Fractions, Ratios & Percents

Mixed numbers, decimals, percentages, proportions, discounts, profit, and percent increase/decrease.

Detailed SSAT Tested Points

This page expands the rational-number part of arithmetic. Students need it for stand-alone questions and for word problems.

Fractions and Mixed Numbers

  • Fractions: simplify, compare, add, subtract, multiply, and divide
  • Mixed numbers: convert between mixed numbers and improper fractions
  • Decimals: convert between fractions, decimals, and percents

Percents

  • Percentages
  • Percent of a number
  • Percent increase/decrease
  • Profit and discounts

Ratios and Proportions

  • Ratios
  • Proportions
  • Set up equivalent ratios
  • Use cross multiplication when appropriate

Estimation

  • Estimate before calculating
  • Use benchmarks such as 1/2, 1/4, 3/4, 10%, and 25%
  • Eliminate unreasonable answer choices

Core Knowledge

Fractions: add and subtract with common denominators.
Ratios: 3:5 means 8 total parts.
Percent: convert to decimals before multiplying.
Percent change: change ÷ original × 100%.
Useful conversions: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 1/8 = 12.5%.

Practice

  1. What is 2/3 + 5/6?
  2. The ratio of cats to dogs is 2:7. If there are 45 animals, how many are dogs?
  3. A jacket costs $80 and is discounted 30%. What is the sale price?
  4. A score rises from 60 to 75. What is the percent increase?
  5. 40% of a number is 28. What is the number?
  6. A recipe uses 4 cups of flour for 10 cookies. How many cups are needed for 25 cookies?
Show Answer Key

1. 3/2 or 1 1/2.

2. 35 dogs. Each part is 5 animals; dogs are 7 parts.

3. $56.

4. 25%.

5. 70.

6. 10 cups.

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