This grade 5 divide fractions lesson explains dividing unit fractions and whole numbers in one printable page, with definitions, a method and a worked example.
To divide a unit fraction by a whole number, split the fraction into equal parts: \(\frac{1}{3} : 4 = \frac{1}{12}\). To divide a whole number by a unit fraction, count the pieces that fit: \(3 : \frac{1}{4} = 12\). Check either answer by multiplying it by the divisor to get the starting number.
Grade 5 Divide Fractions Lesson: key facts
- A unit fraction has a numerator of 1, such as \(\frac{1}{5}\).
- A unit fraction divided by a whole number: \(\frac{1}{n} : k = \frac{1}{n \times k}\).
- A whole number divided by a unit fraction: \(k : \frac{1}{n} = k \times n\).
- Splitting a fraction makes smaller pieces; counting unit fractions in a whole number gives a larger answer.
- Check division by multiplying the quotient by the divisor.
How do you divide a unit fraction by a whole number?
A unit fraction has 1 on top, such as \(\frac{1}{2}\), \(\frac{1}{3}\) or \(\frac{1}{10}\). To find \(\frac{1}{3} : 4\), split one third into 4 equal pieces. Cutting every third of the whole into 4 pieces makes 12 equal pieces in the whole, so each piece is \(\frac{1}{12}\).
\(\frac{1}{n} : k = \frac{1}{n \times k}\). Splitting a piece into more parts makes each part smaller, so the answer is smaller than the starting fraction.
How do you divide a whole number by a unit fraction?
To find \(3 : \frac{1}{4}\), ask how many fourths fit into 3 wholes. Each whole holds 4 fourths, so 3 wholes hold \(3 \times 4 = 12\) fourths.
\(k : \frac{1}{n} = k \times n\). Dividing by a unit fraction counts how many pieces fit, so the answer is larger than the whole number.
How can you check a division answer?
Multiply the answer by the divisor. You should get the starting number back.
| Division | Answer | Check |
|---|---|---|
| \(\frac{1}{4} : 3\) | \(\frac{1}{12}\) | \(\frac{1}{12} \times 3 = \frac{1}{4}\) |
| \(3 : \frac{1}{4}\) | 12 | \(12 \times \frac{1}{4} = 3\) |
How do you solve a division word problem?
- Decide what is being split or counted.
- Write the division equation.
- Draw a model or use the rule.
- Check by multiplying, and answer with units.
Example. Maya has \(\frac{1}{2}\) gallon of lemonade to pour equally into 3 cups. The lemonade is split, so \(\frac{1}{2} : 3 = \frac{1}{6}\) gallon in each cup. Check: \(3 \times \frac{1}{6} = \frac{1}{2}\).
The same lemonade could be counted instead of split: 5 cups of juice poured into 1/4-cup servings gives \(5 : \frac{1}{4} = 20\) servings.
Common mistake: mixing up the two types. \(\frac{1}{2} : 4 = \frac{1}{8}\) is small, but \(4 : \frac{1}{2} = 8\) is large.
Dividing Unit Fractions and Whole Numbers: frequently asked questions
How do you divide a unit fraction by a whole number?
Multiply the denominator by the whole number and keep the numerator 1. For example, \(\frac{1}{5} : 3 = \frac{1}{15}\). A picture helps: cut one fifth into 3 equal pieces.
How do you divide a whole number by a unit fraction?
Multiply the whole number by the denominator of the unit fraction. For example, \(6 : \frac{1}{5} = 6 \times 5 = 30\), because each whole holds 5 fifths.
Why does dividing by a unit fraction make the number bigger?
Dividing by \(\frac{1}{n}\) asks how many pieces of size \(\frac{1}{n}\) fit. Pieces are small, so many fit, and the answer is greater than the whole number.
How do you check a division with fractions?
Multiply the quotient by the divisor. If \(\frac{1}{4} : 3 = \frac{1}{12}\), then \(\frac{1}{12} \times 3\) must equal \(\frac{1}{4}\), and it does.
Which operation does a word problem need?
If something is shared equally, split it: unit fraction divided by a whole number. If you count how many servings or pieces fit, divide the whole number by the unit fraction.
How to use this grade 5 divide fractions lesson
Use this grade 5 divide fractions lesson before the worksheet, then check what you learned with the quiz.
See every chapter on the Grade 5 math page.