Math Core

A recipe might call for "2 and a half cups" of flour. That amount is more than 2 cups but less than 3. A mixed number is a handy way to write amounts like this: a whole number and a fraction together.

What is a mixed number?

Definition

Mixed number

A mixed number has a whole number part and a fraction part that is less than 1.

$2\dfrac{1}{2}$ is read "two and one half." It means $2 + \dfrac{1}{2}$ .

Here is $1\dfrac{3}{4}$ on a number line. It is 1 whole and 3 more fourths:

A fraction whose numerator is bigger than (or equal to) its denominator, like $\dfrac{7}{4}$ , is also more than or equal to 1. Count the fourths on the line above: the dot is on the 7th fourth. So $\dfrac{7}{4}$ and $1\dfrac{3}{4}$ are the same number.

From a fraction to a mixed number

To change $\dfrac{7}{4}$ into a mixed number, pull out as many wholes as you can. Every 4 fourths make 1 whole.

\frac{7}{4} = \frac{4}{4} + \frac{3}{4} = 1 + \frac{3}{4} = 1\frac{3}{4}

A quick way is to divide the numerator by the denominator:

$7 \div 4 = 1$ with a remainder of $3$ .
The quotient is the whole number part: 1.
The remainder is the new numerator: 3. The denominator stays 4.

Changing between the two forms

Fraction to mixed number: divide the numerator by the denominator. The quotient is the whole number, and the remainder goes over the same denominator.

Mixed number to fraction: multiply the whole number by the denominator, then add the numerator. Keep the same denominator.

Worked example: Fraction to mixed number

Write $\dfrac{17}{5}$ as a mixed number.

$17 \div 5 = 3$ with a remainder of $2$ . So there are 3 wholes and 2 fifths left over:

\frac{17}{5} = 3\frac{2}{5}.

Check: 3 wholes is $\dfrac{15}{5}$ , and $\dfrac{15}{5} + \dfrac{2}{5} = \dfrac{17}{5}$ .

From a mixed number to a fraction

To go the other way, turn every whole into pieces. For $2\dfrac{1}{3}$ :

Each whole is 3 thirds, so 2 wholes are $2 \times 3 = 6$ thirds.
Add the 1 more third: $6 + 1 = 7$ thirds.

2\frac{1}{3} = \frac{7}{3}

Worked example: Mixed number to fraction

Write $4\dfrac{5}{6}$ as a fraction.

4 wholes are $4 \times 6 = 24$ sixths. Add 5 more sixths: $24 + 5 = 29$ .

4\frac{5}{6} = \frac{29}{6}

Worked example: A real-life amount

A bakery uses $\dfrac{11}{4}$ bags of flour in a day. Between which two whole numbers of bags is that?

$11 \div 4 = 2$ with a remainder of 3, so $\dfrac{11}{4} = 2\dfrac{3}{4}$ . That is between 2 and 3 bags (closer to 3).

Common mistake

When changing a mixed number to a fraction, don't just stick the numbers together or add them all. $2\dfrac{1}{3}$ is not $\dfrac{3}{3}$ (from $2 + 1$ ) or $\dfrac{21}{3}$ . Remember that each whole is worth 3 thirds, so multiply first: $2 \times 3 + 1 = 7$ .

Tip

A fraction is more than 1 when its numerator is bigger than its denominator. If you ever get a mixed number whose fraction part is 1 or more, like $2\dfrac{5}{4}$ , you still have another whole to pull out: $2\dfrac{5}{4} = 3\dfrac{1}{4}$ .

Practice

Practice 1

Which mixed number does the dot show?

Practice 2

Write $3\dfrac{1}{3}$ as a fraction with denominator 3. What is the numerator?

Type a number.

Practice 3

Which mixed number equals $\dfrac{9}{4}$ ?

Practice 4

When you write $\dfrac{23}{6}$ as a mixed number, what is the whole number part?

Type a number.

Practice 5

Write $2\dfrac{3}{8}$ as a fraction with denominator 8. What is the numerator?

Type a number.

Practice 6

When you write $\dfrac{47}{10}$ as a mixed number, what is the numerator of the fraction part?

Type a number.

Practice 7

Nia ran $\dfrac{13}{5}$ miles. Tom ran $2\dfrac{4}{5}$ miles. Who ran farther?