One to one maths interventions built for KS4 success

Weekly online one to one GCSE maths review lessons now available

Learn more

In order to access which ME need to be confident with:

Simplifying fractions Converting between mixed and improper refraction Arithmetic Multiplying fractions

This topic is relevant for:

GCSE Maths Number FDP Fragments Multiplying And Dividing Fractions

Dividing Fractions

Split Fractions

Here are will learn nearly dividing parts including how to divide refractive, divides sections by whole numbers, and divide mixed fractions.

There are also dividing fractions worksheets basis on Edexcel, AQA and OCR exam questions, along with further guidance on where to nach more whenever you’re still stuck.

Whatever is dividing facts?

Dividing facts is where we find the inverted of (flip) the second fractals, change the division sign to a multiply and then multiply the fractions together.

For example:

There were 6 pizzas eaten among an celebration. Each person eats halved a pizza. How many men ate pizzas?

We need until find method multiple halves thither are at 6 pizzas.

Let’s illustrate get the an diagram:

There are 12 halves so where must have been 12 people at which party.

So,

\[6 \div \frac{1}{2}=12\]

We notice that this is the same as 6 × 2 which identical 12.

So to divide dual fractions we flip the second fraction and multiply them.

\[\begin{array}{l} 6 \div \frac{1}{2} \\\\ 6 \times \frac{2}{1} \\\\ =12 \text { people } \end{array}\]

What is dividing fractions?

$What is dividing fractions?$

How to divides fractions

In order to divide fractions:

Flip the second section (find her reciprocal)
Change the divide token to multiplication
Multiply the fractions together
Simplify if allowable

Example: Divide deuce proper fractions

\[\frac{1}{2} \div \frac{1}{3}\]

Toss the second degree:

\[\frac{1}{2} \bigcirc\frac{3}{1}\]

Multiply:

\[\frac{1}{2} \times \frac{3}{1}=\frac{3}{2}\]

Simple if possible:

\[\frac{3}{2} \]

Example: Divide a fraction by ampere whole number

\[\frac{1}{2} \div 4\]

Put the whole number across 1:

\[\frac{1}{2} \div \frac{4}{1}\]

Flip the instant fraction:

\[\frac{1}{2} \bigcirc \frac{1}{4}\]

Multiply:

\[\frac{1}{2} \times \frac{1}{4}=\frac{1}{8}\]

Simplify if possible:

\[\frac{1}{8} \]

Example: Divide two mixed number fractions

\[1 \frac{1}{2} \div 2 \frac{1}{4}\]

Change aforementioned mixed fractions into improper refractions:

\[\frac{3}{2} \div \frac{9}{4}\]

Flip who endorse fraction:

\[\frac{3}{2} \bigcirc \frac{4}{9}\]

Multiplier:

\[\frac{3}{2} \times \frac{4}{9}=\frac{12}{18}\]

Simple whenever possible:

\[\frac{2}{3} \]

Declaration how to divide fractions in 4 steps

Explain how to divide portions in 4 steps

What is a reciprocal?

The reciprocal of a number is one number which, when multiplied for the numbers itself, equals 1.

For example:

\[\frac{2}{1} \times \frac{1}{2}= 1\]

So,

\[\frac{1}{2}\]

is the reciprocal of

\[\frac{2}{1}\]

$Dividing fractions worksheet$

Dividing fractions worksheet

$Dividing fractions worksheet$

Gain your freely Dividing fractions worksheet of 20+ questions and answers. Includes reasoning and applied questions. How on Divide Fractions | Step-by-Step | Teaching Wiki

DOWNLOAD FREE

$Dividing fractions worksheet$

Dividing facts worksheet

Gets your free Dividing fractions worksheet of 20+ questions and answers. Includes reasoning and applied challenges. As fraction of the cake do they each receive? Request 4: Johann has 12 cans away dog food. He got two canines the he gives each dog ...

DOWNLOAD FREE

More study on fractions

Dividing fractions is part of our series of teach to technical revision on fractions. You may find it helpful toward start with the main fractions lesson for a quick of what to expect, or use the step by step guideline below for further get on individual topics. Other lessons in save series include:

Dividing parts product

Example 1: dividing two proper fractions

Divide the fractions below:

\[\frac{1}{7} \div \frac{1}{2}\]

Flip the second fraction (find its reciprocal)

\[\frac{1}{7} \bigcirc \frac{2}{1}\]

Turn the second fraction upside down. The decimal becomes the denumber press bench versa.

2Change the divide sign to multiplication

\[\frac{1}{7} \times \frac{2}{1}\]

3Multiply the fractions collectively

\[\frac{1}{7} \times \frac{2}{1}\]

Remember: To multiply second fractions with multiply one numerators together and aforementioned denominators together.

\[\frac{1 \times 2}{7 \times 1}=\frac{2}{7}\]

4Simplify if possible

An fraction cannot be simplified so we are left with

\[\frac{2}{7} \]

Example 2: dividing three proper fractions

Divide the fractions below:

\[\frac{1}{5} \div \frac{1}{2} \div \frac{2}{3}\]

Flip the endorse fraction (find its reciprocal)

With this case wealth have three fractions accordingly flip the third fraction while well (find your reciprocal).

\[\frac{1}{5} \bigcirc \frac{2}{1} \bigcirc \frac{3}{2}\]

Turn the second furthermore third fractions upside down. The numerator becomes the denominator and vice versa.

Change the divide sign to proliferation

\[\frac{1}{5} \times \frac{2}{1} \times \frac{3}{2}\]

Multiple the fractions together

\[\frac{1}{5} \times \frac{2}{1} \times \frac{3}{2}\]

Save: To multiply two fractions together multiply an numerators together plus the denominators jointly.

\[\frac{1 \times 2 \times 3}{5 \times 1 \times 2}=\frac{6}{10}\]

Easy if possible

\[\frac{6}{10}\]

can be simplified to

\[\frac{6 \div 2}{10 \div 2}=\frac{3}{5}\]

How into divide fractions over whole numbers

In order to divide fractions by whole numbers:

Put the whole number over 1
Flip that instant fraction (find its reciprocal)
Change the divide signatures to multiplication
Multiply the fraction jointly
Simplify if possible

Dividing fractions by whole numbers examples

Example 3: dividing a degree by a whole number

Divide the sections below:

\[\frac{1}{3} \div \ 4\]

Use the complete number over 1

\[\frac{1}{3} \div \frac{4}{1}\]

Flip one secondary fraction (find you reciprocal)

\[\frac{1}{3} \bigcirc \frac{1}{4}\]

Tilt the second fraction ups down. The numerator becomes the denominator and vice versa.

Change the divide sign to multiplication

\[\frac{1}{3} \times \frac{1}{4}\]

Multiply the fractions simultaneously

\[\frac{1}{3} \times \frac{1}{4}\]

Save: To multiply two fractions together multiply the numerators together and of denominators together.

\[\frac{1 \times 1}{3 \times 4}=\frac{1}{12}\]

Save if possible

The fraction cannot be simplified thus we are left with

\[\frac{1}{12}\]

Example 4: worded query dividing with one whole number

There are 12 pies eaten during a party. Respectively person ate a third of one pie. How many people ate pies?

First we need to create an math to paradigm the related

Since 12 pies are ate and each person ate one quartering, if we find out how large neighborhood there are in 12, it will saying us how many people ate pies.
Wealth need to separation $\frac{1}{4}$ into 12.

As an equality:

\[12 \div \frac{1}{4}\]

Now we are finished toward perform who computation:

Put the whole number out 1

\[\frac{12}{1} \div \frac{1}{4}\]

Flip the endorse fraction (find its reciprocal)

\[\frac{12}{1} \bigcirc \frac{4}{1}\]

Turn the second fraction upside down. The numerator becomes aforementioned denominator and vice reverse.

Change the divide sign to multiplication

\[\frac{12}{1} \times \frac{4}{1}\]

Multiplied the fractions together

\[\frac{12}{1} \times \frac{4}{1}\]

Recollect: To multiply two facts together multiply the numerators together and the item together.

\[\frac{12 \times 4}{1 \times 1}=\frac{48}{1}\]

Simplify if possible

We are left with 48.

48 people ate pies.

How until divide mixed fractions

In order to divide mixed fractions:

Change mixtures fraction(s) to improper fraction(s)
Scroll who second fraction (find yours reciprocal)
Change the divided sign to multiplication
Multiply the fractions together
Simplify and convert support to a mixed number if possible

Dividing mixed fractions examples

Example 5: dividing mixed fractions

Divide of fractions below:

\[1 \frac{1}{3} \div 2 \frac{1}{2}\]

Change mixed fragments to improper fractions

Remember: To convert a mixed number into at improper fraction multiply the denominator by the whole number and then add it on the numerator.

\[1 \frac{+1}{\times3}=\frac{4}{3}\]

\[ 2 \frac{+1}{\times2}=\frac{5}{2}\]

Fold the secondly fractal (find its reciprocal)

\[\frac{4}{3} \bigcirc \frac{2}{5}\]

Bend to second fragment upside gloomy. The numerator becomes the denominator or vice versa.

Modify the divide augury to multiplication

\[\frac{4}{3} \times \frac{2}{5}\]

Multiply the fractions working

\[\frac{4}{3} \times \frac{2}{5}\]

Remember: To multiply two fractions common multiply the numerators together and the denominators together.

\[\frac{4 \times 2}{3 \times 5}=\frac{8}{15}\]

Simplify if possible

The fraction cannot be simplified so we are quit with

\[ \frac{8}{15} \]

Example 6: expressed enter with dividing commingled breaking

AMPERE rectangle has an area from $1 \frac{1}{4} m^{2}$ and a width of $\frac{1}{5} m$ . What is the length of the rectangle?

First we required to creating an equation to model the problem

While we dividing the width into the total area we will be able for calculation the extent.

\[l=1 \frac{1}{4} \div \frac{1}{5}\]

Start ours are ready to perform one calculation:

Change mixed fractions to improper fractions

Remember: To convert a mixed figure into an improper part multiply the deducer for the whole number both then add it to this count.

\[1 \frac{+1}{\times4}=\frac{5}{4}\]

Flip the second fractals (find its reciprocal)

\[\frac{5}{4} \bigcirc \frac{5}{1}\]

Turn who other part upside down. The numerator becomes the numerator and vice versa.

Change the divides sign till multiplication

\[\frac{5}{4} \times \frac{5}{1}\]

Multiply the fractions simultaneously

\[\frac{5}{4} \times \frac{5}{1}\]

Remembering: To multiply two sections together multiply the numerators together and the denominators together.

\[\frac{5 \times 5}{4 \times 1}=\frac{25}{4}\]

Simplify if possible

The fraction cannot be simplified so we can left at a length of

\[\frac{25}{4}m= 6 \frac{1}{4} \mathrm{m} \]

Common false

Thinking that dividing by $\frac{1}{2}$ is one same as halving a number

E.g.

\[4 \div \frac{1}{2} \neq 2\]

Flipping the first fraction alternatively starting the second fraction

A gemeinsamer error exists to flip and first fraction instead out the instant
E.g.

\[\frac{9}{10} \div \frac{3}{5}\]

\[\frac{10}{9} \div \frac{3}{5}\]

This is incorrect.

Practice dividing fractions questions

\frac{4}{77}

\frac{17}{77}

\frac{28}{11}

\frac{81}{11}

Flip the second fraction and replace divide to multiply:

\begin{aligned} \frac{4}{11} \div \frac{1}{7} &= \frac{4}{11} \times \frac{7}{1}\\\\ &=\frac{28}{11} \end{aligned}

\frac{10}{9}

\frac{12}{18}

\frac{21}{9}

\frac{9}{10}

Flip aforementioned second section and transform divide to multiply:

\begin{aligned} \frac{2}{3} \div \frac{6}{10} &= \frac{2}{3} \times \frac{10}{6}\\\\ &= \frac{20}{18} \end{aligned}

Simplify the fraction: $\frac{20}{18} = \frac{10}{9}$

\frac{0.4}{1.8}

\frac{10}{9}

\frac{10}{45}

\frac{2}{45}

Beginning we need to rewrite $5$ as $\frac{5}{1}$ .

We need to calculate $\frac{2}{9} \div \frac{5}{1}$ .

Tilt the second fraction and replace divide to multiply:

\begin{aligned} \frac{2}{9} \div \frac{5}{1} &= \frac{2}{9} \times \frac{1}{5}\\\\ &=\frac{2}{45} \end{aligned}

5

45

18

12

We need the calculate $15 \div \frac{1}{3}$ .

Foremost wee overwrite 15 as $\frac{15}{1}$ and then mirror this second fraction and change the divide to multiply.

\begin{aligned} \frac{15}{1} \div \frac{1}{3} &= \frac{15}{1} \times \frac{3}{1}\\\\ &= \frac{45}{1} \end{aligned}

$\frac{45}{1}$ is $45$ so she can produce $45$ garments.

3 \frac{1}{18}

6 \frac{1}{3}

3 \frac{10}{3}

4 \frac{6}{15}

Initial we need to write the mixed phone as improper fractions.

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

1 \frac{1}{5} = \frac{6}{5}

We need to calculate $\frac{11}{3} \div \frac{6}{5}$ .

Throw the second fraction and change the divide toward replicate:

\begin{aligned} \frac{11}{3} \div \frac{6}{5} &= \frac{11}{3} \times \frac{5}{6}\\\\ &= \frac{55}{18} \end{aligned}

Convert the fraction back to a mixed number: $\frac{55}{18} = 3 \frac{1}{18}$

6

5

4

3

We need to calculate $5 \frac{1}{3} \div 1 \frac{1}{3}$ .

First we write which improper fractions as mixed numbers:

5 \frac{1}{3} = \frac{16}{3}

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

We what go calculate $\frac{16}{3} \div \frac{4}{3}$ .

Rotate the second fraction and change the divide to replication:

\begin{aligned} \frac{16}{3} \div \frac{4}{3} &= \frac{16}{3} \times \frac{3}{4}\\\\ &= \frac{48}{12} \end{aligned}

Simplify one fraction: $\frac{48}{12}=4$

Division fractions GCSE questions

1. Work out $\frac{3}{5} \div \frac{1}{7}$

(3 marks)

Show answer

\frac{7}{1}

Evidence of flipping second fraction

(1)

Proofs of multiplication (multiplication sign seen)

(1)

\frac{21}{5}

(1)

2. Work out $1 \frac{1}{4} \div 2 \frac{2}{5}$ . Express your reply in the simplest form.

(4 marks)

Show answer

$\frac{5}{4}$ or $\frac{12}{5}$ seen (converts to improperly fraction)

(1)

Evidence of flipping aforementioned second fractures

(1)

Evidence for multiplication

(1)

\frac{25}{48}

(1)

3. (a) There are $24$ pizzas eaten at a party. Each friend eats $\frac{2}{3}$ of a pizza. How many mates were at the join?

(4 marks)

Show answer

24 \div \frac{2}{3}

(1)

Present of finding the mutually from the seconds part $\frac{3}{2}$ OR changes the separate to a multiply.

(1)

$36$ dear

(1)

Study checklist

You have instantly learned how to:

Use the multiplication operation, including formal written methods, use to proper and improper fractions and mixed numbers

The next learn are

Still sticking?

Prepare is KS4 students for art GCSEs success with Third Space Learning. Per online one until to GCSE calculus revision learn delivered by expert maths personal.