GCSE Maths Starter 13

GCSE Maths Starter 131. Write down the reciprocal of 32. Write 42 as a product of its prime factors3. Find the perimeter and the shaded area of the

shape below.

4. Expand: 5a(3a+2)

Lesson 13 RatioMathswatch clip (61/94).

• To simplify a ratio (Grade D )• To solve ratio problems using the unitary

method (Grade D)

Flour Sugar

I like simple cakes made only out of flour and sugar . I mix it using a ratio of 2 : 1

2 1:

But the cake will not be big enough !

Repeat the process !

But now my cake is 4 : 2 !!!

4:

: 2

But the cake tastes exactly the same !

Both ratios are equivalent. They can be simplified in the

same way as fractions are simplified.

Two goes into both 4 and 2

21

Flour Sugar

I’m going to try a cake using flour and sugar in a ratio of 2 : 3

2 3:

But the cake will not be big enough !

Repeat the process.

But now my cake has used a ratio of 4 : 6 !!!

4 6

But the cake will taste exactly the same !Two goes into 4 and 6

2 3

2 : 3 is a simplified version of 4 : 6

Write the following ratios in their simplest form.

1) 4 : 8 2) 8 : 12 3) 4 : 124) 6 : 9 5) 10 : 20 6) 8 : 107) 2 : 8 8) 14 : 6 9) 30 : 2010) 7 : 21 11) 8 : 22 12) 9 : 6

1 : 2 2 : 3 1 : 3

2 : 3 1 : 2 4 : 5

1 : 4 7 : 3 3 : 2

1 : 3 4 : 11 3 : 2


1. Helen has 16 DVDs and 24 videos.Write down the ratio of the number of DVDs to the number of

videos.Give your ratio in its simplest form.

2. There are 40 students on a school trip.12 of the students are girls.The rest are boys.Find the ratio of the number of girls to the number of boys.Give your ratio in its simplest form.

3. There are 50 sweets in a packet.24 of the sweets are mints.The rest of the sweets are toffees. Write down the ratio of the number of mints to the number of toffees.Give your ratio in its simplest form.


1. Helen has 16 DVDs and 24 videos.Write down the ratio of the number of DVDs to the number of

videos.Give your ratio in its simplest form. 16:24 = 2:3

2. There are 40 students on a school trip.12 of the students are girls.The rest are boys.Find the ratio of the number of girls to the number of boys.Give your ratio in its simplest form. 12:28 = 3:7

3. There are 50 sweets in a packet.24 of the sweets are mints.The rest of the sweets are toffees. Write down the ratio of the number of mints to the number of toffees.Give your ratio in its simplest form. 24:26 = 12:13


© Boardworks Ltd 2005 8 of 67

Dividing in a given ratio

A ratio is made up of parts.

We can write the ratio 2 : 3 as

2 parts : 3 parts

The total number of parts is

2 parts + 3 parts = 5 parts

Divide £40 in the ratio 2 : 3.

£40 ÷ 5 = £8

We need to divide £40 by the total number of parts.



Divide £40 in the ratio 2 : 3.

Each part is worth £8 so

2 parts = 2 × £8 = £16

and 3 parts = 3 × £8 = £24

£40 divided in the ratio 2 : 3 is

£16 : £24

Always check that the parts add up to the original amount.

£16 + £24 = £40



A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1.

First, find the total number of parts in the ratio.

6 parts + 3 parts + 1 part = 10 parts

Next, divide 750 ml by the total number of parts.

750 ml ÷ 10 = 75 ml

How much of each type of juice is contained in 750 ml of the cocktail?



Each part is worth 75 ml so,

6 parts of orange juice = 6 × 75 ml = 450 ml

3 parts of lemon juice = 3 × 75 ml = 225 ml

1 part of lime juice = 75 ml

Check that the parts add up to 750 ml.

450 ml + 225 ml + 75 ml = 750 ml

A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1.

How much of each type of juice is contained in 750 ml of the cocktail?

Share in the given ratios1. Share £400 between Courtney and Adele in the ratio 2:32. Share £280 between April and Jack in the ratio 2:53. Share £500 between Molly and Toni in the ratio 3:7

Extension work4. Share £240 between Brad and Emma and Louis in the ratio

3:5:125. Share £600 between Kera, Chloe and Raven in the ratio

1:5:66. Share £5 between Jake, Adele and Lucretia in the ratio

7:10:8


Answers1. Courtney = £160 and Adele = £2402. April = £80 and Jack = £2003. Molly =£150 and Toni = £350

Extension work4. Brad = £36 Emma = £60 Louis = £1445. Kera = £50 Chloe = £250 Raven =

£3006. Jake = £1.40 Adele = £2.00 Lucretia =

£1.60


Exam questions


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GCSE Maths Starter 13