How to Form Proportions Using Ratios

Proportions with Ratios

• 1

  Read the following problem: Seth's computer prints 24 pages in 3 minutes. How long would it take him to print 40 pages?

• 2

  Set up a proportion in standard ratio form: 24 pages:3 minutes = 40 pages:x minutes. The variable x represents the unknown time. Notice that the measurements or quantities are in the same place in both ratios.

• 3

  Simplify the ratio to contain only numeric values: 24:3 = 40:x.

• 4

  Cross multiply the outside terms: 24 x (x) = 24x. Cross multiply the inside terms: 3 x 40 = 120. Simplify the equation: 24x = 120.

• 5

  Divide both sides of the equation by 24. This isolates the variable and sets it equal to a specific value. 24x ÷ 24 = 120 ÷ 24. Simplify the equation: x = 5 minutes.

• 6

  Place the value of x back into the ratio: 24:3 = 40:5. Cross-multiply outside terms and the inside terms to check for equality: 24 x 5 = 120 and 3 x 40 = 120.

Proportions with Fractions

• 7

  Read the following problem: If a man who weighs 180 pounds on Earth weighs 60 pounds on the moon, then how much does his partner weigh on Earth if his weight on the moon is 74 pounds.

• 8

  Set up a proportion using fractions: 180 pounds (Earth)/60 pounds (moon) = x pounds (Earth)/74 pounds (moon). Simplify the proportion to only numeric values: 180/60 = x/74.

• 9

  Cross multiply the denominators by the numerators: 180 x 74 = 13,320 and 60 x (x) = 60x. Simplify the equation: 13,320 = 60x.

• 10

  Divide both sides of the equation by 60 to isolate x and to keep the equation balanced: 13,320 ÷ 60 = 60x ÷ 60. Simplify the equation: 222 = x. The man weighs 222 pounds on Earth.

• 11

  Plug the value of x back into the proportion: 180/60 = 222/74. Cross multiply to check for equality: 180 x 74 = 13,320 and 60 x 222 = 13,320.