P4 Mixed Numbers and Improper Fractions

$\frac{7}{4}$ sounds like seven pieces, but those pieces can be regrouped into one whole and $\frac{3}{4}$. A mixed number tells the story in wholes first; an improper fraction keeps every piece in one count.

Parents: let your child point to each complete whole before they read the remainder.

By the end you will be able to change an improper fraction into a mixed number and change a mixed number into an improper fraction.

Improper fraction to mixed number

An improper fraction has enough equal parts to make at least one whole. Divide the numerator by the denominator. The quotient is the number of complete wholes, and the remainder stays over the original denominator.

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Fraction strips: improper to mixed

🤔 Predict first: Which improper fraction is $1\frac{3}{4}$?

$\frac{5}{4}$$\frac{7}{4}$$\frac{8}{4}$

Group the improper fraction

$$7 \div 4 = 1 \text{ remainder } 3$$

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

Mixed number to improper fraction

A mixed number has complete wholes and leftover equal parts. To put it back into one fraction, convert every whole into denominator-sized parts, then add the extra numerator.

Convert the mixed number

$$3 \times 5 = 15$$

$$15 + 2 = 17$$

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

Check the conversion both ways

The two forms are different ways to record the same amount. For $\frac{23}{6}$, division gives three wholes and $\frac{5}{6}$. Reversing the conversion gives three times six plus five, which returns twenty-three.

Reverse-check the improper fraction

$$23 \div 6 = 3 \text{ remainder } 5$$

$$\frac{23}{6} = 3\frac{5}{6}$$

$$3 \times 6 + 5 = 23$$

Practise with worked steps

Practice 1: Convert $\frac{11}{4}$ to a mixed number

Divide the numerator

$$11 \div 4 = 2 \text{ remainder } 3$$

$$\frac{11}{4} = 2\frac{3}{4}$$

$\frac{11}{4}$ is two and $\frac{3}{4}$.

Practice 2: Convert 3 $\frac{2}{5}$ to an improper fraction

Count all the fifths

$$3 \times 5 = 15$$

$$15 + 2 = 17$$

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

The improper fraction is $\frac{17}{5}$.

Practice 3: Convert $\frac{23}{6}$ and check it

Use quotient and remainder

$$23 \div 6 = 3 \text{ remainder } 5$$

$$\frac{23}{6} = 3\frac{5}{6}$$

$$3 \times 6 + 5 = 23$$

The mixed number is three and $\frac{5}{6}$, and the reverse check works.

Watch out — easily mixed up

Follow the fraction path

Start with P3 equivalent fractions if renaming equal amounts is new. Next, use these mixed and improper forms in P4 fraction addition and subtraction.

Quick recap

🎯 Mastery check

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

1. Which mixed number is equal to $\frac{13}{5}$?

   2 $\frac{3}{5}$2 $\frac{2}{5}$3 $\frac{2}{5}$

2. What is 4 $\frac{1}{3}$ as an improper fraction?

   $\frac{12}{3}$$\frac{15}{3}$$\frac{13}{3}$

3. Which pair shows the same amount?

   $\frac{17}{4}$ and 3 $\frac{1}{4}$$\frac{17}{4}$ and 4 $\frac{1}{4}$$\frac{17}{4}$ and 4 $\frac{3}{4}$

4. A ribbon is $\frac{9}{2}$ metres long. What mixed number states its length?

   4 $\frac{2}{9}$ m3 $\frac{1}{2}$ m4 $\frac{1}{2}$ m

5. A recipe uses 2 $\frac{3}{8}$ cups of flour. Which improper fraction is equal?

   $\frac{17}{8}$$\frac{19}{8}$$\frac{21}{8}$

6. For $\frac{29}{7}$, what do the quotient and remainder tell you?

   4 wholes and $\frac{1}{7}$3 wholes and $\frac{1}{7}$4 wholes and $\frac{7}{7}$

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