Math Core

A unit fraction is just one equal part. But what if you eat 3 slices of a pizza, not 1? You can build any fraction by putting unit fractions together.

Counting equal parts

This bar is cut into 4 equal parts, and 3 of them are shaded.

3 of the 4 equal parts are shaded.

Each part is $\dfrac{1}{4}$ . Count the shaded parts: one fourth, two fourths, three fourths. The shaded amount is $\dfrac{3}{4}$ , or three fourths.

So $\dfrac{3}{4}$ is 3 parts that are each $\dfrac{1}{4}$ in size:

\frac{3}{4} = \frac{1}{4} + \frac{1}{4} + \frac{1}{4}

The two numbers in a fraction

Every fraction has a top number and a bottom number, and each one has a job.

Definition

Numerator and denominator

In the fraction $\dfrac{a}{b}$ :

The denominator $b$ (bottom) tells how many equal parts the whole is cut into.
The numerator $a$ (top) tells how many of those parts you count.

A trick for remembering: denominator is down below.

Building a fraction

$\dfrac{a}{b}$ means $a$ parts, where each part is $\dfrac{1}{b}$ of the whole.

Shaded and not shaded

Look at this strip of 6 equal squares:

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5 of the 6 squares are orange, so $\dfrac{5}{6}$ of the strip is orange. 1 square is white, so $\dfrac{1}{6}$ is white. The two parts together make the whole strip: 5 sixths and 1 sixth make 6 sixths.

Common mistake

The denominator is the number of all the equal parts, not the number of parts left over. In the strip above, the denominator is 6 (all the squares), not 1 (the white square).

Worked example: Name the shaded part

What fraction of this strip is blue?

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There are 8 equal squares in all, so the denominator is 8. 2 are blue, so the numerator is 2. The blue part is $\dfrac{2}{8}$ .

Worked example: Pizza party

A pizza is cut into 8 equal slices. Ava and her friends eat 5 slices. What fraction of the pizza did they eat? What fraction is left?

The whole has 8 equal slices, so both fractions have denominator 8.
They ate 5 slices: $\dfrac{5}{8}$ of the pizza.
$8 - 5 = 3$ slices are left: $\dfrac{3}{8}$ of the pizza.

Worked example: Build the whole

A rectangle is cut into thirds. How many thirds are in $\dfrac{2}{3}$ ? How many more thirds do you need to make the whole?

$\dfrac{2}{3}$ is 2 thirds. The whole is 3 thirds, and $3 - 2 = 1$ , so you need 1 more third.

Practice

Practice 1

What fraction of the strip is green? 🟩🟩🟩⬜⬜⬜

Type your answer like 1/2.

Type a number.

Practice 2

In the fraction $\dfrac{3}{4}$ , what is the denominator?

Type a number.

Practice 3

Which fraction means "5 parts, each $\dfrac{1}{8}$ of the whole"?

Practice 4

A pan of brownies is cut into 3 equal pieces. Jay eats 2 pieces. What fraction of the pan is left?

Type your answer like 1/2.

Type a number.

Practice 5

How many eighths are in $\dfrac{7}{8}$ ?

Type a number.

Practice 6

A flag has 6 equal stripes. 4 stripes are red and the rest are white. What fraction of the flag is white?

Type your answer like 1/2.

Type a number.

Practice 7

A bar is cut into fourths. Nia colors $\dfrac{1}{4}$ of it. How many more fourths must she color so the whole bar is colored?

Type a number.