Math Core

If you eat all 4 slices of a pizza cut into fourths, you ate the whole pizza. That means $\dfrac{4}{4}$ and 1 are the same number! Whole numbers can be written as fractions too.

One whole

When the numerator and denominator are the same, you have all the parts. That is one whole.

🟦🟦🟦 is $\dfrac{3}{3}$ of the strip, and it is the whole strip.

\frac{2}{2} = 1 \qquad \frac{3}{3} = 1 \qquad \frac{6}{6} = 1 \qquad \frac{8}{8} = 1

On a number line, the point 1 is the end of the last hop:

All the parts make one whole

When the numerator and denominator are the same, the fraction equals 1.

Going past 1

A number line can keep going past 1. Here it goes to 3, and every whole is cut into halves:

Now look at the dots.

$\dfrac{2}{2}$ is at 1.
$\dfrac{4}{2}$ is at 2.
$\dfrac{6}{2}$ is at 3.

Each whole holds 2 halves. So 3 wholes hold $3 \times 2 = 6$ halves, and $\dfrac{6}{2} = 3$ .

Tip

To write a whole number as a fraction with a given denominator, multiply: 2 wholes cut into fourths is $2 \times 4 = 8$ fourths, so $2 = \dfrac{8}{4}$ .

Wholes that are not cut

What if a whole is not cut at all? Then it has only 1 part, and the denominator is 1.

Imagine 5 whole cookies, none of them broken. Each cookie is 1 part of size "one whole." You have 5 of those parts:

\frac{5}{1} = 5

Definition

Whole numbers as fractions

Any whole number can be written with a denominator of 1: $\dfrac{a}{1} = a$ . A fraction also equals a whole number when its parts fill up whole units exactly, like $\dfrac{8}{4} = 2$ .

Common mistake

$\dfrac{1}{4}$ and $\dfrac{4}{1}$ are not the same! $\dfrac{1}{4}$ is one small piece of a whole. $\dfrac{4}{1}$ is 4 whole things.

Worked example: Write 1 as a fraction

Write 1 as a fraction with a denominator of 6.

One whole cut into sixths has 6 sixths. So $1 = \dfrac{6}{6}$ .

Worked example: Which whole number?

What whole number equals $\dfrac{9}{3}$ ?

Each whole has 3 thirds. Count wholes by threes: 3 thirds is 1 whole, 6 thirds is 2 wholes, 9 thirds is 3 wholes. So $\dfrac{9}{3} = 3$ .

Worked example: Muffin trays

A baker has 2 trays of muffins. Each tray is cut into 6 equal pieces. How many sixths are there? Write the total as a fraction.

Each tray has 6 sixths, and there are 2 trays: $2 \times 6 = 12$ sixths. So 2 trays is $\dfrac{12}{6}$ , and $\dfrac{12}{6} = 2$ .

Practice

Practice 1

What whole number equals $\dfrac{8}{8}$ ?

Type a number.

Practice 2

Fill in the missing numerator so the fraction equals 1: $\dfrac{?}{4} = 1$ .

Type a number.

Practice 3

What whole number equals $\dfrac{7}{1}$ ?

Type a number.

Practice 4

What whole number equals $\dfrac{6}{3}$ ?

Type a number.

Practice 5

Which fraction is not equal to 1?

Practice 6

Write 3 as a fraction with a denominator of 4. What is the numerator?

Type a number.

Practice 7

Tia has some sandwiches, each cut into halves. Altogether she has 10 halves. How many whole sandwiches is that?

Type a number.