EquivalenceEquivalenceFractions, decimals andFractions, decimals and

percentagespercentages

Mental starterMental starter

1515 7575 2323 156156 0.70.7 2.52.5

5252 99 66 5050 2525 8080

1010 6363 44 0.20.2 0.030.03 0.50.5

0.40.4 11 3.53.5 6.256.25 7.27.2 0.90.9

× ÷ 10 100 1000

1/2

0.5

1/4

25%0.25

50%

0.75

3/4

75%1/25

2/4

Some of these mean the sameSome of these mean the same

How can we How can we convert decimals to convert decimals to percentages and percentages and fractions?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.

How can we convert a How can we convert a percentage to a percentage to a fraction?fraction?

‘‘Per cent’ means ‘out of 100’Per cent’ means ‘out of 100’ 25% = 25 out of 100 = 25/10025% = 25 out of 100 = 25/100 We can then cancel this fraction We can then cancel this fraction

down, so, dividing the numerator and down, so, dividing the numerator and denominator by 25 gives us:denominator by 25 gives us:1/4

Decimals to percentages and Decimals to percentages and fractionsfractions

1/10

1/5

3/10

9/20

10/100 = 20/100 =

30/100 = 45/100 =

10% = 20% =

30% =

45% =

0.1 =

0.2 =0.3 =

0.45 =

How can we How can we convert a convert a percentage to a percentage to a decimal?decimal?

Divide by 100Divide by 100So, 25% is the same as

25/100 = 0.25

REMEMBER: WHEN WE DIVIDE BY 100 WE MOVE THE DECIMAL POINT 2 PLACES TO THE LEFT

Percentages to decimalsPercentages to decimals

25% =

38% =

92% =

10% =

10/100 = 25/100 =

38/100 = 92/100 =

0.1

0.25

0.38

0.92

How can we convert How can we convert fractions to decimals fractions to decimals and percentages?and percentages?

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

So, ¼ = 1 divided by 4 =

0.25

As a percentage, ¼ = 0.25 = 25%

Fractions to decimals and Fractions to decimals and percentagespercentages

1/10 =

1/5 =

3/10 = 9/20 =

10/100 = 20/100 =

30/100 = 45/100 =

10%

20%

30%

45%

0.1 =0.2 =0.3 =0.45 =

Equivalent Fractions, Decimals, Equivalent Fractions, Decimals, and Percentagesand Percentages

Copy and complete the following equivalence Copy and complete the following equivalence table:table:

FRACTIONFRACTION PERCENTAGEPERCENTAGE DECIMALDECIMAL0.30.3

60%60%

2/252/25

18%18%

0.960.96

1/21/2

4%4%

3/43/4

30%3/10

3/5 0.6

8% 0.08

9/50 0.18

96%24/25

50%

0.5

1/25 0.040.7575%

Quick conversionsQuick conversions

FRACTIONFRACTIONPERCENTAGEDECIMAL

ExtensionExtensionAs 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 = 102Example 3.

3/25 of 40. As 3/25 is 0.12, this is the same as 0.12 x 40 = 4.8

Rewrite the following using an alternative to the percentage, decimal or fraction given.

Then work out the answer.a) 20% of 75a) 20% of 75 b) 2/25 of 60b) 2/25 of 60 c) 25% of 19c) 25% of 19 d)60% of 550d)60% of 550

e) 3/20 of 90e) 3/20 of 90 f) 0.5 x 64f) 0.5 x 64 g) 3/5 of 7g) 3/5 of 7 h) 0.4 x 270h) 0.4 x 270

i) 75% of 44i) 75% of 44 j) 0.333 x 180j) 0.333 x 180

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