In Grade 5, students multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, such as 23 × 34 or 112 × 223.
The key idea: multiply the numerators and multiply the denominators. Mixed numbers are first rewritten as fractions greater than 1. No common denominator is needed.
Official benchmarkExtend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.
On the FAST test: part of the Grade 5 reporting category Number Sense and Operations with Fractions and Decimals, which is about 23–29% of the test.
Worked Examples
Worked Example 1
Multiplying Two Fractions
23 × 34The overlap is 612 = 12 of the whole.
1Multiply the numerators: 2 × 3 = 6.
2Multiply the denominators: 3 × 4 = 12.
3612 = 12.
Answer: 12
Worked Example 2
Multiplying Mixed Numbers
112 × 223
1Rewrite: 112 = 32 and 223 = 83.
2Multiply: 32 × 83 = 246.
3246 = 4.
Answer: 4
Common Mistakes to Watch For
Multiplying mixed numbers part by part
Wrong:112 × 223 = 226
You can't multiply the wholes and the fractions separately. Rewrite as 32 × 83 = 4.
Multiplying a whole number by the top and bottom
Wrong:34 × 8 = 2432
Write 8 as 81: 34 × 81 = 244 = 6.
Helpful Math Tip
"Of" means multiply: 23 of 34 is 23 × 34. Drawing an area model shows why the answer is smaller than both fractions.
Independent Educational Platform. FastChomp is published by Tropical Learning LLC and is not affiliated with, sponsored by, or endorsed by the Florida Department of Education. FAST and Star assessment names are referenced for informational purposes only. FastChomp practice questions are original educational materials, not official Florida FAST assessment questions.
