Converting between Fractions, Decimals and Percentages
Lesson 1: An Introduction
Learning Objective
To identify and develop an understanding of simple equivalent fractions, decimals and percentages.
Targeting Assessment Objectives A01
Success Criteria
- To recap core skills needed to convert fractions, decimals and percentages.
- To use a 100 square to identify simple equivalents.
- To design a park which shows simple fraction, decimal and percentage equivalents.
Unscramble
Can you unscramble the letters to spell out some of the keywords for today’s lesson?
L D I M C E A
DECIMAL
E C A N G R P T E E
PERCENTAGE
A C O N I R F T
FRACTION
V E U Q I L A N C E E
EQUIVALENCE
V I E D D I
DIVIDE
U I P M Y T L L
MULTIPLY
Extension: Try writing an example or definition for each word.
Did Someone Say ‘Pizza’?
Two friends decide to buy a pizza and they see these offers:
Buy one pizza and get 35% !
Buy one pizza and get !
extra free
extra free
Assuming each pizza is the same base price, which offer is the best and why? Discuss with a partner.
Did Someone Say ‘Pizza’?
Which is the best offer? In fact, neither offer is the best: they are equivalent! It is useful to know how to convert between fractions, decimals and percentages so we can compare them. To ‘convert’ a value, we change it from one system of units to another whilst remaining equivalent. For example, 50% is equivalent to 0.50 or . This is similar to when you exchange currency. For example, you will be given the equivalent value of British pounds in US dollars.
Buy one pizza and get 35% !
extra free
Buy one pizza and get !
extra free
Pause for Thought What do we mean by ‘convert’?
Maths Skills Toolbox
These is a set of skills which we need to recap on to help us convert confidently between fractions, decimals and percentages.
You need to be able to:
- Use the bus stop method for dividing.
- Multiply integers and decimals by 100 without a calculator.
- Divide integers by 100 without a calculator.
- Simplify fractions.
- Use a 100 square to convert fractions, decimals and percentages.
Bus Stop Method
125 5 =
25
Step 1 Set up your bus stop. Remember: the first number goes inside the bus stop and what you’re dividing by goes on the outside.
Step 2 1 ÷ 5 or, in other words, how many 5s go into 1? The answer is 0. So write 0 above the line and carry your 1 over to the 2 to make 12.
Step 3 12 ÷ 5 or, in other words, how many 5s go into 12? The answer is 2, with a remainder of 2. So write 2 above the line and carry the remainder over to the 5.
Step 4 25 ÷ 5 or, in other words, how many 5s go into 25? The answer is 5.
1 2 5
Bus Stop Method
227 4 =
56.75
Step 1 Set up your bus stop. Remember: the first number goes inside the bus stop and what you’re dividing by goes on the outside.
Step 2 2 ÷ 4 or, in other words, how many 4s go into 2? The answer is 0. So write 0 above the line and carry your 2 over to the 2 to make 22.
Step 3 22 ÷ 4 or, in other words, how many 4s go into 22? The answer is 5, with a remainder of 2. So write 5 above the line and carry the remainder over to the 7.
Step 4 27 ÷ 4 or, in other words, how many 4s go into 27? The answer is 6 with a remainder of 3.
2 2 7
Pause for Thought What do we do now?
Dividing Using the Bus Stop Method
Now have a go at the following questions:
- 455 ÷ 5
- 204 ÷ 4
- 329 ÷ 5
- 191 ÷ 2
- 794 ÷ 8
= 91
= 51
= 65.8
= 95.5
= 99.25
Multiplying Numbers by 100
When we multiply a number by 100, we move the digits of the number two places to the left.
42.9 × 100
= 4290
We must make sure we add in the zero to the units column as a placeholder.
Dividing Numbers by 100
When we divide a number by 100, we move the digits of the number two places to the right.
73.2 ÷ 100
= 0.732
We must make sure we add in the zero to the units column as a placeholder.
Your Turn
Now have a go at the following questions:
- 0.45 × 100
- 792 ÷ 100
- 101.3 ÷ 100
- 0.057 × 100
- 1.24 ÷ 100
= 45
= 7.92
= 1.013
= 5.7
= 0.0124
Simplifying Fractions
To simplify a fraction, we must find the highest common factor between its numerator and its denominator. Remember: ‘common’ means that the same integer must divide into the top and the bottom. For example: Write in its simplest terms. 5 would be the highest common factor of 55 and 100.
÷ 5
÷ 5
Your Turn
Now have a go at the following questions:
-
-
-
-
-
Using a Hundred Square
We can use a 100 square to help us convert between fractions, decimals and percentages. Using your squares, fill in the following table.
45%
56%
0.56
0.73
20%
0.01
Design a Park
Your task is to design a park. You can colour in the squares to represent what you have included. For example, you could colour the squares in green to represent trees or blue to represent water, or even colour in the squares grey to indicate a skate-park. All you need to do is include a key and complete the fractions, decimal and percentages equivalence table to indicate the proportion of each item.
Reflection
Go back to the Maths Skills Toolbox.
- Which skills have you mastered today? Convince me you have mastered them.
- Which skills do you still need to practise?
- What is your target for next lesson?
You need to be able to:
- Use the bus stop method for dividing.
- Multiply integers and decimals by 100 without a calculator.
- Divide integers by 100 without a calculator.
- Simplify fractions.
- Use a 100 square to convert fractions, decimals and percentages.
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Transcript
Converting between Fractions, Decimals and Percentages
Lesson 1: An Introduction
Learning Objective
To identify and develop an understanding of simple equivalent fractions, decimals and percentages.
Targeting Assessment Objectives A01
Success Criteria
Unscramble
Can you unscramble the letters to spell out some of the keywords for today’s lesson?
L D I M C E A
DECIMAL
E C A N G R P T E E
PERCENTAGE
A C O N I R F T
FRACTION
V E U Q I L A N C E E
EQUIVALENCE
V I E D D I
DIVIDE
U I P M Y T L L
MULTIPLY
Extension: Try writing an example or definition for each word.
Did Someone Say ‘Pizza’?
Two friends decide to buy a pizza and they see these offers:
Buy one pizza and get 35% !
Buy one pizza and get !
extra free
extra free
Assuming each pizza is the same base price, which offer is the best and why? Discuss with a partner.
Did Someone Say ‘Pizza’?
Which is the best offer? In fact, neither offer is the best: they are equivalent! It is useful to know how to convert between fractions, decimals and percentages so we can compare them. To ‘convert’ a value, we change it from one system of units to another whilst remaining equivalent. For example, 50% is equivalent to 0.50 or . This is similar to when you exchange currency. For example, you will be given the equivalent value of British pounds in US dollars.
Buy one pizza and get 35% !
extra free
Buy one pizza and get !
extra free
Pause for Thought What do we mean by ‘convert’?
Maths Skills Toolbox
These is a set of skills which we need to recap on to help us convert confidently between fractions, decimals and percentages.
You need to be able to:
Bus Stop Method
125 5 =
25
Step 1 Set up your bus stop. Remember: the first number goes inside the bus stop and what you’re dividing by goes on the outside.
Step 2 1 ÷ 5 or, in other words, how many 5s go into 1? The answer is 0. So write 0 above the line and carry your 1 over to the 2 to make 12.
Step 3 12 ÷ 5 or, in other words, how many 5s go into 12? The answer is 2, with a remainder of 2. So write 2 above the line and carry the remainder over to the 5.
Step 4 25 ÷ 5 or, in other words, how many 5s go into 25? The answer is 5.
1 2 5
Bus Stop Method
227 4 =
56.75
Step 1 Set up your bus stop. Remember: the first number goes inside the bus stop and what you’re dividing by goes on the outside.
Step 2 2 ÷ 4 or, in other words, how many 4s go into 2? The answer is 0. So write 0 above the line and carry your 2 over to the 2 to make 22.
Step 3 22 ÷ 4 or, in other words, how many 4s go into 22? The answer is 5, with a remainder of 2. So write 5 above the line and carry the remainder over to the 7.
Step 4 27 ÷ 4 or, in other words, how many 4s go into 27? The answer is 6 with a remainder of 3.
2 2 7
Pause for Thought What do we do now?
Dividing Using the Bus Stop Method
Now have a go at the following questions:
= 91
= 51
= 65.8
= 95.5
= 99.25
Multiplying Numbers by 100
When we multiply a number by 100, we move the digits of the number two places to the left.
42.9 × 100
= 4290
We must make sure we add in the zero to the units column as a placeholder.
Dividing Numbers by 100
When we divide a number by 100, we move the digits of the number two places to the right.
73.2 ÷ 100
= 0.732
We must make sure we add in the zero to the units column as a placeholder.
Your Turn
Now have a go at the following questions:
= 45
= 7.92
= 1.013
= 5.7
= 0.0124
Simplifying Fractions
To simplify a fraction, we must find the highest common factor between its numerator and its denominator. Remember: ‘common’ means that the same integer must divide into the top and the bottom. For example: Write in its simplest terms. 5 would be the highest common factor of 55 and 100.
÷ 5
÷ 5
Your Turn
Now have a go at the following questions:
Using a Hundred Square
We can use a 100 square to help us convert between fractions, decimals and percentages. Using your squares, fill in the following table.
45%
56%
0.56
0.73
20%
0.01
Design a Park
Your task is to design a park. You can colour in the squares to represent what you have included. For example, you could colour the squares in green to represent trees or blue to represent water, or even colour in the squares grey to indicate a skate-park. All you need to do is include a key and complete the fractions, decimal and percentages equivalence table to indicate the proportion of each item.
Reflection
Go back to the Maths Skills Toolbox.
You need to be able to: