Year 5: Fractions, decimals and percentages
Part of the Year 5 decimals and percentages chapter. Chapter overview · whole chapter on one page
Fractions, decimals and percentages
Some fractions are easy to write as percentages. The bar below is split into 5 equal parts and 2 are shaded, so it shows 2/5. To change a fraction to a percentage, make the bottom number 100. The top number is then the percentage.
Multiply the top and the bottom by the same number to make 100. Since 5 × 20 = 100, we multiply 2/5 by 20/20: 2/5 = 40/100 = 40%. The square shows the same amount: 40 of the 100 squares are shaded.
Key ideas
- Make the bottom number 100 and the top number is the percentage: 2/5 = 40/100 = 40%.
- Useful equivalents: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 2/5 = 40%, 4/5 = 80%.
- If the bottom is 10, 20, 25 or 50, you can multiply it to make 100: 3/10 = 30/100 = 30%, 9/25 = 36/100 = 36%.
- Decimals and percentages: 0.25 = 25/100 = 25%.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 5 × 20 = 100, so multiply the top and the bottom by 20.2⁄5 = 40⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.40⁄100 = 40%
- Write the answer. 40%
Check. 40 ÷ 100 = 0.4, and 2 ÷ 5 = 0.4. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 4 × 25 = 100, so multiply the top and the bottom by 25.3⁄4 = 75⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.75⁄100 = 75%
- Write the answer. 75%
Check. 75 ÷ 100 = 0.75, and 3 ÷ 4 = 0.75. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.9⁄25 = 36⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.36⁄100 = 36%
- Write the answer. 36%
Check. 36 ÷ 100 = 0.36, and 9 ÷ 25 = 0.36. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Watch out
1/5 is NOT 15%. Make the bottom 100 and you get 20/100 = 20%. Also, 3/4 is not 34%: 3/4 = 75/100.Exercise 7F Fractions, decimals and percentages
Non-calculatorKey words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 2 × 50 = 100, so multiply the top and the bottom by 50.1⁄2 = 50⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.50⁄100 = 50%
- Write the answer. 50%
Check. 50 ÷ 100 = 0.5, and 1 ÷ 2 = 0.5. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 4 × 25 = 100, so multiply the top and the bottom by 25.1⁄4 = 25⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.25⁄100 = 25%
- Write the answer. 25%
Check. 25 ÷ 100 = 0.25, and 1 ÷ 4 = 0.25. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 4 × 25 = 100, so multiply the top and the bottom by 25.3⁄4 = 75⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.75⁄100 = 75%
- Write the answer. 75%
Check. 75 ÷ 100 = 0.75, and 3 ÷ 4 = 0.75. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 5 × 20 = 100, so multiply the top and the bottom by 20.1⁄5 = 20⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.20⁄100 = 20%
- Write the answer. 20%
Check. 20 ÷ 100 = 0.2, and 1 ÷ 5 = 0.2. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 5 × 20 = 100, so multiply the top and the bottom by 20.3⁄5 = 60⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.60⁄100 = 60%
- Write the answer. 60%
Check. 60 ÷ 100 = 0.6, and 3 ÷ 5 = 0.6. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 5 × 20 = 100, so multiply the top and the bottom by 20.4⁄5 = 80⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.80⁄100 = 80%
- Write the answer. 80%
Check. 80 ÷ 100 = 0.8, and 4 ÷ 5 = 0.8. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 10 × 10 = 100, so multiply the top and the bottom by 10.1⁄10 = 10⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.10⁄100 = 10%
- Write the answer. 10%
Check. 10 ÷ 100 = 0.1, and 1 ÷ 10 = 0.1. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 10 × 10 = 100, so multiply the top and the bottom by 10.9⁄10 = 90⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.90⁄100 = 90%
- Write the answer. 90%
Check. 90 ÷ 100 = 0.9, and 9 ÷ 10 = 0.9. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 4 × 25 = 100, so multiply the top and the bottom by 25.1⁄4 = 25⁄100
- Write the decimal point. The bottom number has 2 zeros, so the last digit is in the hundredths column. Fill the empty places with zeros.0.25
- Write the answer. 0.25
Check. 1 ÷ 4 = 0.25. ✓
Watch out. The bottom number shows where the last digit goes: 100 means hundredths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 5 × 2 = 10, so multiply the top and the bottom by 2.1⁄5 = 2⁄10
- Write the decimal point. The bottom number has 1 zero, so the last digit is in the tenths column. Fill the empty places with zeros.0.2
- Write the answer. 0.2
Check. 1 ÷ 5 = 0.2. ✓
Watch out. The bottom number shows where the last digit goes: 10 means tenths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 5 × 2 = 10, so multiply the top and the bottom by 2.4⁄5 = 8⁄10
- Write the decimal point. The bottom number has 1 zero, so the last digit is in the tenths column. Fill the empty places with zeros.0.8
- Write the answer. 0.8
Check. 4 ÷ 5 = 0.8. ✓
Watch out. The bottom number shows where the last digit goes: 10 means tenths. Write 0.07 for 7 hundredths, not 0.7.
Key words. A decimal uses a point (the decimal point) to show parts of a whole. The places after the point are tenths (one of ten equal parts), hundredths (one of a hundred equal parts) and thousandths (one of a thousand equal parts).
Method. Make the bottom number 10, 100 or 1,000. Then write the top number with the decimal point in the right place.
- Make the bottom number 10, 100 or 1,000. 5 × 2 = 10, so multiply the top and the bottom by 2.3⁄5 = 6⁄10
- Write the decimal point. The bottom number has 1 zero, so the last digit is in the tenths column. Fill the empty places with zeros.0.6
- Write the answer. 0.6
Check. 3 ÷ 5 = 0.6. ✓
Watch out. The bottom number shows where the last digit goes: 10 means tenths. Write 0.07 for 7 hundredths, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 10 × 10 = 100, so multiply the top and the bottom by 10.3⁄10 = 30⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.30⁄100 = 30%
- Write the answer. 30%
Check. 30 ÷ 100 = 0.3, and 3 ÷ 10 = 0.3. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 20 × 5 = 100, so multiply the top and the bottom by 5.7⁄20 = 35⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.35⁄100 = 35%
- Write the answer. 35%
Check. 35 ÷ 100 = 0.35, and 7 ÷ 20 = 0.35. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 20 × 5 = 100, so multiply the top and the bottom by 5.1⁄20 = 5⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.5⁄100 = 5%
- Write the answer. 5%
Check. 5 ÷ 100 = 0.05, and 1 ÷ 20 = 0.05. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 50 × 2 = 100, so multiply the top and the bottom by 2.3⁄50 = 6⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.6⁄100 = 6%
- Write the answer. 6%
Check. 6 ÷ 100 = 0.06, and 3 ÷ 50 = 0.06. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.9⁄25 = 36⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.36⁄100 = 36%
- Write the answer. 36%
Check. 36 ÷ 100 = 0.36, and 9 ÷ 25 = 0.36. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.17⁄25 = 68⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.68⁄100 = 68%
- Write the answer. 68%
Check. 68 ÷ 100 = 0.68, and 17 ÷ 25 = 0.68. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.1⁄25 = 4⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.4⁄100 = 4%
- Write the answer. 4%
Check. 4 ÷ 100 = 0.04, and 1 ÷ 25 = 0.04. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.3⁄25 = 12⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.12⁄100 = 12%
- Write the answer. 12%
Check. 12 ÷ 100 = 0.12, and 3 ÷ 25 = 0.12. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Equivalent means the same value written in a different way. A fraction, a decimal and a percentage can all be equivalent to each other.
Method. Change both to percentages, then compare.
- Change 3/4 to a percentage. Make the bottom 100: 3/4 = 75/100.3⁄4 = 75%
- Compare with 70%. Compare the two percentages.75% > 70%
- Write the answer. 3⁄4 is more.
Check. 3/4 = 0.75 and 70% = 0.7. ✓
Watch out. Compare like with like: both as percentages.
Key words. Equivalent means the same value written in a different way. A fraction, a decimal and a percentage can all be equivalent to each other.
Method. Change each one to a percentage, then put them in order.
- Change each one to a percentage. Use the method that fits each number.
Number As a percentage 0.6 60% 2⁄5 40% 35% 35% - Put them in order, smallest first. The smallest percentage is the smallest amount.35% < 40% < 60%
- Write the answer. 35%, 2/5, 0.6
Check. 35% = 0.35, 2/5 = 0.4 and 0.6. These are in order. ✓
Watch out. Changing everything to percentages makes the comparison easy.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 20 × 5 = 100, so multiply the top and the bottom by 5.7⁄20 = 35⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.35⁄100 = 35%
- Write the answer. 35%
Check. 35 ÷ 100 = 0.35, and 7 ÷ 20 = 0.35. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.18⁄25 = 72⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.72⁄100 = 72%
- Write the answer. 72%
Check. 72 ÷ 100 = 0.72, and 18 ÷ 25 = 0.72. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 25 × 4 = 100, so multiply the top and the bottom by 4.4⁄25 = 16⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.16⁄100 = 16%
- Write the answer. 16%
Check. 16 ÷ 100 = 0.16, and 4 ÷ 25 = 0.16. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 4 × 25 = 100, so multiply the top and the bottom by 25.1⁄4 = 25⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.25⁄100 = 25%
- Write the answer. 25%
Check. 25 ÷ 100 = 0.25, and 1 ÷ 4 = 0.25. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Scale the fraction so that the bottom number is 100. The top number is then the percentage.
- Make the bottom number 100. Per cent means out of 100. 5 × 20 = 100, so multiply the top and the bottom by 20.1⁄5 = 20⁄100
- Read the top number as the percentage. The top number, out of 100, is the percentage.20⁄100 = 20%
- Write the answer. 20%
Check. 20 ÷ 100 = 0.2, and 1 ÷ 5 = 0.2. Both are the same decimal. ✓
Watch out. Multiply the top AND the bottom by the same number. Do not add to them.
Key words. Equivalent means the same value written in a different way. A fraction, a decimal and a percentage can all be equivalent to each other.
Method. Add the percentages for walking and cycling, then take the total away from 100%.
- Add the walkers and the cyclists. A quarter walk and a fifth cycle, so add 25% and 20%.25% + 20% = 45%
- Take the total away from 100%. The rest of the pupils go some other way.100% − 45% = 55%
- Write the answer. 55%
Check. 25% + 20% + 55% = 100%. ✓
Watch out. The whole class is 100%. Use it to find the missing part.
Key words. Equivalent means the same value written in a different way. A fraction, a decimal and a percentage can all be equivalent to each other.
Method. Write 1/5 as a percentage. Then compare it with 15%.
- Write 1/5 with the bottom number 100. Multiply the top and the bottom by 20, because 5 × 20 = 100.1⁄5 = 20⁄100
- Read the percentage. The top number is the percentage.20⁄100 = 20%
- Write the answer. No. 1/5 = 20%, not 15%.
Check. 20% = 0.2 = 1/5. ✓
Watch out. Always make the bottom number 100 before you read the top number.
Key words. A fraction has a numerator (the top number) and a denominator (the bottom number). Multiplying the top and the bottom by the same number makes an equivalent fraction.
Method. Write each fraction with denominator 25 as a percentage. Keep the one between 30% and 35%.
- Write the fractions with bottom number 25. Each one-25th is 4%, because 25 × 4 = 100.Each one-25th is 4%
- Check the fractions near 30% to 35%. Look at the percentages for the fractions near the range.
Fraction Percentage Between 30% and 35%? 6⁄25 24% no 7⁄25 28% no 8⁄25 32% yes 9⁄25 36% no 10⁄25 40% no - Write the answer. Only one fraction is between 30% and 35%.8/25 = 32%
Check. 8/25 = 32%, and 30% < 32% < 35%. ✓
Watch out. Write each fraction as a percentage, not as a decimal. One-25th is always 4%.