Dividing Fractions by Whole Numbers Word Problems
Measure a fractional amount using a whole-number group size. See why the fraction of a group differs from the leftover amount.
Which whole does the answer describe?
Noah has 1 1/2 units of a measured material. A full measuring group holds 2 units. He wants to know how many groups his amount represents, including part of a group. This is a question about amounts, so a fraction of a group is useful. It is not a count of people or a count of finished objects.
Before calculating, compare the amounts. Noah has less than the 2 units needed for one full group, so the answer should be positive and below one. The division equation is 1 1/2 ÷ 2. Keep the total first and the full-group amount second.
Use equal-sized parts to see three fourths
The upper bar is one full group: 2 units, split into four half-unit sections. The lower bar is the available 1 1/2 units, split into three sections of exactly the same size. Noah has three of the four sections needed to fill the group, so he has 3/4 of a group.
One half-unit section is 1/2 of an original measuring unit, but only 1/4 of the two-unit group. The fraction changes because the whole being described changes. Ask the child to point to one original unit and then to one full group before naming the answer.
The equation is 3/2 ÷ 2 = 3/4. Check it by rebuilding the available amount: 3/4 group × 2 units per group = 3/2 units. The check connects the fraction to the story, rather than just confirming a rule.
A whole group and part of another
Now Noah has 2 1/2 units. The full-group measure is still 2 units. He can fill one group and has half an original unit left. That leftover half-unit is not half of a full group: the group is twice as large as one original unit.
Four half-unit sections fill the first group. The fifth section is one of the four sections required for another full group. It is 1/4 of a group, giving 1 1/4 groups altogether. As an improper fraction, that is 5/4 groups.
Why the denominator is multiplied
Write a whole-number divisor as a fraction over one. Dividing by 2 is the same as multiplying by 1/2. Thus 5/2 ÷ 2 = 5/2 × 1/2 = 5/4. In the diagram, a two-unit group contains four halves, so every half-unit contributes one fourth of a group. There are five such contributions.
For a total written as a/b and a whole-number group size n, the group contains b × n pieces of size 1/b. The available amount contains a such pieces. Comparing those counts gives a/(b × n) groups. Simplify only after keeping track of the quantity being counted.
Do not divide the denominator alone by n. That would make the fraction larger instead of measuring the amount in larger groups. Do not reverse the total and the group size. The multiplication check should return the original total.
Compare the answer with both one and the original number
A quotient can be above one while still being smaller than the original number. In 5/2 ÷ 2 = 5/4, the available amount exceeds one full group, so the answer exceeds one group. But 5/4 is smaller than 5/2 because the divisor is greater than one.
These are two different comparisons. First compare the total with the group size to decide whether the answer is below or above one group. Then check that dividing a positive number by a whole number greater than one makes its numerical value smaller. Do not assume that every division answer must be below one.
The same equation can answer a different story
The equation 3/2 ÷ 2 can also describe sharing 1 1/2 units equally between two people. In that story, the answer is 3/4 unit per person. On this worksheet, however, the 2 is the amount in one full group, so the answer is 3/4 of a group. The arithmetic agrees, but the units and what the divisor means are different.
Have the child complete “The divisor tells me ___” and “My answer counts ___.” This makes the reading part of solving the problem. The printed questions consistently use the measuring-group meaning; they do not silently switch to equal sharing.
What the four questions include
Each set has two answers below one group and two above one group. The total is a positive non-whole amount below 6, and the full-group amount is a whole number from 2 through 5. Answers are exact non-whole fractions below 3. Values use simplified equivalent fractions with denominators from 1, 2, 3, 4, 5, 6, 8, 10, and 12.
Draw both amounts at the same scale, write the equation, and label the answer in groups. Equivalent mixed numbers are also correct. These questions include non-unit fractions and mixed amounts; they are selected Grade 6 practice rather than a complete Grade 5 unit-fraction division set.
Keep partial groups in the answer. This worksheet does not ask how many complete items can be made or how many containers must be purchased. Those questions would require a different interpretation of the quotient.
Make a practice set
Select the worksheet, answer key, or both. When both are selected, the answer key prints after the questions. Keep it separate if you want your student to work independently.
After your student finishes
Ask what the divisor measures and what the answer counts. Multiply the number of groups by the full-group amount to recover the total.
Word problemsDividing Whole Numbers by Unit Fractions Word Problems
Count fractional-foot cable pieces in a whole-number length, using equal groups and multiplication to check.
4 problems · Answer key included
More about division · Grade 6 worksheets
Grade 6 selected skill connection: Selected 6.NS.A.1 fraction-quotient interpretation: non-whole total divided by a whole-number measuring-group size. Includes non-unit fractions and mixed totals, beyond the Grade5 unit-fraction-only subset. Not every division context. See the Common Core standards for this grade. This worksheet does not cover every requirement in the standard.