Fractions
Comparing & Adding/Subtracting Mixed Fractions
To compare or add unlike fractions, change them to the same denominator (the LCM) first. For mixed fractions, add or subtract the whole numbers and the fractions, regrouping when needed.
So 1½ + 2¼ = 3¾, and 3½ − 1¾ = 1¾ (after borrowing).
Example 1: Add 1½ + 2¼.
½ = 2/4, so 1 2/4 + 2 1/4 = 3 3/4 = 3¾.
Example 2: Subtract 3½ − 1¼.
3 2/4 − 1 1/4 = 2 1/4 = 2¼.
Quick recap
- Make denominators equal before comparing or adding unlike fractions.
- Mixed fractions: work on wholes and fractions, regroup if needed.
✓ Quick check
What is 2¼ + 1¼?
2¼ + 1¼ = 3 2/4 = 3½.
Which fraction is bigger, ⅔ or ¾?
As 8/12 and 9/12, ¾ is bigger.
Multiplying Fractions
To multiply two fractions, multiply the numerators together and the denominators together: ½ × ⅓ = 1/6.
To multiply a fraction by a whole number, multiply the numerator by the whole number: ¾ × 8 = 24/4 = 6.
Example 1: Multiply ⅖ × ⅗.
(2 × 3)/(5 × 5) = 6/25.
Example 2: Multiply ⅔ × 9.
(2 × 9)/3 = 18/3 = 6.
Quick recap
- Fraction × fraction: multiply tops, multiply bottoms.
- Fraction × whole: multiply the numerator by the whole number.
✓ Quick check
What is ½ × ¼?
(1 × 1)/(2 × 4) = 1/8.
What is ⅗ × 10?
(3 × 10)/5 = 30/5 = 6.
Dividing Fractions
To divide a fraction by a whole number, multiply the denominator by that number: ½ ÷ 2 = ¼.
To divide a whole number by a unit fraction, ask how many of that fraction fit in: 3 ÷ ½ = 6, because there are 6 halves in 3.
Example 1: Divide ¾ ÷ 3.
Multiply the denominator by 3: 3/(4 × 3) = 3/12 = ¼.
Example 2: Divide 4 ÷ ½.
There are 2 halves in each whole, so 4 ÷ ½ = 8.
Quick recap
- Fraction ÷ whole: multiply the denominator by the whole number.
- Whole ÷ unit fraction: count how many fit (3 ÷ ½ = 6).
✓ Quick check
What is ⅔ ÷ 2?
2/(3 × 2) = 2/6 = ⅓.
What is 5 ÷ ½?
There are 2 halves in each whole, so 5 ÷ ½ = 10.
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