equals or 6.17 instead of a nice whole number.[4]

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• The algebraic method above works with any proportion. But for a specific proportion, there is often a faster way to use algebra to find the answer. As you learn more algebra, this will get easier.

  As a small thank you, we’d like to offer you a $30 gift card (valid at GoNift.com). Use it to try out great new products and services nationwide without paying full price—wine, food delivery, clothing and more. Enjoy!

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Article SummaryX

To solve proportions, start by taking the numerator, or top number, of the fraction you know and multiplying it with the denominator, or bottom number, of the fraction you don’t know. Next, take that number and divide it by the denominator of the fraction you know. Now you can replace x with this final number. For example, to figure out “x” in the problem 3/4 = x/8, multiply 3 x 8 to get 24, then divide 24 / 4 to get 6, or the value of x. To learn how to use proportions to determine percentages, read on!

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