Percent as a Proportion
Part of the Decimals, Percents & Ratios section of Coddy's Pre-Algebra journey. Lesson 50 of 56.
A percent is a ratio out of 100: per cent means per hundred. So the question what percent of 30 is 18? is a proportion with a missing number: n/100 = 18/30, where n is the percent.
30 does not turn into 100 by multiplying by a whole number, so simplify first. 18/30 divides by 6 to give 3/5. Now 5 times 20 is 100, so scale the top by 20 as well: 3 times 20 is 60. 18 is 60 percent of 30.
Why is simplifying allowed? 18/30 and 3/5 are the same ratio, so they share the same percent. Simplify until the bottom is a number that divides 100 (2, 4, 5, 10, 20, 25 and 50 do), then use the scale factor exactly as in any proportion. When no simplifying gets there, as with 1/3, divide the top by the bottom and multiply by 100 instead.
Challenge
A class has 36 learners, and 9 of them walk to school. What percent walk? The board shows the proportion, the percent n over 100 equal to part over whole. Find n and type your claim.
Try it yourself
Solve for n
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Decimals, Percents & Ratios
4Dividing Decimals
Dividing by a DecimalDividing by 10 and 100Dividing by a Whole NumberUnit PriceRecap: Dividing7Percent Problems
Finding the WholeDiscountsTax and TipsPercent IncreasePercent DecreaseRecap: Percent Problems10Proportions
Solving a ProportionCross ProductsScale DrawingsPercent as a ProportionRecap: Proportions