Mastering Ratios: Share Amounts and Calculate Values
LO
: TBAT share amounts using a ratio.
By the end of the lesson
:
Be able to calculate how much one share of an amount
is worth given a ratio.
Be able to calculate how much one person would get of
an amount using a ratio.
Be able to calculate how much everybody gets of an
amount using a ratio.
Ratio
Ratio
Sharing
A packet contains 10 sweets.
What different ways could you share the
sweets among…..
CORE - 2 people?
CHALLENGE - 3 people?
SUPER CHALLENGE - 4 people?
What is a Ratio?
A
ratio
can be thought of as an
unfair
sharing
or unequal sharing
of an amount.
An example of a Ratio?
Imagine you had a bag of 10
sweets.
An example of a Ratio?
You
only like
the
lemon
flavoured
sweets
.
So you give your friend the
blackcurrant flavoured sweets.
What is a Ratio?
This is an example of a ratio.
You have
unfairly shared
your sweets.
You have had
7 sweets
, while your
friend has had
3 sweets
.
We can write this in maths as a ratio.
The Ratio
7 : 3
7 : 3
How the method works
Share
Share
25
25
sweets into a ratio of
sweets into a ratio of
2
2
:
:
3
3
1)
2
2
+
+
3
3
=
=
5
5
2)
25
25
÷
÷
5
5
=
=
5
5
3)
2
2
x
x
5
5
= 10
= 10
3
3
x
x
5
5
= 15
= 15
=
=
25
25
=
=
5
5
How the method works
Share
Share
45
45
sweets into a ratio of
sweets into a ratio of
5
5
:
:
4
4
1)
5
5
+
+
4
4
=
=
9
9
2)
45
45
÷
÷
9
9
=
=
5
5
3)
5
5
x
x
5
5
= 25
= 25
4
4
x
x
5
5
= 20
= 20
=
=
45
45
=
=
5
5
How the method works
Share
Share
36
36
sweets into a ratio of
sweets into a ratio of
1
1
:
:
5
5
1)
1
1
+
+
5
5
=
=
6
6
2)
36
36
÷
÷
6
6
=
=
6
6
3)
1
1
x
x
6
6
= 6
= 6
5
5
x
x
6
6
= 30
= 30
=36
=36
=
=
6
6
How the method works
Share
Share
20
20
sweets into a ratio of
sweets into a ratio of
1
1
:
:
3
3
1)
1
1
+
+
3
3
=
=
4
4
2)
20
20
÷
÷
4
4
=
=
5
5
3)
1
1
x
x
5
5
= 5
= 5
3
3
x
x
5
5
= 15
= 15
=20
=20
=
=
5
5
How the method works
Share
Share
72
72
sweets into a ratio of
sweets into a ratio of
5
5
:
:
3
3
1)
5
5
+
+
3
3
=
=
8
8
2)
72
72
÷
÷
8
8
=
=
9
9
3)
5
5
x
x
9
9
= 45
= 45
3
3
x
x
9
9
= 27
= 27
=72
=72
=
=
9
9
How the method works
Share
Share
48
48
sweets into a ratio of
sweets into a ratio of
3
3
:
:
1
1
1)
3
3
+
+
1
1
=
=
4
4
2)
48
48
÷
÷
4
4
=
=
12
12
3)
3
3
x
x
12
12
= 36
= 36
1
1
x
x
12
12
= 12
= 12
=48
=48
=
=
12
12
Slightly harder question
Alison and Henry shared some sweets in a ratio
Alison and Henry shared some sweets in a ratio
of
of
3
3
:
:
5
5
. Henry got 15 sweets as a result.
. Henry got 15 sweets as a result.
How many sweets were there to begin with?
How many sweets were there to begin with?
=15
=15
=
=
3
3
=
=
24
24
Just with numbers…….
The Method
The Method
Share
Share
10
10
sweets in a ratio of
sweets in a ratio of
7
7
:
:
3
3
1)
Add up the ratios.
Add up the ratios.
7
7
+
+
3
3
=
=
10
10
2)
Find one share. We divide our amount by
Find one share. We divide our amount by
the last answer.
the last answer.
10 ÷
10 ÷
10
10
=
=
1
1
3)
Multiply our ratios by this answer.
Multiply our ratios by this answer.
7
7
x
x
1
1
= 7
= 7
3
3
x
x
1
1
= 3
= 3
Example
Share
Share
20
20
sweets into a ratio of
sweets into a ratio of
3
3
:
:
2
2
1)
Add up the ratios.
Add up the ratios.
3
3
+
+
2
2
=
=
5
5
2)
Find one share. We divide our amount by
Find one share. We divide our amount by
the last answer.
the last answer.
20
20
÷
÷
5
5
=
=
4
4
3)
Multiply our ratios by this answer.
Multiply our ratios by this answer.
3
3
x
x
4
4
= 12
= 12
2
2
x
x
4
4
= 8
= 8
Your go……
Share
Share
30
30
sweets into a ratio of
sweets into a ratio of
4
4
:
:
1
1
1)
Add up the ratios.
Add up the ratios.
4
4
+
+
1
1
=
=
5
5
2)
Find one share. We divide our amount by
Find one share. We divide our amount by
the last answer.
the last answer.
30
30
÷
÷
5
5
=
=
6
6
3)
Multiply our ratios by this answer.
Multiply our ratios by this answer.
4
4
x
x
6
6
= 24
= 24
1
1
x
x
6
6
= 6
= 6
Your go……
Share
Share
45
45
sweets into a ratio of
sweets into a ratio of
5
5
:
:
4
4
1)
Add up the ratios.
Add up the ratios.
5
5
+
+
4
4
=
=
9
9
2)
Find one share. We divide our amount by
Find one share. We divide our amount by
the last answer.
the last answer.
45
45
÷
÷
9
9
=
=
5
5
3)
Multiply our ratios by this answer.
Multiply our ratios by this answer.
5
5
x
x
5
5
= 25
= 25
4
4
x
x
5
5
= 20
= 20
Your go……
Share
Share
24
24
sweets into a ratio of
sweets into a ratio of
2
2
:
:
1
1
1)
Add up the ratios.
Add up the ratios.
2
2
+
+
1
1
=
=
3
3
2)
Find one share. We divide our amount by
Find one share. We divide our amount by
the last answer.
the last answer.
24
24
÷
÷
3
3
=
=
8
8
3)
Multiply our ratios by this answer.
Multiply our ratios by this answer.
2
2
x
x
8
8
= 16
= 16
1
1
x
x
8
8
= 8
= 8
Questions
Answers
Which of these can you now do?
All
: will be able to calculate how much one share of an
amount is worth given a ratio.
Most
: will be able to calculate how much one person would
get of an amount using a ratio.
Some
: will be able to calculate how much everybody gets
of an amount using a ratio.
RATIO
SPOT THE MISTAKE
Share 48 sweets into a ratio of 4:2
Share 48 sweets into a ratio of 4:2
Step 1) 4 x 2 = 8
Step 1) 4 x 2 = 8
Step 2) 48 ÷ 8 = 6
Step 2) 48 ÷ 8 = 6
Step 3) 4 x 6 = 24
Step 3) 4 x 6 = 24
2 x 6 = 12
2 x 6 = 12
SPOT THE MISTAKE
Share 36 sweets into a ratio of 4:2
Share 36 sweets into a ratio of 4:2
Step 1) 4 + 2 = 6
Step 1) 4 + 2 = 6
Step 2) 36 ÷ 6 = 6
Step 2) 36 ÷ 6 = 6
Step 3) 4 x 6 = 24
Step 3) 4 x 6 = 24
24 x 6 = 144
24 x 6 = 144
•
Now rate yourself for this lesson/topic
using the following code:
•
U –
Little (unsatisfactory) effort!
•
S –
Some effort, still room for improvement!!
•
E –
Excellent effort!!!
•
Little understanding
•
Some understanding, not completely sure
•
Excellent understanding
LO
:
TBAT break down more complex ratio questions.
Starter
Calculate
Ratio
LO
:
TBAT break down more complex ratio questions.
Answers
Ratio
How the method works
Share
Share
45
45
sweets into a ratio of
sweets into a ratio of
5
5
:
:
4
4
1)
5
5
+
+
4
4
=
=
9
9
2)
45
45
÷
÷
9
9
=
=
5
5
3)
5
5
x
x
5
5
= 25
= 25
4
4
x
x
5
5
= 20
= 20
=
=
45
45
=
=
5
5
How the method works
Share
Share
36
36
sweets into a ratio of
sweets into a ratio of
1
1
:
:
5
5
1)
1
1
+
+
5
5
=
=
6
6
2)
36
36
÷
÷
6
6
=
=
6
6
3)
1
1
x
x
6
6
= 6
= 6
5
5
x
x
6
6
= 30
= 30
=36
=36
=
=
6
6
How the method worked
Share
Share
45
45
sweets into a ratio of
sweets into a ratio of
5
5
:
:
4
4
1)
5
5
+
+
4
4
=
=
9
9
2)
45
45
÷
÷
9
9
=
=
5
5
3)
5
5
x
x
5
5
= 25
= 25
4
4
x
x
5
5
= 20
= 20
=
=
45
45
=
=
5
5
Slightly harder question
Alison and Henry shared some sweets in a ratio
Alison and Henry shared some sweets in a ratio
of
of
3
3
:
:
5
5
. Henry got 15 sweets as a result.
. Henry got 15 sweets as a result.
How many sweets were there to begin with?
How many sweets were there to begin with?
=15
=15
=
=
3
3
=
=
24
24
Example
Two people shared some money in a ratio of
Two people shared some money in a ratio of
4
4
:
:
7
7
.
.
The first person got £16 as a result.
The first person got £16 as a result.
How much money did they share?
How much money did they share?
=£16
=£16
=£4
=£4
=
=
11 x £4 = £44
11 x £4 = £44
Question
Two people shared some money in a ratio of
Two people shared some money in a ratio of
3
3
:
:
5
5
.
.
The first person got £24.
The first person got £24.
How much did they share in total?
How much did they share in total?
=£24
=£24
=£8
=£8
=
=
8 x £8 = £64
8 x £8 = £64
Question
Two people shared some money in a ratio of
Two people shared some money in a ratio of
7
7
:
:
5
5
.
.
The second person got £25 as a result.
The second person got £25 as a result.
How much money did they share?
How much money did they share?
=£25
=£25
=£5
=£5
=
=
12 x £5 = £60
12 x £5 = £60
Question
Three people shared some money in a ratio of
Three people shared some money in a ratio of
4
4
:
:
3:
3:
5
5
. The second person got £21 as a result.
. The second person got £21 as a result.
How much money did they share?
How much money did they share?
=£21
=£21
=£7
=£7
=
=
12 x £7 = £84
12 x £7 = £84
Questions
Bronze
Bill and Jane share some money in the ratio of 3:4.
Bill gets £21, how much does Jane get?
=£21
=£21
=£7
=£7
= 4 x £7
= 4 x £7
= £28
= £28
Silver
Noah, Ben and Jen share some Easter eggs in the ratio
2:5:7, Ben gets 60, how many do Noah and Jen get?
=£60
=£60
= £60 ÷ 5
= £60 ÷ 5
= £12
= £12
= 2 x £12
= 2 x £12
= £24
= £24
= 7 x £12
= 7 x £12
= £84
= £84
Gold
Kyle, Geri & Mo buy a bag of sweets. The bag contains 60
sweets.
Geri gets double Kyle’s amount. Mo gets the same as Geri.
How many sweets do they get each?
=60
=60
= 60 ÷ 5
= 60 ÷ 5
= 12
= 12
G
G
eri gets
eri gets
= 2 x 12
= 2 x 12
= 24
= 24
Mo gets
Mo gets
= 2 x 12
= 2 x 12
= 24
= 24
Questions
Bronze
Benny and Carl share some money in the ratio of 3:5,
Benny gets £36, how much does Carl get?
=£
=£
36
36
=£36÷3
=£36÷3
=£12
=£12
= 4 x £12
= 4 x £12
= £48
= £48
Silver
Nigel, Frankie and Sara share some chocolate buttons
in the ratio 3:5:1, Frankie gets 75, how many do Nigel
and Sara get?
=£75
=£75
= £
= £
75
75
÷5
÷5
=£15
=£15
= 4 x £15
= 4 x £15
= £60
= £60
Gold
Hal, Ori & Perri buy a bag of sweets. The bag contains 68
sweets.
Perri gets double Ori’s amount. Hal gets half as much as Perri.
How many sweets do they get each?
=68
=68
= 68 ÷ 4
= 68 ÷ 4
= 17
= 17
P
P
erri gets
erri gets
= 2 x 17
= 2 x 17
= 34
= 34
Hal
Hal
gets
gets
= 1 x 17
= 1 x 17
= 17
= 17
GCSE Questions
•
Attempt the past paper questions.
•
Now rate yourself for this lesson/topic
using the following code:
•
U –
Little (unsatisfactory) effort!
•
S –
Some effort, still room for improvement!!
•
E –
Excellent effort!!!
•
Little understanding
•
Some understanding, not completely sure
•
Excellent understanding
Explore the concept of ratios through practical examples of sharing sweets among different numbers of people. Learn how to calculate the worth of one share, determine individual shares, and distribute amounts fairly using ratios. Discover the methods of dividing sweets into ratios and understand the unequal sharing of quantities.
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Presentation Transcript
Ratio LO: TBAT share amounts using a ratio. By the end of the lesson: Be able to calculate how much one share of an amount is worth given a ratio. Be able to calculate how much one person would get of an amount using a ratio. Be able to calculate how much everybody gets of an amount using a ratio.
Sharing A packet contains 10 sweets. What different ways could you share the sweets among .. CORE - 2 people? CHALLENGE - 3 people? SUPER CHALLENGE - 4 people?
What is a Ratio? A ratio can be thought of as an unfair sharing or unequal sharing of an amount.
An example of a Ratio? Imagine you had a bag of 10 sweets.
An example of a Ratio? You only like the lemon flavoured sweets. So you give your friend the blackcurrant flavoured sweets.
What is a Ratio? This is an example of a ratio. You have unfairly shared your sweets. You have had 7 sweets, while your friend has had 3 sweets. We can write this in maths as a ratio.
The Ratio 7 : 3
How the method works Share 25 sweets into a ratio of 2:3 =25 =5 2 + 3 = 5 25 5 = 5 2 x 5 = 10 3 x 5 = 15 1) 2) 3)
How the method works Share 45 sweets into a ratio of 5:4 =45 =5 5 + 4 = 9 45 9 = 5 5 x 5 = 25 4 x 5 = 20 1) 2) 3)
How the method works Share 36 sweets into a ratio of 1:5 =36 =6 1 + 5 = 6 36 6 = 6 1 x 6 = 6 5 x 6 = 30 1) 2) 3)
How the method works Share 20 sweets into a ratio of 1:3 =20 =5 1 + 3 = 4 20 4 = 5 1 x 5 = 5 3 x 5 = 15 1) 2) 3)
How the method works Share 72 sweets into a ratio of 5:3 =72 =9 5 + 3 = 8 72 8 = 9 5 x 9 = 45 3 x 9 = 27 1) 2) 3)
How the method works Share 48 sweets into a ratio of 3:1 =48 =12 3 + 1 = 4 48 4 = 12 3 x 12 = 36 1 x 12 = 12 1) 2) 3)
Just with numbers. The Method Share 10 sweets in a ratio of 7:3 1) Add up the ratios. 7 + 3 = 10 2) Find one share. We divide our amount by the last answer. 10 10 = 1 3) Multiply our ratios by this answer. 7 x 1 = 7 3 x 1 = 3
Example Share 20 sweets into a ratio of 3:2 1) Add up the ratios. 3 + 2 = 5 2) Find one share. We divide our amount by the last answer. 20 5 = 4 3) Multiply our ratios by this answer. 3 x 4 = 12 2 x 4 = 8
Your go Share 30 sweets into a ratio of 4:1 1) Add up the ratios. 4 + 1 = 5 2) Find one share. We divide our amount by the last answer. 30 5 = 6 3) Multiply our ratios by this answer. 4 x 6 = 24 1 x 6 = 6
Your go Share 45 sweets into a ratio of 5:4 1) Add up the ratios. 5 + 4 = 9 2) Find one share. We divide our amount by the last answer. 45 9 = 5 3) Multiply our ratios by this answer. 5 x 5 = 25 4 x 5 = 20
Your go Share 24 sweets into a ratio of 2:1 1) Add up the ratios. 2 + 1 = 3 2) Find one share. We divide our amount by the last answer. 24 3 = 8 3) Multiply our ratios by this answer. 2 x 8 = 16 1 x 8 = 8
Questions Bronze Silver Gold Share 24into the following ratios: Share 36 into the following ratios: Share 48cminto the following ratios: a) 2:1 2:1 4:2 b) 3:1 3:1 3:5 c) 5:1 1:5 1:7 d) 2:4 7:5 1:5:6
Answers Bronze Silver Gold Share 24 into the following ratios Share 36 into the following ratios Share 48cm into the following ratios 16:8 24: 12 32cm:16cm 18:6 27: 9 18cm:30cm 20:4 6: 30 6cm:42cm 8:16 21: 15 4cm:20cm:24cm
RATIO Which of these can you now do? All: will be able to calculate how much one share of an amount is worth given a ratio. Most: will be able to calculate how much one person would get of an amount using a ratio. Some: will be able to calculate how much everybody gets of an amount using a ratio.
SPOT THE MISTAKE Share 48 sweets into a ratio of 4:2 Step 1) 4 x 2 = 8 Step 2) 48 8 = 6 Step 3) 4 x 6 = 24 2 x 6 = 12
SPOT THE MISTAKE Share 36 sweets into a ratio of 4:2 Step 1) 4 + 2 = 6 Step 2) 36 6 = 6 Step 3) 4 x 6 = 24 24 x 6 = 144
Self Evaluation Now rate yourself for this lesson/topic using the following code: U Little (unsatisfactory) effort! S Some effort, still room for improvement!! E Excellent effort!!! Little understanding Some understanding, not completely sure Excellent understanding
Ratio LO: TBAT break down more complex ratio questions. Starter Calculate 27 x 3 273 x 34 72 4 436 4 23 23 + 32 (2 + 3)2 + 7 x 2 8 2 x 3
Ratio LO: TBAT break down more complex ratio questions. Answers 27 x 3 = 81 273 x 34 = 9282 72 4 = 18 436 4 = 109 23 = 2 x 2 x 2 = 8 23 + 32 = 17 (2 + 3)2 + 7 x 2 = 39 8 2 x 3 = 2
How the method works Share 36 sweets into a ratio of 1:5 1) 1 + 5 = 6 2) 36 6 = 6 3) 1 x 6 = 6 5 x 6 = 30 =36 =6
How the method worked Share 45 sweets into a ratio of 5:4 1) 5 + 4 = 9 2) 45 9 = 5 3) 5 x 5 = 25 4 x 5 = 20 =45 =5
Slightly harder question Alison and Henry shared some sweets in a ratio of 3:5. Henry got 15 sweets as a result. How many sweets were there to begin with? =24 =15 =3
Example Two people shared some money in a ratio of 4:7. The first person got 16 as a result. How much money did they share? =11 x 4 = 44 = 16 = 4
Question Two people shared some money in a ratio of 3:5. The first person got 24. How much did they share in total? =8 x 8 = 64 = 24 = 8
Question Two people shared some money in a ratio of 7:5. The second person got 25 as a result. How much money did they share? =12 x 5 = 60 = 25 = 5
Question Three people shared some money in a ratio of 4:3:5. The second person got 21 as a result. How much money did they share? =12 x 7 = 84 = 21 = 7
Questions Bill and Jane share some money in the ratio of 3:4, Bill gets 21, how much does Jane get? Bronze Noah, Ben and Jen share some Easter eggs in the ratio 2:5:7, Ben gets 60, how many do Noah and Jen get? Silver Kyle, Geri & Mo buy a bag of sweets. The bag contains 60 sweets. Geri gets double Kyle s amount. Mo gets the same as Geri. How many sweets do they get each? Gold
Bronze Bill and Jane share some money in the ratio of 3:4. Bill gets 21, how much does Jane get? = 21 = 7 = 4 x 7 = 28
Silver Noah, Ben and Jen share some Easter eggs in the ratio 2:5:7, Ben gets 60, how many do Noah and Jen get? = 60 = 60 5 = 12 = 2 x 12 = 24 = 7 x 12 = 84
Gold Kyle, Geri & Mo buy a bag of sweets. The bag contains 60 sweets. Geri gets double Kyle s amount. Mo gets the same as Geri. How many sweets do they get each? =60 Kyle Jerri = 60 5 = 12 Jerri Geri gets = 2 x 12 = 24 Mo gets = 2 x 12 = 24 Mo Mo
Questions Benny and Carl share some money in the ratio of 3:5, Benny gets 36, how much does Carl get? Bronze Nigel, Frankie and Sara share some chocolate buttons in the ratio 3:5:1, Frankie gets 75, how many do Nigel and Sara get? Silver Hal, Ori & Perri buy a bag of sweets. The bag contains 68 sweets. Perri gets double Ori s amount. Hal gets half as much as Perri. How many sweets do they get each? Gold
Bronze Benny and Carl share some money in the ratio of 3:5, Benny gets 36, how much does Carl get? = 36 = 36 3 = 12 = 4 x 12 = 48
Silver Nigel, Frankie and Sara share some chocolate buttons in the ratio 3:5:1, Frankie gets 75, how many do Nigel and Sara get? = 75 = 75 5 = 15 = 4 x 15 = 60
Gold Hal, Ori & Perri buy a bag of sweets. The bag contains 68 sweets. Perri gets double Ori s amount. Hal gets half as much as Perri. How many sweets do they get each? =68 Ori Perri = 68 4 = 17 Perri Perri gets = 2 x 17 = 34 Hal gets = 1 x 17 = 17 Hal
GCSE Questions Attempt the past paper questions.
Self Evaluation Now rate yourself for this lesson/topic using the following code: U Little (unsatisfactory) effort! S Some effort, still room for improvement!! E Excellent effort!!! Little understanding Some understanding, not completely sure Excellent understanding
