In Grade 5, students explore two kinds of division with unit fractions (fractions with 1 on top): a unit fraction divided by a whole number, like 13 ÷ 4, and a whole number divided by a unit fraction, like 5 ÷ 12.
13 ÷ 4 asks "if 13 is split into 4 equal parts, how big is each part?" (smaller). 5 ÷ 12 asks "how many halves are in 5?" (bigger).
Official benchmarkExtend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.
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
Unit Fraction ÷ Whole Number
13 ÷ 4
1Split 13 into 4 equal parts.
2Each part is 14 of 13.
314 × 13 = 112.
Answer: 112
Worked Example 2
Whole Number ÷ Unit Fraction
5 ÷ 12
1How many halves are in 5?
2Each whole has 2 halves.
35 × 2 = 10 halves.
Answer: 10
Common Mistakes to Watch For
Getting a smaller answer when dividing by a unit fraction
Wrong:3 ÷ 14 = 34
Ask how many fourths are in 3. Each whole has 4 fourths, so 3 ÷ 14 = 12.
Getting a bigger answer when dividing a unit fraction
Wrong:12 ÷ 3 = 32
Splitting a half into 3 parts makes each part smaller: 12 ÷ 3 = 16.
Helpful Math Tip
Draw it. A bar split into halves, then each half split into 3, shows 12 ÷ 3 = 16 right away.
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.
