Proportion
In short: Proportion is an equation that says two ratios are equal, such as 3/5 = 21/35, and it is used to find a missing value when quantities scale together.
7th GradeRatios and Percents7.RP.A.2
What is Proportion?
A proportion links two equal ratios with an equals sign. If 2 inches on a map stand for 15 miles, then 7 inches stand for however many miles keeps the same ratio, and that relationship is written as a proportion.
Precisely, \(\frac{a}{b} = \frac{c}{d}\) with \(b\) and \(d\) nonzero. When three of the numbers are known, the fourth can be found. Units must match across the two ratios: inches over miles on both sides.
How to spot it
- A story gives one pair, such as miles for a number of inches, and asks for a different amount.
- Two ratios are written as fractions and joined by an equals sign.
- A scale, a recipe or a rate must be stretched to a new size.
- One of the four numbers is replaced by a letter.
The method
- Write the first ratio with matching units, such as inches over miles.
- Write the second ratio in the same order, with the unknown as a letter.
- Set the two fractions equal and solve for the unknown, for example by cross multiplying.
- Check that the two ratios simplify to the same value, and include the unit in the answer.
Proportion: solved example
Problem
On a trail map of a Utah park, 2 inches represent 15 miles. Two trailheads are 7 inches apart on the map. How many miles apart are they?
Solution
Set up \(\frac{2}{15} = \frac{7}{m}\). Cross multiply: \(2m = 15 \cdot 7 = 105\).
Divide: \(m = 52.5\). The trailheads are 52.5 miles apart.
Try it
Question 1
Solve \(\frac{9}{4} = \frac{x}{20}\).
Show the answer
\(4x = 180\), so \(x = 45\).
Question 2
A printer prints 36 pages in 4 minutes. At that pace, how many pages in 15 minutes?
Show the answer
\(\frac{36}{4} = \frac{p}{15}\), so \(4p = 540\) and \(p = 135\) pages.
Proportion vs. Equivalent Ratios
Equivalent ratios are two ratios that have the same value, such as 2 : 15 and 14 : 105. A proportion is the equation that states this equality, and it is the tool you use to find a missing term.
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Whole dictionary: A–Z · 7th Grade · Ratios and Percents