GCSE Maths Starter 13
1. Write down the reciprocal of 3
2. Write 42 as a product of its prime factors
3. Find the perimeter and the shaded area of the
shape below.
4. Expand: 5a(3a+2)
5. 123 × 26
Lesson 13 Ratio
Mathswatch clip (61/94).
• To simplify a ratio (Grade D )
• To solve ratio problems using the unitary
method (Grade D)
I like simple
cakes
madeisonly
But now
my cake
4 : 2out
!!!of flour
and sugar . I mix it using a ratio of 2 : 1
Both
ratios
are equivalent.
But
the
cake
tastes
Two
goes
into
both
4
But
the
cake
will
notin
be
They
can
be
simplified
Repeat
the
process
exactly
the
same
!! the
and
2
big
enough
!
same way as fractions are
simplified.
Flour
2
2
4
:
::
1 Sugar
21
I’m going to try a cake using flour and
But now my cake has used a ratio of 4 : 6 !!!
sugar in a ratio of 2 : 3
But
will
be
But
2 :the
3thecake
iscake
a simplified
willnot
taste
Repeat
the
process.
Two
goes
into
44 and
big
enough
!: 6 !6
exactly
version
the
of same
Flour
2
24
:
3
63
Sugar
Lesson 13 Ratio
Mathswatch clip (61/94).
1)
4)
7)
10)
1:2
4:8
2:3
6:9
1:4
2:8
1:3
7 : 21
Write the following ratios in their simplest
form.
2:3
1:3
2)
8 : 12
3)
4 : 12
1:2
4:5
5)
10 : 20
6)
8 : 10
7:3
3:2
8)
14 : 6
9)
30 : 20
4 : 11
3:2
11)
8 : 22
12)
9:6
Lesson 13 Ratio
Mathswatch clip (61/94).
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.
Lesson 13 Ratio
Mathswatch clip (61/94).
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
Dividing in a given ratio
Divide £40 in the ratio 2 : 3.
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
We need to divide £40 by the total number of parts.
£40 ÷ 5 = £8
8 of 67
© Boardworks Ltd 2005
Dividing in a given ratio
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
9 of 67
© Boardworks Ltd 2005
Dividing in a given ratio
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?
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
10 of 67
© Boardworks Ltd 2005
Dividing in a given ratio
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?
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
11 of 67
© Boardworks Ltd 2005
Lesson 13 Ratio
Mathswatch clip (61/94).
Share in the given ratios
1. Share £400 between Courtney and Adele in the ratio 2:3
2. Share £280 between April and Jack in the ratio 2:5
3. Share £500 between Molly and Toni in the ratio 3:7
Extension work
1. Share £240 between Brad and Emma and Louis in the ratio
3:5:12
2. Share £600 between Kera, Chloe and Raven in the ratio 1:5:6
3. Share £5 between Jake, Adele and Lucretia in the ratio 7:10:8
Lesson 13 Ratio
Mathswatch clip (61/94).
Answers
1. Courtney = £160 and Adele = £240
2. April = £80 and Jack = £200
3. Molly =£150 and Toni = £350
Extension work
1. Brad = £36
Emma = £60
2. Kera = £50
Chloe = £250
3. Jake = £1.40 Adele = £2.00
£1.60
Louis = £144
Raven = £300
Lucretia =
Lesson 13 Ratio
Mathswatch clip (61/94).
Exam questions