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## Lesson 8.1.3

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**Lesson 8.1.3**Percent Increases and Decreases**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases California Standards: Number Sense 1.3 Convert fractions to decimals and percents and use these representations inestimations, computations, and applications. Number Sense 1.6 Calculate the percentage of increases and decreases of a quantity. What it means for you: You’ll see how to use percents to show how much a quantity has gone up or down by. • Key words: • percent • increase • decrease • compare**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases When a number goes up or down, you can use percents to describe how much it has changed by. This can come in useful in real-life situations like comparing price rises or working out sale discounts.**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases You Can Increase a Number by a Given Percent You can increase a number by a certain percent of itself. So, say if you want to increase a number by 10%, you have to work out what 10% is, then add this to the original number.**20**100 20% of 50 = × 50 = 10 Lesson 8.1.3 Percent Increases and Decreases Example 1 Increase 50 by 20%. Solution First work out 20% of 50: This is the amount you need to increase 50 by: 50 + 10 = 60 So, 50 increased by 20% is 60. Solution follows…**8**100 8% of 14 cm = × 14 cm = 0.08 × 14 cm = 1.12 cm Lesson 8.1.3 Percent Increases and Decreases Example 2 A photograph with a length of 14 cm is enlarged. This increases its length by 8%. What is the final length of the enlarged photograph? Solution First work out 8% of 14 cm: This is the amount you need to increase 14 cm by: 14 cm + 1.12 cm = 15.12 cm The length of the enlarged photograph is 15.12 cm. Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Guided Practice In Exercises 1–4, find the total after the increase. 1. 100 is increased by 10% 2. 20 is increased by 5% 110 21 3. 165 is increased by 103% 4. 40 is increased by 20.5% 334.95 48.2 5. Sarah goes out for lunch. Her bill comes to $15. She wants to leave an extra 17% as a tip for the server. How much should Sarah leave in total? $17.55 Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases You Can Describe an Increase as a Percent When a number goes up, you can give the increase as a percent of theoriginal number.**x × 24 = 3**100 Lesson 8.1.3 Percent Increases and Decreases Example 3 A loaf of bread has 24 slices. As a special buy, a larger loaf is sold, which contains 27 slices. What is the percent increase in the number of slices? Solution 27 – 24 = 3 First find the increase in the number of slices: x% of 24 is 3 Call x the percent increase and write an equation: x × 24 = 300 Multiply both sides by 100 x = 12.5 Divide both sides by 24 The number of slices has increased by 12.5%. Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Guided Practice 6. Reynaldo has 140 marbles. He buys 63 more. By what percent has he increased the size of his marble collection? 45% 7. A company increases its number of staff from 1665 to 1998. What is this as a percent increase? 20% Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases You Can Decrease a Number by a Given Percent Too You can also decrease a number by a percentof itself.**15**100 15% of 80 = × 80 = 0.15 × 80 = 12 Lesson 8.1.3 Percent Increases and Decreases Example 4 Decrease 80 by 15%. Solution First work out 15% of 80: This is the amount you decrease 80: 80 – 12 = 68 So, 80 decreased by 15% is 68. Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Guided Practice In Exercises 8–11, find the total after the decrease. 8. 100 is decreased by 15% 9. 40 is decreased by 35% 10. 37 is decreased by 8% 11. 10 is decreased by 3.9% 100 × 0.15 = 15, 100 – 15 = 85 40 × 0.35 = 14, 40 – 14 = 26 37 × 0.08 = 2.96, 37 – 2.96 = 34.04 10 × 0.039 = 0.39, 10 – 0.39 = 9.61 12. Tandi has saved $152. She spends 25% of her savings on a shirt. How much does Tandi have left? 152 × 0.25 = 38152 – 38 =$114 Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases You Can Describe a Decrease as a Percent When a number goes down, you can use a percentto describe how much it has changed by. The decrease is described as a percent of theoriginal number.**× 12.8 feet = 3.2 feet**x 100 Lesson 8.1.3 Percent Increases and Decreases Example 5 A river is 12.8 feet deep on January 1. By September 1, the depth has fallen to 9.6 feet. Find the percent decrease in the river depth. Solution First find the amount that the depth is decreased by: 12.8 feet – 9.6 feet = 3.2 feet Call x the percent decrease and write an equation. x% of 12.8 feet is 3.2 feet x × 12.8 feet = 320 feet Multiply both sides by 100 x = 25 Divide both sides by 12.8 feet The river depth has decreased by 25%. Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Guided Practice Find the percent decreases in Exercises 13–14. 13. 90 is reduced to 81 14. 4 is reduced to 3.5 10% 12.5% 15. Jon is selling buttons for a fund-raiser. He starts with 280 buttons and sells all but 21. What percent of his stock has Jon sold? 92.5% Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Use Percents to Compare Changes You can use percent increases and decreasesto comparehow much two numbers have changed relative to each other. For example: Snowman 2:7 foot 6 foot Snowman 1:6 foot 5 foot Snowman 1 and Snowman 2 have both lost the same amount in height as they’ve melted — 1 ft. 17% decrease 14% decrease But the percent decrease is greater for Snowman 1 — 1 ft is a bigger change relative to 6 ft than to 7 ft.**× 160¢ = 5¢**× 40¢ = 5¢ x x 100 100 Lesson 8.1.3 Percent Increases and Decreases Example 6 In a store, a bagel is 40¢ and a loaf of bread is $1.60. The store raises the price of both items by 5¢. Which has the larger percent increase in cost? Solution The price of both items is increased by 5¢. So the percent increase in the cost of a bagel is: (5¢ × 100) ÷ 40¢ = 12.5, so a 12.5% increase. And the percent increase in the cost of a loaf is: You need to have the original value and the increase in the same units. $1.60 has been converted to 160¢ here. (5¢ × 100) ÷ 160¢ = 3.125, so a 3.125% increase. The bagel shows the larger percent increase in cost. Solution follows…**Lesson**1.1.1 Lesson 8.1.3 Percent Increases and Decreases Guided Practice 16. Cindy has 250 baseball cards. Jim has 200 baseball cards. Both buy 50 extra cards. Whose collection increased by the larger percent? Cindy: (50 × 100) ÷ 250 = 20% increaseJim: (50 × 100) ÷ 200 = 25% increaseSo, Jim’s collection increased by the larger percent. 17. Ava and Ian have a contest to see whose sunflower will increase in height by the greatest percent. Ava’s starts 10 cm high and grows to 100 cm. Ian’s starts 20 cm high and grows to 110 cm. Who won? Ava: (90 × 100) ÷ 10 = 900% increaseIan: (110 × 100) ÷ 20 = 550% increaseSo, Ava won. Solution follows…**Lesson**8.1.3 Percent Increases and Decreases Independent Practice In Exercises 1–6, find the amount after the percent change. 1. Increase 200 by 25% 2. Decrease 200 by 75% 3. Increase 49 by 7% 4. Decrease82 by 56% 5. Increase 50 by 142.6% 6. Decrease 80 by 33.2% 250 50 52.43 36.08 121.3 53.44 Solution follows…**Lesson**8.1.3 Percent Increases and Decreases Independent Practice 7. At store A, apples used to cost $1.50 a pound. Then the price rose by 6%. What is the new cost of a pound of apples? $1.59 8. Kiona’s brother Otis is 115.5 cm tall. The last time he was measured, his height was 110 cm. Find the percent increase in his height. 5% Solution follows…**Lesson**8.1.3 Percent Increases and Decreases Independent Practice 9. Last year, School C had 120 6th grade students. This year they have 5% fewer 6th graders. How many fewer students is this? 10. Mr. Hill’s house rental costs $900 a month. He moves to a house with a rental of $828 a month. Find the percent decrease in his rental. 11. Duena collects comic books. 10 years ago, Comic A was worth $70 and Comic B was worth $40. Now Comic A is worth $84 and Comic B is worth $49. Which has shown the greater percent increase in value? 6 8% Comic B Solution follows…**Lesson**8.1.3 Percent Increases and Decreases Round Up Percent increases and decreases tell you how big a change in a number is when you compare it to the original amount. It’s useful to be able to work them out in real-life situations, especially when you’re thinking about tips and discounts — and you’ll learn more about them in Section 8.2.