Decimals and percentages – Year 7 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Line up the points and write 3.6 as 3.60: \(4.75+3.60=\)8.35.
   2. Write 12.3 as 12.30 and subtract: \(12.30-5.78=\)6.52. Check: \(6.52+5.78=12.3\).
   3. Write 2.14 as 2.140: \(0.906+2.140=\)3.046.
   4. Write 20 as 20.000: \(20.000-7.365=\)12.635.
   5. Fill gaps with zeros: \(15.40+8.07+0.90=\)24.37.

2. Answer to Question 2

   1. \(32\times4=128\); one decimal place in the question, so 12.8.
   2. \(6\times7=42\); two decimal places in total, so 0.42.
   3. \(45\times12=540\); three decimal places in total, so 0.540, which is 0.54.
   4. \(72\div6=12\) and 7.2 is ten times smaller than 72, so 1.2.
   5. Multiply both by 100: \(240\div8=\)30.
   6. Multiply both by 10: \(0.45\div9=\)0.05. Check: \(0.05\times0.9=0.045\).

3. Answer to Question 3

   Fraction	Decimal	Percentage
   \(\dfrac{3}{4}\)	0.75	75%
   \(\dfrac{7}{20}\)	0.35	35%
   \(\dfrac{3}{25}\)	0.12	12%
   \(\dfrac{3}{8}\)	0.375	37.5%
   \(\dfrac{9}{200}\)	0.045	4.5%

   Method: to go from a decimal to a percentage multiply by 100, and to go back divide by 100. \(\dfrac{3}{4}=3\div4=0.75\). \(0.35=\dfrac{35}{100}=\dfrac{7}{20}\) after dividing by 5. \(12\%=\dfrac{12}{100}=\dfrac{3}{25}\). \(\dfrac{3}{8}=3\div8=0.375\). \(0.045=\dfrac{45}{1000}=\dfrac{9}{200}\).

4. Answer to Question 4

   1. Divide by 10: \(80\div10=\)£8.
   2. 25% is a quarter: \(64\div4=\)16 kg.
   3. 10% = £12, so 30% = £36 and 5% = £6. Then 35% = \(36+6=\)£42.
   4. 1% = \(250\div100=2.5\), so 7% = \(7\times2.5=\)17.5 m.
   5. 12.5% is one eighth: \(400\div8=\)50.

5. Answer to Question 5

   1. An increase of 10% means 110%, multiplier 1.1: \(60\times1.1=\)£66.
   2. A decrease of 20% leaves 80%, multiplier 0.8: \(150\times0.8=\)£120.
   3. 115% gives multiplier 1.15: \(40\times1.15=\)46 kg. (15% of 40 is 6.)
   4. 75% remains, multiplier 0.75: \(84\times0.75=\)£63. (25% of 84 is 21.)

6. Answer to Question 6

   1. Write as a fraction and convert: \(\dfrac{18}{24}=\dfrac{3}{4}=0.75=\)75%.
   2. \(\dfrac{7}{50}=\dfrac{14}{100}=\)14%.
   3. Use the same units first: 1.5 m = 150 cm. \(\dfrac{45}{150}=0.3=\)30%.
   4. 2 kg = 2000 g. \(\dfrac{350}{2000}=0.175=\)17.5%.

7. Answer to Question 7

   1. 20% off leaves 80%, multiplier 0.8. Trainers \(65\times0.8=\)£52, football \(18\times0.8=\)£14.40, tracksuit \(48\times0.8=\)£38.40.
   2. She spends \(52+14.40+38.40=\)£104.80. Full price \(65+18+48=£131\), so she saves \(131-104.80=\)£26.20 (which is 20% of £131).
   3. Second shop: \(70\times0.75=£52.50\). The first shop is cheaper by \(52.50-52=\)50p.
   4. Take a further 10% off the sale price: \(38.40\times0.9=\)£34.56.

8. Answer to Question 8

   1. Divide mark by total and multiply by 100: Asha \(\dfrac{36}{40}=\)90%, Ben \(\dfrac{27}{30}=\)90%, Cara \(\dfrac{45}{60}=\)75%, Dev \(\dfrac{17}{20}=\)85%, Ella \(\dfrac{70}{80}=\)87.5%.
   2. The highest percentage is 90%, so Asha and Ben are joint best, even though their raw marks are different.
   3. The lowest is Cara with 75%, which is above 70%, so everyone passed.
   4. Out of 100 her mark would equal her percentage: \(\dfrac{70}{80}=0.875=87.5\%\). Yes, she is right.

9. Answer to Question 9

   1. 3% of £200: \(200\times0.03=\)£6 per year.
   2. 2% of £250: \(250\times0.02=\)£5 per year.
   3. Simple interest is the same each year. Priya: \(200+4\times6=\)£224. Max: \(250+4\times5=\)£270.
   4. \(200+6n>230\) means \(6n>30\), so \(n>5\). After 5 years she has exactly £230, so she first has more after 6 years (£236).

10. Answer to Question 10

    1. 12% more means 112%: \(8500\times1.12=\)9 520 steps.
    2. 15% fewer means 85% of Tuesday: \(9520\times0.85=\)8 092 steps.
    3. Change \(=8092-8500=-408\). \(\dfrac{-408}{8500}=-0.048\), so a decrease of 4.8%.
    4. 8 500, 9 520 and 8 092 are all below 10 000, so he did not meet his target on any day.

11. Answer to Question 11

    1. The percentages must total 100%: \(100-45-20-15=\)20% honey.
    2. 1% of 500 g is 5 g. Oats \(45\times5=\)225 g, nuts 100 g, fruit 75 g, honey 100 g (total 500 g).
    3. 40% = 240 g, so 1% = \(240\div40=6\) g and 100% = 600 g.
    4. Second bar 240 g of oats, first bar 225 g, so the second has \(240-225=\)15 g more.

12. Answer to Question 12

    1. Percentage points are subtracted directly: \(85-18=\)67%.
    2. A drop of 12% of the current level leaves 88%: \(67\times0.88=58.96\), about 59%.
    3. Percentage points are a simple difference (85% to 67%). A drop of 18% is 18% of 85, which is 15.3 points, leaving 69.7%, a smaller drop.
    4. 85% of 4000: \(4000\times0.85=\)3 400 mAh.

13. Answer to Question 13

    1. \(100-38-24-18=\)20% choose a sandwich.
    2. 1% of 250 is 2.5. Pizza \(38\times2.5=\)95, pasta 60, salad 45, sandwich 50 (total 250).
    3. 15% more salad means 115%: \(45\times1.15=51.75\), about 52 pupils.
    4. One day: \(250\times2.40=£600\). Five days: \(600\times5=\)£3 000.

14. Answer to Question 14

    1. 15% off leaves 85%: \(320\times0.85=\)£272.
    2. First take £40 off: £280. Then 5% off: \(280\times0.95=\)£266.
    3. \(272-266=6\), so deal B is cheaper by £6.
    4. 12% of £266: \(266\times0.12=\)£31.92.

15. Answer to Question 15

    1. Adding 20% VAT means 120%: \(480\times1.2=\)£576.
    2. £560 is 120% of the price before VAT, so divide by 1.2: \(560\div1.2=\)£466.67.
    3. Compare prices with VAT: \(576-560=16\). The second laptop is cheaper by £16.
    4. 10% off leaves 90%: \(576\times0.9=\)£518.40.

16. Answer to Question 16

    1. Multiply year by year. Year 1: \(24000\times1.05=25200\). Year 2: \(25200\times1.03=25956\). Year 3: \(25956\times0.98=25436.88\), about 25 437.
    2. \(\dfrac{25437-24000}{24000}=0.0599\), so about 6.0%.
    3. Each percentage is applied to a different amount (the population at that time), so they cannot simply be added. Here the true answer is 5.99%, close to 6% only by chance.
    4. \(25437-24000=\)1 437 more people.

17. Answer to Question 17

    1. A: 75% of 80 is £60. B: \(\dfrac{2}{3}\) of 80 is £53.33. C: \(80-20=\)£60.
    2. £53.33 is the lowest price, so shop B is cheapest (a third is more than 25%).
    3. 10% off £60 leaves 90%: \(60\times0.9=\)£54.
    4. \(\dfrac{20}{80}=\dfrac{1}{4}=\)25%, the same as shop A.

18. Answer to Question 18

    1. Ali multiplied wrongly: \(0.15\times60=9\), since 10% is 6 and 5% is 3. The answer is 9.
    2. Beth found the increase but not the new price. The new price is \(80+20=\)£100.
    3. Carl lost the decimal point: \(32\times5=160\), with two decimal places, gives 1.6.
    4. Dina used the wrong number. The fall is £10, and \(\dfrac{10}{50}=\)20%, not 40%.

19. Answer to Question 19

    1. Each year interest = 4% of the start amount. Year 1: 40, end 1 040. Year 2: \(1040\times0.04=41.60\), end 1 081.60. Year 3: \(1081.60\times0.04=43.26\), end 1 124.86.
    2. From the table, after 3 years she has £1 124.86.
    3. Simple interest gives £40 a year: \(1000+120=1120\). Compound gives \(1124.86-1120=\)£4.86 more.
    4. Year 4: \(1124.86\times1.04=1169.85\). Year 5: \(1169.85\times1.04=1216.65\). She first exceeds £1 200 after 5 years.

20. Answer to Question 20

    1. Sale: \(50\times0.8=40\). Increase: \(40\times1.2=\)£48.
    2. No. The 20% decrease was of £50 (£10) but the 20% increase was of £40 (only £8), so the price ends £2 lower.
    3. To get from £40 back to £50 we need £10 more: \(\dfrac{10}{40}=\)25% increase.
    4. Let the price be P. Increase: \(1.2P\). Decrease: \(0.8\times1.2P=0.96P\). 0.96 is 96%, so the price is 4% lower than at the start, whatever P is.