Percentages Decimals Percentages Learning Objectives To convert between

Percentages Decimals Percentages Learning Objectives To convert between percentages, fractions and decimals To answer worded questions involving these conversions

Fractions, decimals and percentages are just three ways of representing the same amount. ½ 0. 5 50%

Percentage Fraction The word "percent" is derived from the Latin per centum meaning "by the hundred". Write the percentage amount as a fraction over 100, then simplify. 25 ÷ 25 1 = 25% = 100 ÷ 25 4

Write the percentage amount as a fraction over 100, then simplify. 25 ÷ 25 1 = 25% = 100 ÷ 25 4 Write each of these percentages as a fraction in its lowest terms. Remember to show your workings as above. a. 8% b. 50% c. 25% d. 35% e. 90% f. 75%

Percentage Decimal If 25% = 25, this also means 25÷ 100 Divide the percentage amount by 100. 25 ÷ 100 = 0. 25 25% = 100

Divide the percentage amount by 100. 25 = 25÷ 100 = 0. 25 25% = 100 Write each percentage as a decimal. Remember to show your workings. a. 27% b. 85% c. 13% d. 6% e. 80% f. 32%

Fraction Decimal Divide the numerator by the denominator. You may use a calculator. 3 = 3÷ 25 = 0. 12 25

Divide the numerator by the denominator. 3 = 3÷ 25 = 0. 12 25 Write each fraction as a decimal. Remember to show your workings as above. a. 9 15 b. 3 40 c. 19 25 d. 5 16 e. 1 20 f. 1 8

Multiply the decimal by the amount needed to make it a whole number, and write it as a fraction over the multiplier. Then cancel it down to it’s lowest term. 3 6 ÷ 2 0. 6 X 10 = = 10 ÷ 2 5 Write each decimal as a fraction in its lowest terms. Remember to show your workings as above. a 0. 12 b. 0. 4 c. 0. 45 d. 0. 68 e. 0. 25 f. 0. 625

Decimal Percentage A percentage needs to be out of a hundred, so multiply the decimal by 100 and then put in the percentage sign. 32 0. 32 x 100 = = % 100 32

A percentage needs to be out of a hundred, so multiply the decimal by 100 and then put in the percentage sign. 32 0. 32 x 100 = = % 100 32 Write each decimal as a percentage. Remember to show your workings as above. a. 0. 29 b. 0. 55 c. 0. 03 d. 0. 16 e. 0. 6 f. 1. 25

Fraction Percentage A percentage needs to be out of a hundred, so multiply fraction to make the denominator 100, then add the percentage sign. 6 x 4 25 x 4 24 = 24% = 100

A percentage needs to be out of a hundred, so multiply fraction to make the denominator 100, then add the percentage sign. 6 x 4 = 24% 25 x 4 100 Write each fraction as a percentage. Remember to show your workings as above. a. 7 25 b. 3 10 c. 19 20 d. 17 50 e. 11 40 f. 7 8

Questions 1. 2. 3. 4. 5. 6. 7. 8. Of the 300 members of a social club 50% are men. How many members are women? Gillian came home and told her dad that she got 100% of her spellings correct. She told her mum that there were 25 spellings to learn. How many spellings did Gillian get wrong? Every year a school library likes to replace 1% of its books. One year the library had 2000 books. How many did it replace? If 23% of pupils go home for lunch, what percentage do not go home for lunch? If 61% of the population takes part in the National Lottery, what percentage do not take part? If 37% of members of a gym are males, what percentage of the members are females? I calculated that 28% of my time is spent sleeping and 45% is spent working. How much time is left to spend doing something else? In one country, 24. 7% of the population is below the age of 16 and 13. 8% of the population is aged over 65. How much of the population is aged from 16 to 65 inclusive?

Plenary – copy this triangle into your book and answer the questions A question about today’s lesson you would like answered One thing I knew already One new thing I have learnt

Answers a. 8% = 8 = 2 100 25 b. 50% = 50 = 1 100 2 c. 25% = 25 = 1 100 4 d. 35% = 35 = 7 100 20 e. 90% = 90 = 9 100 10 f. 75% = 75 = 3 100 4. . .

Answers a. 27% = 27 100 b. 27% = 85 100 c. 27% = 13 100 d. 27% = 6 100 e. 80% = 80 100 f. 32% = 32 100 = 27÷ 100 = 0. 27 = 85÷ 100 = 0. 85 = 13÷ 100 = 0. 13 = 6÷ 100 = 0. 06 = 80÷ 100 = 0. 8 = 32÷ 100 = 0. 32

Answers a. 9 = 9÷ 15 =0. 6 15 b. 3 = 3÷ 40 = 0. 075 40 c. 19 = 19÷ 25 = 0. 76 25 d. 5 = 5÷ 16 = 0. 3125 16 e. 1 = 1÷ 20 = 0. 05 20 f. 1 = 1÷ 8 = 0. 125 8

Answers a. 0. 12% = 12 = 3 100 25 b. 0. 4% = 4 = 2 10 5 c. 0. 45% = 45 = 9 100 10 d. 0. 68% = 68 = 34 100 50 e. 0. 25% = 25 = 1 100 4 f. 0. 625% = 625 = 5 1000 8. . .

Answers a. 0. 29 = 0. 29 x 100 = 29% a. 0. 55 = 0. 55 x 100 = 55% a. 0. 03 = 0. 03 x 100 = 3% a. 0. 16 = 0. 16 x 100 = 16% a. 0. 6 = 0. 6 x 100 = 60% a. 1. 25 = 1. 25 x 100 = 125%

Answers a. 7 25 b. 3 10 c. 19 20 d. 17 50 e. 11 40 f. 7 8 x 4 = 28% x 4 100 x 10 = 30% x 10 100 x 5 = 95% x 5 100 x 2 = 34% x 2 100 x 2. 5 = 27. 5% x 2. 5 100 x 12. 5 = 87. 5% x 12. 5 100

Answers 150 2. 0 3. 20 4. 77% 5. 39% 6. 63% 7. 27% 8. 61. 5% 1.