Fraction and Division

What happens when three whole cakes must be shared among four children? The answer is not a whole number of cakes. Division can name a fraction, and the same division can then show the fraction's decimal value.

Parents: let your child predict the share or the division before opening each worked panel. Keep the parent whole named so the fraction and decimal describe the same amount.

By the end you'll be able to use equal sharing to write a fractional quotient, and express a fraction as a decimal by dividing its numerator by its denominator.

Suppose three identical cakes are shared equally among four children. Each cake is one whole cake. The four children receive equal shares of all three wholes, so each child receives $\frac{3}{4}$ of one cake.

🤔 Predict first: Two whole pizzas are shared equally among five children. What does one child receive?

Compare one whole cake with the

\frac{3}{4}

-cake share. Four equal shares account for all three whole cakes.

Equal sharing: keep each whole visible

Predict first: Three whole cakes are shared equally among four children. What does one child receive?

Share the whole cakes

3 \text{ whole cakes} \div 4 \text{ children} = \frac{3}{4} \text{ cake per child}

Whole-number division can have a fractional quotient

The quotient is the answer to a division. When the dividend and divisor are whole numbers but the dividend is too small to give each group a whole object, the quotient can be a .

For the cake story, the quotient notation and the sharing picture say the same thing.

Write the quotient as a fraction

3 \div 4 = \frac{3}{4}

\text{3 whole cakes shared into 4 equal shares} = \frac{3}{4} \text{ cake per share}

The numerator is the dividend and the denominator is the divisor. Keep the named unit beside the answer so you do not accidentally swap the two numbers.

Express a fraction as a decimal by division

To write a fraction as a , divide the numerator by the denominator. If the numerator is too small at first, place zeroes after the decimal point and continue the same division.

Turn the fraction into a decimal

\frac{3}{4} = 3 \div 4 = 0.75

Turn the fraction into a decimal

\frac{7}{8} = 7 \div 8 = 0.875

For example, $\frac{2}{5}$ gives $\frac{4}{10}$ when the numerator is divided by the denominator.

A short decimal bridge

\frac{2}{5} = 2 \div 5 = 0.4

🤔 Predict first: To express $\frac{7}{8}$ as a decimal, which division matches the fraction?

Practise with worked steps

Start here — share two whole sandwiches among five children

Two identical whole sandwiches are shared equally among five children. What fraction of one sandwich does each child receive?

Name the equal share

2 \div 5 = \frac{2}{5}

\text{Each child receives } \frac{2}{5} \text{ of one sandwich}

The answer is $\frac{2}{5}$ of a sandwich per child.

Build up — write 3 ÷ 4 in both forms

Write three divided by four as a fraction and as a decimal.

Keep the three representations together

3 \div 4 = \frac{3}{4} = 0.75

The answer is $\frac{3}{4}$ and 0.75.

Challenge — express

\frac{7}{8}

as a decimal

Express $\frac{7}{8}$ as a decimal.

Divide the numerator by the denominator

\frac{7}{8} = 7 \div 8 = 0.875

The answer is 0.875.

Watch out — easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

Three whole cakes are shared equally among four children. What does each child get?
Write 5 ÷ 8 as a fraction.
What is $\frac{3}{4}$ as a decimal?
What is $\frac{7}{8}$ as a decimal?
Which situation gives EACH CHILD $\frac{2}{5}$ of one pizza?
Which operation changes $\frac{7}{8}$ into a decimal?

Equal sharing names the fraction