Multiplying and Dividing Fractions — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. The product of two fractions is the result when you multiply them.
The result of multiplying two or more numbers is called the product. When multiplying two fractions, you multiply numerators together and denominators together.
2. The reciprocal of 34 is 43.
The reciprocal of a fraction is found by flipping it — swapping numerator and denominator. The reciprocal of 34 is 43.
3. The reciprocal of 5 written as a fraction is 15.
5 = 51. The reciprocal is 15. Any non-zero number multiplied by its reciprocal equals 1.
4. Reducing 812 to simplest form means dividing numerator and denominator by their GCF.
GCF(8,12)=4. 8÷4=2, 12÷4=3. 812 in simplest form is 23. Always simplify products after multiplying.
5. Cross-cancellation lets you divide a numerator and a denominator by a common factor before multiplying.
Cross-cancellation (or cross-reducing) simplifies fractions before multiplying. Dividing a numerator of one fraction and the denominator of another by a common factor makes computation easier.
6. 23 × 34 = 12 after cross-cancelling the 3s.
Cross-cancel: the 3 in the numerator of 23 and the 3 in the denominator of... wait — cross-cancel the 3 in 34's numerator with 3 in 23's denominator. Result: 21 × 14 = 24 = 12.
7. To divide by a fraction, multiply by its reciprocal.
The rule for dividing fractions is 'Keep, Change, Flip': keep the first fraction, change ÷ to ×, flip (take the reciprocal of) the second fraction.
8. The product of 58 × 45 in simplest form is 12.
Cross-cancel: 5 and 5 → 1; 4 and 8 → divide by 4 gives 1 and 2. Result: 11 × 12 = 12.
9. When a fraction is in simplest form, its numerator and denominator share no common factor other than 1.
A fraction is in simplest form (lowest terms) when GCF(numerator, denominator) = 1. For example, 34 is in simplest form; 68 is not.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
23 × 35
→ 25
29
47 × 78
→ 12
14
12 × 49
→ 29
25
56 × 310
→ 14
12
23×35=615=25; 47×78=2856=12; 12×49=418=29; 56×310=1560=14.