Percents

1. Percents Definition: A percent is another way of showing a fraction whose denominator is 100. Percent means parts per hundred. The word percent comes from the Latin phrase per centum, which means each | hundred. In mathematics, we use the symbol % for percent.

2. Percents Population of China: 1,321,851,888 (July 2007 est.) ----------- out of ----------- Population of the world: 6,602,224,175 It’s hard to grasp the relationship when China’s population is written as a fraction of world population. But turn it into a percent…. Almost exactly 20% Just about 20 out of every one hundred people in the world lives in China.

3. Percents • This proportion is the key to solving percent problems. You should memorize it.

4. Percents

5. Let’s say that 4 out of 16 people in this class absolutely love math. We could represent that as a ratio 4 to 16 or . If we want to know what percentage of people surveyed love math, we look for an equivalent fraction with a denominator of 100.

6. To solve any basic percent problem we use the same steps: • Write two fractions bars with = between, and write 100 as the second fraction’s denominator • Fill in the information we have according to the model.

7. 3. Multiply along the diagonal whatever direction we have two numbers (not the ?) In this case – 4 x 100 = 400 4. Divide the answer from step 4 by the remaining number (in this case 16) 400/16 = 25

8. Percents • GED percent problems will give you two out of the 3 necessary pieces of information. (Note that the 100 on the bottom right doesn’t change)

9. Example 1 – Finding the part • What is 20% of 300? • Step 1 – • Step 2 – we know the percent and the total. We’re trying to find the part, so

10. Example 1 – Finding the part • Step 4 – • Cross multiply  20 x 300 = 6000 • Step 5 – • divide by the remaining number 6000/100 = 60 20% of 300 is 60

11. Example 2 – Finding the total • 18 is 15% of what number? • Step 1 – • Step 2 – we know the part and the percent. We’re trying to find the total, so

12. Example 2 – Finding the total • Step 4 – • Cross multiply  18 x 100 = 1800 • Step 5 – • divide by the remaining number 1800/15= 120 15% of 120 is 18

13. Example 3 – Finding the percent • 70 is what percent of 800? • Step 1 – • Step 2 – we know the part and the total. We’re trying to find the percent, so

14. Example 3 – Finding the percent • Step 3– • Cross multiply  70 x 100 = 7000 • Step 4 – • divide by the remaining number 7000/800 = 8.75 70 is 8.75% of 800

15. You try: • 50 is what percent of 250? • What is 30% of 500? • 18 is 6% of what number? (press pause)

16. You try: • 50 is what percent of 250? (50 x 100)/250 = 20 • What is 30% of 500?  (30x 500)/100 = 150 • 18 is 6% of what number?  (18 x 100)/6 = 300

17. Percents • Some problems using percents are a little more complicated. • Markup • Discount • Tax • Percent Change

18. Percents Mark-up Fred Meyer buys potted palms from a local grower for $3.50 each. They sell them to the public at a 90% markup What is 90% markup? 90 x 3.50 = 315 315 ÷ 100 = 3.15

19. Percents • Mark-up Fred Meyer buys potted palms from a local grower for $3.50 each. They sell them to the public at a 90% markup • Markup is $3.15 – this is added to the original cost of the plant to reach the sale price. • $3.50 + $3.15 = $6.65

20. Percents • Discount – Fred Meyer is having a 20% off sale on potted palms. How much are the plants now? • They are selling for $6.65 • We need to find 20% of $6.65

21. Percents • Discount – Fred Meyer is having a 20% off sale on potted palms. How much are the plants now? • They are selling for $6.65 • We need to find 20% of $6.65

22. Percents 20 x 6.65 = 133 133 ÷ 100 = 1.33 The discount is $1.33, so the price is now 6.65 – 1.33 = 5.32 Sale price: $5.32

23. Percents • Tax – If Washington State sales tax is 7% and you buy a potted palm at the sale price, how much will you pay at the register?

24. Percents • Tax – If Washington State sales tax is 7% and you buy a potted palm at the sale price, how much will you pay at the register? • We need to find 7% of 5.32

25. Percents 7 x 5.32 = 37.24 37.24 ÷ 100 = .3724 (since we’re talking about money we round to the nearest cent - .37)

26. Percents • The price of the plant was $5.32 and the tax is 37¢, so we need to add the tax to the price to get the final total: • 5.32 + .37 = 5.69 • The total price at the register is $5.69

27. Percents • Percent Change Problems – amount of change becomes part, original becomes total.

28. Percents • % Increase • James used to make $8.50/hr. His boss gave him a raise, and now he makes $8.84/hr. What percent raise did James get?

29. Percents • Percent Increase • James used to make $8.50/hr. His boss gave him a raise, and now he makes $8.84/hr. What percent raise did James get? • The original was 8.50, and the amount it changed by is 8.84 – 8.50 = .34

30. .34 x 100 = 34 34 ÷ 8.5 = 4 James received a 4% raise.

31. Percents • Percent Decrease • A cookbook was reduced from $20 to $15. What percent off was the book?

32. Percents 5 x 100 = 500 500 ÷ 20 = 25 The book was 25% off – The price had been decreased by 25%

33. Percents • Try the practice on pages 130 – 133 of the book. • Do GED Practice pages 15 – 17 and submit your answers using the answer sheet on BB.