Fractions, decimals and percentages This activity is about converting between fractions, decimals and percentages. Information sheet Converting between decimals and fractions To change a decimal to a fraction: use the place value of the last digit ÷ 5 85 17 For example 0.85 = 100 = 20 ÷ 5 hundredths b On a calculator press: 85 a c 100 = To change a fraction to a decimal: divide the top by the bottom 4 For example 5 = 4 5 = 0.8 Converting between percentages and fractions or decimals To write a % as a fraction or decimal: divide by 100 For example 64% = 64 100 = 0.64 64 16 or 64% = 100 = 25 b On a calculator press: 64 a c 100 = To write a decimal or fraction as a %: multiply by 100 For example 0.125 = 0.125 100 = 12.5% 2 2 5 = 5 100 (i.e. of 100%) = 40% or = 2 5 100 = 40% On a calculator press: 2 5 100 = 40% Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 1 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Try these 1 Write these decimals as fractions: 0.3 = …………. 0.5 = …………. 0.6 = …………. 0.02 = …………. 0.05 = …………. 0.25 = …………. 0.36 = …………. 0.125 = …………. 2 Write these fractions as decimals: 7 1 2 3 10 = ………………. 5 = ………………. 5 = ………………. 4 = ………………… 7 2 9 7 8 = ………………. 3 = ………………. 20 =………………. 25 = ………………… 3 Write these percentages as decimals: 3% = …………. 30% = …………. 25% = …………. 80% = …………. 8% = …………. 12% = …………. 67% = …………. 17.5% = …………. Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 2 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org 4 Write these percentages as fractions: 20% = …………. 75% = …………. 5% = …………. 30% = …………. 40% = …………. 15% = …………. 24% = …………. 35% = …………. 5 Write these decimals as percentages: 0.25 = …………. 0.5 = …………. 0.7 = …………. 0.07 = …………. 0.45 = …………. 0.09 = …………. 0.4 = …………. 0.375 = …………. 6 Write these fractions as percentages: 1 1 9 3 10 = …………. 5 = …………. 10 = …………. 4 = …………. 4 17 1 2 5 = …………. 20 = …………. 3 = …………. 3 = …………. Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 3 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org At the end of the activity Explain how to convert ... • a decimal to a fraction • a fraction to a decimal • a percentage to a fraction or decimal • a fraction or decimal to a percentage. Give some examples of real contexts where ... • decimals are used • fractions are used • percentages are used. Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 4 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Fractions, decimals and percentages Fractions to decimals to percentages Complete this table. Fraction Decimal Percentage 1 10 1 5 3 10 2 5 1 2 3 5 7 10 4 5 9 10 1 4 3 4 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 5 of 14 © Nuffield Foundation 2011 ● downloaded from www.fsmq.org Fill the gaps in the table. Percentage Fraction Decimal 10% 0.2 3 10 40% 0.5 3 5 70% 0.8 9 10 25% 3 4 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 6 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – fractions to percentages Set A I am Who is I am Who is I am Who is 1? 1? 3 ? 100% 2 50% 5 20% 4 I am Who is I am Who is I am Who is 1 ? 1 ? 3 ? 75% 10 10% 4 25% 10 I am Who is I am Who is I am Who is 2 ? 7 ? 4 ? 30% 5 40% 10 70% 5 I am Who is I am Who is I am Who is 3 ? 9 ? 1? 80% 5 60% 10 90% Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 7 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – fractions to percentages Set B I am Who is I am Who is I am Who is ? 100% 1 50% 1 ? 20% 3 ? 2 5 4 I am Who is I am Who is I am Who is 75% 1 ? 10% 1 ? 25% 3 ? 10 4 10 I am Who is I am Who is I am Who is 30% 2 ? 40% 7 ? 70% 4 ? 5 10 5 I am Who is I am Who is I am Who is ? ? 11? 80% 3 60% 9 90% 20 5 10 I am Who is I am Who is I am Who is 3 1 14 55% ? 6% ? 33 1 % ? 50 3 3 25 I am Who is I am Who is I am Who is 5 19 37 56% ? 62 1 % ? 95% ? 8 2 20 50 I am Who is I am Who is I am Who is 3 ? 2 ? 7 ? 74% 8 37 % 25 8% 20 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 8 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org I am Who is I am Who is I am Who is 2 1 11 35% ? 66 2 % ? 12 % ? 3 3 8 50 I am I am I am Who is Who is Who is 1 ? 18 ? 7 ? 22% 20 5% 25 72% 8 I am Who is I am Who is I am Who is 1 ? 17 ? 21? 87 % 25 4% 50 34% 50 I am Who is I am Who is I am Who is 13 ? 9 ? 29 ? 42% 25 52% 20 45% 50 I am Who is I am Who is I am Who is 16 ? 8 ? 1 ? 58% 25 64% 25 32% 50 I am Who is I am Who is I am Who is 23 ? 49 ? 11? 2% 25 92% 50 98% 25 1 I am Who is I am2 Who is I am Who is 41? 13 ? 7 ? 44% 50 82% 20 65% 50 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 9 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org I am Who is I am Who is I am Who is 22 ? 31? 17 ? 14% 25 88% 50 62% 20 I am I am I am Who is Who is Who is 4 ? 23 ? 21? 85% 25 16% 50 46% 25 I am Who is I am Who is I am Who is 39 ? 3 ? 13 ? 84% 50 78% 20 15% 50 I am Who is I am Who is I am Who is 6 ? 43 ? 19 ? 26% 25 24% 50 86% 25 I am Who is I am Who is I am Who is 3 ? 9 ? 9 ? 76% 25 12% 50 18% 25 I am Who is I am Who is I am Who is 27 ? 17 ? 1? 36% 50 54% 25 68% Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 10 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – percentages to fractions Set C I am Who is I am Who is I am Who is 1 1 3 1 50%?2 20%?5 75%?4 I am Who is I am Who is I am Who is 1 1 3 10%10 ? 25%4 ? 30%?10 I am Who is I am Who is I am Who is 2 7 4 40%?5 70%?10 80%?5 I am Who is I am Who is I am Who is 3 9 60%?5 90%?10 100%? Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 11 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org Follow me – percentages to fractions Set D I am Who is I am Who is I am Who is 1 50%?1 20%?1 75%?3 2 5 4 I am Who is I am Who is I am Who is 10%?1 25%?1 30%?3 10 4 10 I am Who is I am Who is I am Who is 40%?2 70%?7 80%?4 5 10 5 I am Who is I am Who is I am Who is 11 60%?3 90%?9 55%?20 5 10 I am Who is I am Who is I am Who is 3 33 14 6%?50 33%? 100 56%?25 I am Who is I am Who is I am Who is 63 19 37 63%? 100 95%?20 74%?50 I am Who is I am Who is I am Who is 37 2 37%? 100 8%?25 35%? Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 12 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org I am Who is I am Who is I am Wh11o is 67 13 50 67%? 100 13%? 100 22%? I am Wh1o is I am Who18 is I am Who is 20 25 5%? 72%? 87%? I am Who1 is I am Who17 is I am Who21 is 87 25 50 50 100 4%? 34%? 42%? I am Who13 is I am Who9 is I am Who29 is 25 20 50 52%? 45%? 58%? I am Who16 is I am Who8 is I am Who1 is 25 25 50 64%? 32%? 2%? I am Who23 is I am Who49 is I am Who11 is 25 50 25 92%? 98%? 44%? I am Who41 is I am Who13 is I am Who is 50 20 82%? 65%? 14%? 7 20 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 13 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org I am Who is I am Who is I am Who is 22 31 17 88%?25 62%?50 85%?20 I am Who is I am Who is I am Who is 4 23 21 16%?25 46%?50 84%?25 I am Who is I am Who is I am Who is 39 3 13 78%?50 15%?20 26%?50 I am Who is I am Who is I am Who is 6 43 19 24%?25 86%?50 76%?25 I am Who is I am Who is I am Who is 3 9 9 12%?25 18%?50 36%?25 I am Who is I am Who is I am Who is 27 17 54%?50 68%?25 100%? 7 50 Nuffield Free-Standing Mathematics Activity ‘Fractions, decimals and percentages’ Student sheets Copiable page 14 of 14 © Nuffield Foundation 2012 ● downloaded from www.fsmq.org .