Fractions and Decimals • Topic 7 of 7

Operations on Fractions

To add or subtract fractions, rewrite them with a common denominator, then add or subtract the numerators. To multiply, multiply the numerators and the denominators straight across, cancelling common factors first to keep numbers small. To divide, multiply by the reciprocal of the second fraction (flip and multiply). Always reduce the final answer to lowest terms. With mixed numbers, convert to improper fractions before multiplying or dividing. These four operations underpin ratio, rate and algebra questions throughout the SAT, so accuracy and speed here pay off across the whole test.

✅ Solved examples

1. Add 1/4 + 2/3.
Common denominator 12: 3/12 + 8/12 = 11/12.
2. Multiply 2/3 × 3/5.
Multiply across: 6/15, which reduces to 2/5.
3. Divide 3/4 ÷ 2/3.
Multiply by the reciprocal: 3/4 × 3/2 = 9/8 = 1 1/8.
4. Subtract 5/6 − 1/4.
Common denominator 12: 10/12 − 3/12 = 7/12.

✏️ Practice — try these, take hints as needed

1. Add 1/2 + 1/3.
Common denominator is 6.
3/6 + 2/6.
Add the numerators.
5/6.
2. Multiply 3/8 × 4/9.
Multiply across: 12/72.
Or cancel first: 3 and 9, 4 and 8.
Reduce 12/72.
1/6.
3. Divide 5/6 ÷ 1/3.
Flip the second: 5/6 × 3/1.
15/6.
Reduce.
5/2 (or 2 1/2).
4. Subtract 7/10 − 1/5.
Common denominator 10.
7/10 − 2/10.
Subtract.
1/2.
5. Add 2/5 + 3/10.
Common denominator 10.
4/10 + 3/10.
Combine and simplify.
7/10.

📝 Topic test — 8 questions

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