Lesson 5 of 1524
Proportions and percent sentences
Two ratios that name the same comparison can be cross-multiplied.
Practice this chapterA proportion is an equality of two fractions, a/b = c/d. Cross-multiplying says a × d = b × c.
“What percent of 40 is 10?” is the proportion 10/40 = p/100.
“20% of what number is 9?” is a different sentence: 0.20 × n = 9, so you divide.
Cross-multiply
a/b = c/d → ad = bc
Multiply on the diagonal, then solve for the missing number.
Worked example
Solve 3/5 = x/20.
- 1The two ratios are equal, so their cross products are equal: 3 × 20 = 5 × x.
- 23 × 20 = 60, so the equation is 60 = 5x.
- 3Divide both sides by 5: x = 60 / 5 = 12.
- 4Check the ratios. 3/5 = 0.6, and 12/20 = 0.6. They name the same comparison.
Result: x = 12
Why. Cross-multiplying is valid because the fractions are equal. 3 is to 5 as 12 is to 20, since both pairs simplify to the same ratio, 3 to 5.
“Percent of a number” multiplies. “Percent of what number” divides. Read which quantity is missing.
Practice margin
This chapter
A fresh set from this chapter only. Choose 10 or 20. Multiple choice and fill-in, with no repeat inside the set.