Numeracy Worksheet Name... Percentages

Transcription

1 What's a Percentage? The symbol for percent is %. are out of 100. That means the whole thing (or the whole lot) equals 100%, and 20% means 20 parts out of cat is 100% cat.. 50% = 50 parts out of 100 or 50 / 100 which of course is the same as the fraction ½ or the decimal 0.5. If 100% is the whole thing 50% is half of it. There are fractions and decimal equivalents for all percentages. Here are some of the most useful. Percentage 100% 75% 50% 10% 1% Fraction 1 75 / 100 or 3 / 4 50 / 100 or 1 / 2 10 / 100 or 1 / 10 1 / 100 Decimal Convertions Converting to Decimals is easy you just divide by 100. To convert Decimals to you multiply by 100. Converting to Fractions is even easier. A percentage is always out of 100. So all you do is write the percentage as the top and 100 as the bottom of the fraction. To convert Fractions to, first convert the fraction to a decimal using a calculator then convert the Decimal to Percentage by multiplying by 100. Now Convert These Numbers 1. 28% to a decimal 2. 1 /5 to a percentage 3. 60% to a fraction to a percentage 5. 72% to a decimal /100 to a percentage 7. 90% to a fraction to a percentage /50 to a percentage 10. [Harder] 12.5% to a fraction n2.l1 percentages.doc/mar 2004 N2/L1.3

2 Percentage Of Something Often we need to know a percentage of something. For example if this cake is 35% fat how much is this in grams? Method 1 The cake weighs 120g. To find out what 35% of this is you first convert the percentage to a decimal and multiply by the x 120 = 42 So there are 42g of fat in this cake. Now Try These Method 2 Remember that 35% means 35 parts out of 100 so another way of doing this calculation is divide 120 by 100 to find 1% and then multiplying by 35. 1% of 120g is = 1.2g 35% of 120g is 1.2g x 35 = 42g 1. 90% of a 150g beef burger is actually beef. What is this amount in grams? 2. The table shows where Jill's monthly salary of 1,400 goes. Fill in the actual amounts spent. At the supermarket 15% Clothes 10% Utility bills 5% Council tax 9% Running a car 8% Mortgage 35% Charity Giving 3% Entertainment 5% Saving for holiday 10% Total 100% 1, Calculate 10% of these: 10% of % of % of 370km 10% of Calculate 5% of these 5 % of 99 5% of 306cm 5% of 50m 5% of 200ml 5. If 30g of the carrot cake above is sugar, what percentage of the cake is sugar? n2.l1 percentages.doc/mar 2004 N2/L1.9

3 6. This is how John spends his monthly salary of 1,600. Fill in what percentage of his salary he spends on each item. Food Clothes Utility bills Council tax Running a car Mortgage Charity Giving 0.00 Entertainment Saving for holiday Total 1, % 7. [Harder]The rate of VAT in 2004 is 17.5%. Can you work out an easy way of calculating VAT. 8. Using your method. Work out the VAT for the following items [hint: round the VAT to nearest whole penny] n2.l1 percentages.doc/mar 2004 N2/L1.9

4 Percentage Increase or Decrease We often need to increase or decrease a number by a certain percentage. For example Khalid has been offered a salary increase of 5% and he wants to know how much he will be earning after the increase. Now try these Khalid earns 24,000 5% of 24,000 is 1,200 so his new salary will be 24, ,200 = 25, Sandra has taken out a low-start mortgage. The terms of the mortgage state that the amount Sandra pays increases by 20% at the end of each of the first 5 years. Fill in the rows in the table below so that Sandra knows how much she will be paying each year. Year and onwards 2. Sandra knows that 20% x 5 = 100% so she thought her payments from year 6 onwards were going to be 240 ( % of 120). Why was she wrong? 3. Because people have moved to the city for work, the population of the village of Owlsbottom has declined by 15% in the last 5 years. If there were 780 people in the village 5 years ago who many are there now? Show your working. 4. Mona wants to lose 25% of her body weight. If she weighs 90kg now how much will she weigh after her diet? 5. Work out the total price for these items if vat is 17.5%. Printer VAT Computer VAT Slippers VAT DVD VAT n2.l1 percentages.doc/mar 2004 N2/L1.10

5 What's a Percentage? The symbol for percent is %. are out of 100. That means the whole thing (or the whole lot) equals 100%, and 20% means 20 parts out of cat is 100% cat.. 50% = 50 parts out of 100 or 50 / 100 which of course is the same as the fraction ½ or the decimal 0.5. If 100% is the whole thing 50% is half of it. There are fractions and decimal equivalents for all percentages. Here are some of the most useful. Percentage 100% 75% 50% 10% 1% Fraction 1 75 / 100 or 3 / 4 50 / 100 or 1 / 2 10 / 100 or 1 / 10 1 / 100 Decimal Convertions Converting to Decimals is easy you just divide by 100. To convert Decimals to you multiply by 100. Converting to Fractions is even easier. A percentage is always out of 100. So all you do is write the percentage as the top and 100 as the bottom of the fraction. To convert Fractions to, first convert the fraction to a decimal using a calculator then convert the Decimal to Percentage by multiplying by 100. Now Convert These Numbers 1. 28% to a decimal /5 to a percentage 20% 3. 60% to a fraction 60 / 100 or 3 / to a percentage 83% 5. 72% to a decimal /100 to a percentage 19% 7. 90% to a fraction 90 / 100 or 9 / to a percentage 4% /50 to a percentage 74% 10. [Harder] 12.5% to a fraction 1 / 8 n2.l1 percentages - answers.doc/mar 2004 N2/L1.3

6 Percentage Of Something Often we need to know a percentage of something. For example if this cake is 35% fat how much is this in grams? Method 1 The cake weighs 120g. To find out what 35% of this is you first convert the percentage to a decimal and multiply by the x 120 = 42 So there are 42g of fat in this cake. Now Try These Method 2 Remember that 35% means 35 parts out of 100 so another way of doing this calculation is divide 120 by 100 to find 1% and then multiplying by 35. 1% of 120g is = 1.2g 35% of 120g is 1.2g x 35 = 42g 1. 90% of a 150g beef burger is actually beef. What is this amount in grams? 135g 2. The table shows where Jill's monthly salary of 1,400 goes. Fill in the actual amounts spent. At the supermarket 15% 210 Clothes 10% 140 Utility bills 5% 70 Council tax 9% 126 Running a car 8% 112 Mortgage 35% 490 Charity Giving 3% 42 Entertainment 5% 70 Saving for holiday 10% 140 Total 100% 1, Calculate 10% of these: 10% of % of % of 370km 37km 10% of Calculate 5% of these 5 % of % of 306cm 15.3cm 5% of 50m 2.5m 5% of 200ml 10ml 5. If 30g of the carrot cake above is sugar, what percentage of the cake is sugar? 25% n2.l1 percentages - answers.doc/mar 2004 N2/L1.9

7 6. This is how John spends his monthly salary of 1,600. Fill in what percentage of his salary he spends on each item. Food % Clothes % Utility bills % Council tax 80 5% Running a car % Mortgage % Charity Giving 0 0% Entertainment % Saving for holiday 64 4% Total 1, % 7. [Harder]The rate of VAT in 2004 is 17.5%. Can you work out an easy way of calculating VAT. An easy way of working out VAT is to calculate 10% (by dividing by 10). Half this number to find 5% and half it again to get 2.5%. Add the 10%, 5% and 2.5% figures together. 8. Using your method. Work out the VAT for the following items [hint: round the VAT to nearest whole penny] p n2.l1 percentages - answers.doc/mar 2004 N2/L1.9

8 Percentage Increase or Decrease We often need to increase or decrease a number by a certain percentage. For example Khalid has been offered a salary increase of 5% and he wants to know how much he will be earning after the increase. Now try these Khalid earns 24,000 5% of 24,000 is 1,200 so his new salary will be 24, ,200 = 25, Sandra has taken out a low-start mortgage. The terms of the mortgage state that the amount Sandra pays increases by 20% at the end of each of the first 5 years. Fill in the rows in the table below so that Sandra knows how much she will be paying each year. Year and onwards Sandra knows that 20% x 5 = 100% so she thought her payments from year 6 onwards were going to be 240 ( % of 120). Why was she wrong? Because you add 20% to the last year's payments (which is always more than 120), not the original Because people have moved to the city for work, the population of the village of Owlsbottom has declined by 15% in the last 5 years. If there were 780 people in the village 5 years ago who many are there now? Show your working. 15% of 780 is 780 x 0.15 = 117 or 78 (10%) + 39 (5%) = = 663 an alternative way of doing this sum is there are 85% left so 780 x 0.85 = Mona wants to lose 25% of her body weight. If she weighs 90kg now how much will she weigh after her diet? 67.5 kg 5. Work out the total price for these items if vat is 17.5%. Printer VAT (or 300) Computer VAT (or 999) Slippers VAT 4.00 DVD VAT n2.l1 percentages - answers.doc/mar 2004 N2/L1.10