 Convert Between Improper Fractions and Mixed Numbers | KS3 Maths

## What you need to know

Things to remember:

• To convert an improper fraction into a mixed number you divide it as usual.
• The whole number part of the division is the whole of the mixed number.
• The remainder goes on top of the fraction.
• To convert a mixed number into an improper fraction, you multiply the whole number by the denominator, and add it to the numerator.
• To add fractions, the denominators need to be the same. If the fractions have different denominators, we look for a common multiple of these and look for equivalent fractions.

Mixed Numbers to Improper Fractions

Convert $3\dfrac{2}{6}$ into an improper fraction.

Step 1: Multiply the whole number by the bottom of the fraction

$$3\times6=18$$

Step 2: Add the number in Step 1 to the top of the fraction

$$18+2=20$$

Step 3: Put the number in Step 2 over the bottom of the fraction.

$$3\frac{2}{6}=\frac{20}{6}$$

Improper Fractions to Mixed Numbers

Convert $\dfrac{49}{9}$ into a mixed number.

Step 1: Do the division to find the whole number and the remainder.

$$\frac{49}{9}=49\div9=5\text{ remainder }4$$

Whole = 5

Remained = 4

Step 2: Put the remainder over the fraction.

$$\frac{4}{9}$$

Step 3: Put the whole number from Step 1 and the fraction from Step 2 together.

$$\frac{49}{9}=5\frac{4}{9}$$

Questions won’t always tell you that you have to convert, so we need to see when we have to.

When we’re adding or subtracting mixed and improper fractions, we can do them in three steps.

Step 1: Write the mixed number as an improper fraction.

Step 2: Make the denominators the of the two fractions the same.

– We need to do this because denominators have to be the same when adding or subtracting fracitons.

Step 3: Add or subtract the fractions.

Step 4: Convert to a mixed number if required.

Adding mixed numbers and improper fractions.

Write $3\dfrac{2}{7}+\dfrac{5}{4}$ as a single mixed number

Step 1: Write the mixed number as an improper fraction.

Hint: Remember, to convert a mixed number into an improper fraction, we multiply the whole number by the denominator and add it to the numerator.

$$3\times7=21$$

$$21+3=24$$

$$\frac{24}{7}$$

Step 2: Make the denominators the of the two fractions the same.

Hint: We can make the denominators the same by looking for a common multiple, this is often easiest by just multiplying them together.

$$\frac{24}{7}=\frac{24\times4}{7\times4}=\frac{96}{28}$$

$$\frac{5}{4}=\frac{5\times7}{4\times7}=\frac{35}{28}$$

Step 3: Add or subtract the fractions.

We are adding the fractions here.

$$\frac{96}{28} +\frac{35}{28}=\frac{131}{28}$$

Step 4: Convert to a mixed number if required.

$$\frac{131}{28}=4\frac{19}{28}$$

Subtracting Mixed Numbers and Improper Fractions

Find the value of $2\dfrac{3}{5}-\dfrac{13}{6}$

Step 1: Write the mixed number as an improper fraction.

Hint: Remember, to convert a mixed number into an improper fraction, we multiply the whole number by the denominator and add it to the numerator.

$$2\times5=10$$

$$10+3=13$$

$$\frac{13}{5}$$

Step 2: Make the denominators the of the two fractions the same.

$$\frac{13}{5}=\frac{13\times6}{5\times6}=\frac{78}{30}$$

$$\frac{13}{6}=\frac{13\times5}{6\times5}=\frac{65}{28}$$

Step 3: Add or subtract the fractions.

$$\frac{78}{30}-\frac{65}{30}=\frac{13}{30}$$

Step 4: Convert to a mixed number if required.

When multiplying or dividing mixed numbers and improper fractions we can do them in three steps

Step 1: Write the mixed number as an improper fraction.

Step 2: Multiply or divide the fractions.

Step 3: Convert to a mixed number if required.

Write $5\dfrac{2}{3}\times\dfrac{9}{4}$ as a single mixed number

Step 1: Write the mixed number as an improper fraction.

$$5\times3=15$$

$$15+2=17$$

$$\frac{17}{3}$$

Step 2: Multiply or divide the fractions.

Remember, we are multiplying here

$$\frac{17}{3}\times\frac{9}{4}=\frac{17\times9}{3\times4}=\frac{153}{12}=\frac{51}{4}$$

Step 3: Convert to a mixed number if required.

$$\frac{51}{4}=12\frac{3}{4}$$

Find the value of $4\dfrac{2}{7}\div\dfrac{5}{3}$

Step 1: Write the mixed number as an improper fraction.

$$4\times7=28$$

$$28+2=30$$

$$\frac{30}{7}$$

Step 2: Multiply or divide the fractions.

To divide we have to flip the second fraction and turn it into a multiplication question.

$$\frac{30}{7}\div\frac{5}{3}=\frac{30}{7}\times\frac{3}{5}=\frac{90}{35}=\frac{18}{7}$$

## Example Questions

Step 1: Write the mixed number as an improper fraction.

Hint: Remember, to convert a mixed number into an improper fraction, we multiply the whole number by the denominator and add it to the numerator.

$$3\times8=24$$

$$24+7=31$$

$$\frac{21}{8}$$

Step 2: Make the denominators the of the two fractions the same.

$$\frac{31}{8}=\frac{31\times5}{8\times5}=\frac{155}{40}$$

$$\frac{27}{5}=\frac{27\times8}{5\times8}=\frac{216}{40}$$

Step 3: Add or subtract the fractions.

$$\frac{155}{40}-\frac{216}{40}=\frac{-61}{40}=-\frac{61}{40}$$

Step 1: Write the mixed number as an improper fraction.

$$5\times9=45$$

$$45+4=49$$

$$\frac{49}{9}$$

Step 2: Multiply or divide the fractions.

$$\frac{49}{9}\times\frac{13}{3}=\frac{637}{27}$$

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