Grade 6 Fractions: All Operations

All operations with fractions

What You'll Learn

Choose correct operation
Solve efficiently

📖All Ops

Use all your skills! Adding or subtracting: find a common denominator first. Multiplying: multiply tops and bottoms. Dividing: keep, change, flip, then multiply.

💡Mixed numbers

To add or subtract mixed numbers, work with the whole numbers and the fractions. Not enough to subtract? Regroup 1 whole: 5 1/4 − 2 3/4 = 4 5/4 − 2 3/4 = 2 2/4 = 2 1/2.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
2/3 − 1/2 = ?
1. The denominators are different, so rename both fractions with a common denominator, 6.
2. Multiply the top and bottom by 2: 2 × 2 = 4 and 3 × 2 = 6, so 2/3 = 4/6.
3. Multiply the top and bottom by 3: 1 × 3 = 3 and 2 × 3 = 6, so 1/2 = 3/6.
4. Subtract the numerators and keep the denominator: 4 − 3 = 1, so the difference is 1/6.
5. So 2/3 − 1/2 = 1/6.
Answer: 1/6
Example 2
1/10 × 2/3 = ?
1. Multiply the numerators: 1 × 2 = 2.
2. Multiply the denominators: 10 × 3 = 30.
3. 1/10 × 2/3 = 2/30.
4. The greatest number that divides both 2 and 30 is 2.
5. Divide the top and bottom by 2: 2 ÷ 2 = 1 and 30 ÷ 2 = 15, so 2/30 = 1/15.
6. So 1/10 × 2/3 = 1/15.
Answer: 1/15
Example 3
4/5 ÷ 1/12 = ?
1. Keep the first fraction, change ÷ to ×, and flip the second: 1/12 becomes 12/1.
2. 4/5 ÷ 1/12 = 4/5 × 12/1.
3. Multiply the numerators: 4 × 12 = 48. Multiply the denominators: 5 × 1 = 5.
4. That gives 48/5.
5. So 4/5 ÷ 1/12 = 48/5.
Answer: 48/5