Mental Fraction Arithmetic
Working with fractions mentally requires memorizing common equivalents and using shortcuts. Know that 1/2 = 50%, 1/3 ≈ 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, and 1/10 = 10%. These building blocks let you compute any common fraction quickly.
Converting Fractions to Percentages
Divide numerator by denominator, then multiply by 100. For 3/8: 3 ÷ 8 = 0.375, × 100 = 37.5%. Shortcut for denominators that divide into 100: 1/4 = 25/100 = 25%, 1/5 = 20/100 = 20%, 3/5 = 60/100 = 60%.
Finding Fractions of Numbers
To find a/b of N: divide N by b, then multiply by a. For 2/3 of 90: 90 ÷ 3 = 30, then 30 × 2 = 60. This “divide then multiply” approach avoids dealing with fractions entirely — you work with whole numbers throughout.
Adding and Subtracting Fractions
For fractions with different denominators, find the least common denominator mentally. For 1/5 + 1/4: LCD is 20. Convert: 4/20 + 5/20 = 9/20. With practice, common LCDs (12, 20, 24, 60) are recognized instantly, making fraction addition nearly as fast as whole number addition.
Practice Examples
Example 1: 3/8 as a percentage?
- Divide 3 by 8: 3 ÷ 8 = 0.375
- Multiply by 100: 37.5%
Answer: 37.5%
Example 2: What is 2/3 of 90?
- Divide 90 by 3 = 30
- Multiply by 2 = 60
Answer: 60
Example 3: 1/5 + 1/4 = ?
- Find LCD: 20
- 1/5 = 4/20, 1/4 = 5/20
- 4/20 + 5/20 = 9/20
Answer: 9/20