Equivalence

1
Equivalence

• Fractions, decimals and percentages

2
Mental starter


10
100
1000
3
Some of these mean the same
1/2
3/4
2/4
50
75
1/25
1/4
0.75
25
0.25
0.5
4
How can we convert decimals to percentages and
fractions?
To convert decimals to percentages we multiply
by 100.
So, 0.6
60
Remember, when we multiply by 100 we move the
decimal point 2 places to the right.
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How can we convert a percentage to a fraction?

• Per cent means out of 100
• 25 25 out of 100 25/100
• We can then cancel this fraction down, so,
  dividing the numerator and denominator by 25
  gives us

1/4
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Decimals to percentages and fractions
1/10
10/100
10
0.1
1/5
20/100
20
0.2
30
3/10
30/100
0.3
45
9/20
45/100
0.45
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How can we convert a percentage to a decimal?

• Divide by 100

25/100 0.25
So, 25 is the same as
REMEMBER WHEN WE DIVIDE BY 100 WE MOVE THE
DECIMAL POINT 2 PLACES TO THE LEFT
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Percentages to decimals
10/100
10
0.1
25
25/100
0.25
38
38/100
0.38
92
92/100
0.92
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How can we convert fractions to decimals and
percentages?

• If we divide the numerator by the denominator we
  get a decimal

So, ¼ 1 divided by 4
0.25
As a percentage, ¼ 0.25 25

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Fractions to decimals and percentages
1/10
10/100
10
0.1
1/5
20/100
20
0.2
3/10
30/100
30
0.3
9/20
45/100
45
0.45
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How can we find percentages?
10 of 100
100 /10
10
5 of 100
Half of 10 of 100
5
10 of 260
26
260/10
5 of 260
Half of 10 of 260
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Harder percentages
We can use our answers for 10 and 5 of any
number to find further percentages
So, if 10 of 620
62
And 5 of 620
31
Then 15 will equal 10 5
62 31
93
What would 20 of 620 be?
124
And 35 of 620?
217
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Equivalent Fractions, Decimals, and Percentages

• Copy and complete the following equivalence table

30
3/10
3/5
0.6
8
0.08
0.18
9/50
96
24/25
50
0.5
1/25
0.04
0.75
75
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Quick conversions

• FRACTION

PERCENTAGE
DECIMAL
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Extension
As a decimal, a fraction, and a percentage are
all different ways of writing the same thing, we
can sometimes make a calculation easier by using
an equivalent form instead of the decimal,
fraction or percentage given.
Example 1.
20 of 35. As 20 is 1/5, this is the same as 1/5
x 35 1/7
Example 2.
0.3 x 340. As 0.3 is 30, this is the same as 30
of 340. 10 of 340 is 34. So, 30 of 340 3 x 34
102
Example 3.
3/25 of 40. As 3/25 is 0.12, this is the same as
0.12 x 40 4.8
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Rewrite the following using an alternative to the
percentage, decimal or fraction given. Then work
out the answer.
1/5 x 75 15
0.08 x 60 4.8
¼ x 19 4 ¾
0.6 x 550 330
0.15 x 90 13.5
½ x 64 32
0.6 x 7 4.2
4/10 x 270 108
¾ x 44 33
1/3 x 180 60