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# How to Calculate Ratios in Math

Updated August 11, 2017

The phrase "comparing apples to oranges" refers to the futility of attempting to compare two very unlike objects; with ratios, you can at least compare their amounts. The ratio of two different quantities expresses how one quantity stacks up against the other. It is important to remember the order of comparison when calculating the ratio, since different orders will result in different ratios. Learning to calculate ratios correctly can help put things in order and perspective.

Determine the order in which the amounts will be compared. For example, imagine you have 10 oranges and 40 apples and decide to compare the number of oranges to apples.

Write the comparison as a fraction. For the example, 10 oranges to 40 apples equals 10/40.

Calculate all the factors of the numerator and denominator, or top and bottom, of the fraction. For the example, the factors, or numbers that can be multiplied together to obtain a certain number, of 10 are 1, 2, 5, and 10. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Divide the numerator and the denominator of the fraction by the greatest common factor. The greatest common factor is the largest factor that both numbers share. The greatest common factor for 10 and 40 is 10, so dividing both 10 and 40 by 10 results in 1 and 4. The fraction is simplified to 1/4.

Write the simplified fraction with a colon separating the numbers. In the example, 1/4 becomes 1:4, which means "1 to 4." Oranges have a 1 to 4 ratio to oranges, meaning there is 1 orange for every 4 apples.