Fractions & Decimals
Multiplying, Dividing & Reciprocals
To multiply fractions, multiply numerators and denominators. To divide, multiply by the reciprocal of the second fraction (turn it upside down). The reciprocal of a/b is b/a, and the reciprocal of a whole number n is 1/n.
Example 1: Multiply ⅔ × ¾.
(2 × 3)/(3 × 4) = 6/12 = ½.
Example 2: What is the reciprocal of ⅗?
Turn it upside down: 5/3.
Quick recap
- Divide by multiplying by the reciprocal.
- Reciprocal of a/b is b/a; of n is 1/n.
✓ Quick check
What is ¾ ÷ ⅜?
¾ × 8/3 = 24/12 = 2.
What is the reciprocal of 7?
The reciprocal of 7 is 1/7.
Mixed Operations & Word Problems
When an expression has several operations, follow the order: brackets, then × and ÷, then + and −. Convert mixed numbers to improper fractions before multiplying or dividing.
For example, ½ + ¼ × 2 = ½ + ½ = 1, and 2½ × 2 = 5/2 × 2 = 5.
Example 1: Simplify ½ + ¼ × 2.
Multiply first: ¼ × 2 = ½, then ½ + ½ = 1.
Example 2: Multiply 2½ × 2.
5/2 × 2 = 5.
Quick recap
- Order: brackets, then × and ÷, then + and −.
- Change mixed numbers to improper fractions first.
✓ Quick check
What is ⅖ × 10?
(2 × 10)/5 = 20/5 = 4.
What is ¾ of 16?
16 ÷ 4 = 4, and 4 × 3 = 12.
Decimal Multiplication & Division
To multiply by 10, 100 or 1000, move the decimal point right; to divide, move it left. To multiply two decimals, multiply as whole numbers and place the point with the total number of decimal places. To divide by a decimal, make the divisor a whole number first.
Example 1: Multiply 1.2 × 0.5.
12 × 5 = 60, with two decimal places: 0.60 = 0.6.
Example 2: Divide 4.5 ÷ 0.5.
Multiply both by 10: 45 ÷ 5 = 9.
Quick recap
- × 10/100/1000 moves the point right; ÷ moves it left.
- To divide by a decimal, make the divisor a whole number first.
✓ Quick check
What is 0.6 × 0.4?
6 × 4 = 24, with two decimal places: 0.24.
What is 3.6 ÷ 0.6?
Multiply both by 10: 36 ÷ 6 = 6.
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