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When adding or subtracting fractions, a common denominator is essential. For multiplication and division, denominators play no role in the operation itself. Multiplication involves simply cross‑multiplying numerators and denominators. Division follows the same principle but adds one extra step: invert the divisor.
Before tackling division, review multiplication. In a product of the form a/b × c/d, the specific denominator values are irrelevant. Multiply the numerators together and the denominators together to form the result.
Example: ⅖ × ⅓. Multiply across: (2 × 1) / (5 × 3) = 2/15. Since 2 and 15 share no common factor, the fraction is already in simplest form.
Division is essentially multiplication by the reciprocal. Take the second fraction (the divisor), flip it to obtain its reciprocal, and replace the division sign with a multiplication sign. Thus, a/b ÷ c/d becomes a/b × d/c.
Apply the multiplication rule: multiply numerators and denominators to obtain a d / b c.
Example 1: 1/3 ÷ 8/9. Flip the second fraction to get 9/8 and multiply: (1 × 9) / (3 × 8) = 9/24 = 3/8 after simplification.
Example 2: 11/10 ÷ 5/7. Here the first fraction is improper. Flip the divisor: 7/5 and multiply: (11 × 7) / (10 × 5) = 77/50. No further simplification is possible.
Multiplication and division are reciprocal operations; flipping a fraction is taking its reciprocal. When you divide, you first convert the divisor to its reciprocal, then perform multiplication. Remembering that both steps involve reciprocals helps avoid mistakes.
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