5th Grade Dividing Unit Fractions and Whole Numbers Lesson (Free PDF)

Q: Why is \frac{1}{2} \div 3 equal to \frac{1}{6} and not \frac{3}{2}?

Dividing \frac{1}{2} by 3 cuts one half into 3 equal pieces, so each piece is smaller than \frac{1}{2}. Six of those pieces make one whole, so each piece is \frac{1}{6}. The answer \frac{3}{2} comes from multiplying by 3 by mistake.

Q: Why does dividing 5 by \frac{1}{4} give 20?

Each whole contains 4 fourths. Five wholes contain 5 \times 4 = 20 fourths. The question asks how many pieces of size \frac{1}{4} fit in 5, so the answer is larger than 5.

5th Grade math lesson: Dividing Unit Fractions and Whole Numbers – Maths PDF

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This divide unit fractions lesson for 5th Grade covers dividing unit fractions and whole numbers (Common Core 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c), with a free PDF to print.

Dividing with unit fractions follows two patterns. A unit fraction divided by a whole number gets smaller: 1/3 ÷ 4 = 1/12, because each piece is cut again. A whole number divided by a unit fraction gets bigger: 4 ÷ 1/3 = 12, because each whole holds 3 pieces. Check every answer with multiplication.

Grade 5 · Common Core State Standards: 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c

Key facts in this divide unit fractions lesson

Key facts

A unit fraction has a numerator of 1, like 1/4 or 1/8.
A unit fraction divided by a whole number n is 1 over (denominator times n).
A whole number divided by a unit fraction 1/b equals the whole number times b.
Check any quotient by multiplying it by the divisor to get the dividend.
Bar models and number lines show how many pieces there are.

What does it mean to divide a unit fraction by a whole number?

A unit fraction has a 1 on top, like \(\frac{1}{2}\), \(\frac{1}{3}\) or \(\frac{1}{5}\). When you divide it by a whole number, you cut it into equal smaller pieces. Picture \(\frac{1}{3}\) of a pizza shared by 4 friends. Each friend gets \(\frac{1}{12}\) of the whole pizza.

Dividing \(\frac{1}{3}\) into 4 equal pieces makes twelfths.

Vocabulary

Unit fraction: a fraction with a numerator of 1. Quotient: the answer to a division problem. Dividend: the number being divided.

What does it mean to divide a whole number by a unit fraction?

Now the question is, “How many pieces fit?” The problem \(3\div\frac{1}{4}\) asks how many fourths are in 3 wholes. Each whole holds 4 fourths, so 3 wholes hold \(3\times4=12\) fourths.

Three wholes contain 12 pieces that are each \(\frac{1}{4}\) of a whole.

How can a number line show the division?

Start at 0 and make jumps that are the size of the unit fraction. Count the jumps until you reach the whole number. For \(2\div\frac{1}{3}\) you make 6 jumps of \(\frac{1}{3}\) to land on 2.

Six jumps of \(\frac{1}{3}\) reach 2, so \(2 \div \frac{1}{3} = 6\).

How do you check a division answer?

Division and multiplication are partners. Multiply the quotient by the divisor and you should get the dividend back.

Multiplying the answer by the divisor returns the starting number.

Two patterns to remember

\(\frac{1}{b}\div n=\frac{1}{b\times n}\): the pieces get smaller, so the quotient is less than the unit fraction.
\(n\div\frac{1}{b}=n\times b\): there are more pieces than wholes, so the quotient is greater than \(n\).

What are the steps to solve a problem?

Read the problem. Decide: is a unit fraction being cut up, or are you counting pieces in a whole number?
Draw a bar model or number line to see the pieces.
Multiply the correct numbers to find the number of pieces or the new size of a piece.
Check by multiplying the quotient by the divisor.

Example: Maya has \(\frac{1}{4}\) pound of raisins. She puts them equally into 2 bags. Each bag gets \(\frac{1}{4}\div2=\frac{1}{8}\) pound. Check: \(\frac{1}{8}\times2=\frac{2}{8}=\frac{1}{4}\).

Divide unit fractions lesson: questions and answers

Why is \(\frac{1}{2} \div 3\) equal to \(\frac{1}{6}\) and not \(\frac{3}{2}\)?

Dividing \(\frac{1}{2}\) by 3 cuts one half into 3 equal pieces, so each piece is smaller than \(\frac{1}{2}\). Six of those pieces make one whole, so each piece is \(\frac{1}{6}\). The answer \(\frac{3}{2}\) comes from multiplying by 3 by mistake.

Why does dividing 5 by \(\frac{1}{4}\) give 20?

Each whole contains 4 fourths. Five wholes contain \(5 \times 4 = 20\) fourths. The question asks how many pieces of size \(\frac{1}{4}\) fit in 5, so the answer is larger than 5.

What is a unit fraction?

A unit fraction is a fraction with 1 as the numerator, such as \(\frac{1}{3}\), \(\frac{1}{5}\), or \(\frac{1}{10}\). It shows one equal part of a whole.

How can I check my division answer?

Multiply the quotient by the divisor. If you get the dividend, the answer is right. For example, \(\frac{1}{8} \times 2 = \frac{1}{4}\) confirms that \(\frac{1}{4} \div 2 = \frac{1}{8}\).

When should I use a number line or a bar model?

Use a bar model when you cut a fraction into smaller pieces. Use a number line when you count how many equal jumps reach a whole number. Both pictures lead to the same answer.

How to use this divide unit fractions lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

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