Fractions, decimals and percentages Equivalence Fractions, decimals and percentages

Mental starter 15 75 23 156 0.7 2.5 52 9 6 50 25 80 10 63 4 0.2 0.03 0.5 0.4 1 3.5 6.25 7.2 0.9 Individual whiteboards Revision of multiplying and dividing by powers of 10 Pick pupil, number, operation, and power of 10 × ÷ 10 100 1000

Some of these mean the same 1/2 3/4 2/4 50% 75% 1/25 1/4 0.75 This could be done using the interactive whiteboard so the pairs can be physically moved together Match pairs. Spot odd one out and equivalent fractions 25% 0.25 0.5

How can we convert decimals to percentages and fractions? To convert decimals to percentages we multiply by 100. So, 0.6 = 60% Have example percentage to decimal conversion on whiteboard to emphasise connection and inverse operation. Remember, when we multiply by 100 we move the decimal point 2 places to the right.

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: Percent means ‘out of 100’ 1/4

Decimals to percentages and fractions 10/100 = 1/10 0.1 = 10% = 1/5 0.2 = 20% = 20/100 = 30% = 0.3 = 30/100 = 3/10 Pupils do question 1 of exercise 4D page 46: decimals to percentages and fractions 45% = 0.45 = 45/100 = 9/20

How can we convert a percentage to a decimal? Divide by 100 25/100 = 0.25 So, 25% is the same as Divide by 100 REMEMBER: WHEN WE DIVIDE BY 100 WE MOVE THE DECIMAL POINT 2 PLACES TO THE LEFT

Percentages to decimals 10/100 = 10% = 0.1 25% = 25/100 = 0.25 38% = 38/100 = 0.38 Pupils do question 2 of exercise 4D page 46: converting percentages to decimals and fractions 92% = 92/100 = 0.92

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%

Fractions to decimals and percentages 1/10 = 10/100 = 0.1 = 10% 1/5 = 20/100 = 0.2 = 20% 3/10 = 30/100 = 0.3 = 30% Use calculator Pupils do question 3 of exercise 4D page 46: converting fractions to percentages and decimals Already covered decimals to fractions in lesson 4.2. Pupils can hold up answers on individual whiteboards 9/20 = 45/100 = 0.45 = 45%

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 = 13

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 Pupils do question 5 of exercise 4D page 46: calculating percentages in multiples of 5 and 10 What would 20% of 620 be? 124 And 35% of 620? 217

Equivalent Fractions, Decimals, and Percentages Copy and complete the following equivalence table: FRACTION PERCENTAGE DECIMAL 0.3 60% 2/25 18% 0.96 1/2 4% 3/4 3/10 30% 3/5 0.6 8% 0.08 0.18 9/50 24/25 96% 50% 0.5 1/25 0.04 75% 0.75

Quick conversions FRACTION DECIMAL PERCENTAGE Extension work Pupils copy diagram and complete with steps

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

Then work out the answer. Rewrite the following using an alternative to the percentage, decimal or fraction given. Then work out the answer. a) 20% of 75 b) 2/25 of 60 c) 25% of 19 d)60% of 550 e) 3/20 of 90 f) 0.5 x 64 g) 3/5 of 7 h) 0.4 x 270 i) 75% of 44 j) 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