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How to Factor Ratios

Ratios are comparisons of two groups, group x and group y. The comparison is written in a mathematical form as x:y or x/y. Factoring is the process of dividing a ratio and breaking it down to its simplest form. In fractional terms, think of it as reducing the ratio to its lowest possible form. Factoring or reducing ratios simplifies sometimes-large numbers down to manageable proportions for mathematical use. Instead of comparing the ratio 210:354, you can break it down to a smaller ratio, 35:59, which makes any mathematical application involving the ratio much easier to comprehend and work with.

Instructions

  1. Basic Ratio Factoring

    • 1

      Examine the ratio 14 to 28, also written as 14:28 or 14/28.

    • 2

      Find the greatest common factor. The first step to every factoring problem is to find and remove the GCF from the problem. In this case, the GCF is 14.

    • 3

      Divide both parts of the ratio by the GCF and write the quotients as the new ratio, which is 1:2.

    Factoring Ratio Proportions

    • 4

      Examine the ratio proportion 36:54 = 16:24.

    • 5

      Factor the GCF out of the first ratio, writing the remainder as the new ratio. The GCF is 18 so 36:54 reduces to 2:3.

    • 6

      Factor the GCF out of the second ratio and write the remainder as the new ratio. The GCF is 8 so 16:24 reduces to 2:3. Because they are equal, the ratios are the same, which is 2:3 = 2:3.

    Factoring Ratio Problems

    • 7

      Read the word problem: Jan has a bag with 50 marbles. She has 13 red marbles, 12 blue marbles, 10 yellow marbles and 15 tiger-eye marbles. Write ratios for the following: blue marbles to yellow marbles, tiger-eye marbles to the total marbles and red marbles to blue marbles. Factor the answers to simplest form.

    • 8

      Find the number of blue marbles (12) and the number of yellow marbles (10). Write a ratio comparing those two groups, and it is 12:10. Simplify the ratio by pulling out the GCF -- it is 2 -- and writing the remainder as the simplified ratio 6:5.

    • 9

      Find the number of tiger-eye marbles (15) and the total number of marbles (50). Write a ratio and then factor it to its simplest form, which is 15:50 = 3:10.

    • 10

      Find the amount of red marbles and the number of blue marbles and write a ratio, which is 13:12. This ratio will not factor further because 13 is already in its simplest form.

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