Contents. More or Less. Additional Practice. Answers to Check Your Work. Section D

Transcription

1 Contents Section Enlarge or Reduce 26 iscount 28 Sales Tax 29 Growing Interest 31 Summary 32 Check Your Work 33 Additional Practice Answers to Check Your Work Contents v

2 Enlarge or Reduce Maritza, Laura, and Jamel are opening a new store called Roll On. To advertise the grand opening, Maritza and Jamel designed a flyer with a picture of an in-line skater. Here is the picture that Maritza and Jamel want to use for the flyer. They realized that the picture had to be reduced to fit on the flyer. Laura suggested that they use a photocopier to see what the reduced picture would look like. Jamel and Maritza agreed. They found a photocopier that could reduce originals to 25 percent and enlarge originals to 400 percent. 26

3 1. Reflect What does it mean to reduce to 25 percent and enlarge to 400 percent? Give examples to illustrate your explanation. 2. a. Suppose they reduce the picture to 50%. What will the new width and length be? Show your calculations. b. Complete the arrow string to describe a reduction to 50%. GRAN OPENING You are invited to the grand opening of Roll On, a store for in-line skaters. Come see our great selection at 3563 Main Street. original length reduced length The result of this reduction is still too large to fit on the flyer. Maritza suggests, Just take the reduced copy and reduce it again to 50%. Then we will see if that fits. 3. a. What are the width and length after two successive reductions to 50%? b. escribe the calculation to make two reductions of 50%. c. How can they get the same result, starting with the original and using just one reduction? The group has gone to a lot of trouble to find the effect of a reduction. It would be a lot easier if the print shop had a chart that shows the measurements of an object after it is reduced. 4. Copy and fill in the table below for making a reduction to 30%. Original Length (in cm) Length Reduced to 30% 5. a. How can you use a calculator to find the effect of a reduction to 30%? b. Use arrow language to describe this calculation. Section : 27

4 The group wants to make a poster using the original picture. This time the picture has to be enlarged. 6. Find the dimensions of a picture 10 centimeters (cm) by 15 cm enlarged to 200%. Show your calculations. The result is too small for the poster, so they decide to enlarge the original picture to 250%. 7. a. Find the dimensions of the picture (10 cm by 15 cm) enlarged to 250%. Show your calculations. b. Use arrow language to describe this calculation. Suppose you want to make an enlargement to 200%. The photocopier you are using enlarges to only 150%. 8. a. Will two enlargements to 150% give the desired result? Explain. b. Find two enlargements that can be used with this photocopier to produce a final enlargement as close as possible to 200%. Copy the arrow string to describe your result. original length. enlarged length iscount $12.80 discount 25% Maritza and Jamel went to the Office Supply Store to buy a frame for the poster. There were several frames for sale. Maritza liked the one shown on the left. 9. a. What is the discount in dollars? b. Maritza calculated the discount with one multiplication: 0.25 $ Explain why this is correct. The percent bar can be helpful for finding an explanation. $0 $12.80 discount 25% 0% 100% c. Calculate the sale price for this frame. 28

5 $ a. Explain one multiplication that can be used to calculate the discount of this frame. b. Find the sale price of this frame. Maritza and Jamel decided to buy this frame. When they checked out, they saw the cashier use a calculator to calculate the sale price. discount 35% Reflect Explain why this method works for calculating the sale price. Sales Tax Maritza and Jamel paid more than $9.75 for the frame. When they looked at the bill, they noticed a sales tax added to their purchase. Sales taxes help pay for local community services. In many cities, the sales tax is 8%. So for an item priced at $20, you pay $20 plus 8% of $20. Here are three ways to calculate the sales tax (8%) for a $20 purchase. One method uses a ratio table. 12. a. Copy the ratio table and fill in the dollar amounts for an 8% tax. Price (in dollars) % Tax (in dollars) b. Use this ratio table to find the sales tax (8%) for a $20 purchase. Another method uses a percent bar. $0 $10 $20 0% 50% 100% 13. Copy this percent bar in your notebook and use it to find the sales tax (8%) for a $20 purchase. Section : 29

6 A third method uses arrow language. Price Tax amount It helps to remember the benchmark relationships for 1%, which are and a. What fraction corresponds to 8%? b. What decimal corresponds to 8%? c. Use arrow language (and a calculator) to show how to find the sales tax (8%) for a $20 purchase. 15. Copy the chart and fill in the last two rows. Use a sales tax of 19%. Price in ollars $ $10.00 $1.00 Tax in ollars Total Cost with Tax Laura wants to compute the final cost of an item with a 19% sales tax, using one multiplication calculation. She uses arrow language to show what to multiply. Price 1.19 Total cost with tax 16. a. Explain why this arrow language is correct. b. Write the arrow string for calculating the total cost with an 8% sales tax. As Maritza and Jamel left Save Supermarket, Jamel bought the items on the left. 17. Find Jamel s total bill, with a sales tax of 8% included. Maritza paid $12.63 at Save Supermarket. She wonders how much of the dollar amount is tax. The sales tax is 8%. 18. a. How can Maritza find out using arrow language? b. Calculate the tax Maritza paid. 30

7 Growing Interest Laura visited the local bank to open business accounts for their new store, Roll On. She spoke with Leticia Beligrado. When she finished setting up the accounts, she asked Ms. Beligrado to make a donation for the grand opening. Ms. Beligrado was willing to donate a $250 savings account as a grand opening prize, but she wanted to make the prize more attractive by specifying that the money must stay in the bank for three years. The savings account earns 2% interest every year. 19. Reflect Research the savings plans available at your local bank. Write a paragraph describing the options. If you win the grand opening prize, you would begin with $250 in the savings account. With a 2% annual interest rate, the bank would add 2% of $250 by the end of the first year. As a result, you would have 102% of the original prize. $0 $250 0% 100% 102% 20. a. How much money would you have after one year? b. The savings account would earn an additional 2% of the new balance by the end of the next year. How much money would be in your account at the end of the second year? c. At the end of the third year? The money in the account grows quite nicely in just a few years. 21. Reflect Explain why the total interest earned grows larger each year. Section : 31

8 In this section, you studied percent increase and decrease and applied it to resizing pictures and calculating sales tax and interest. There are many tools you can use to calculate a percent increase or decrease. Use a ratio table. For a percent increase, to find the tax and total cost using a sales tax of 8%: Price in ollars $100 $10 $1 $12 Tax in ollars $8 $0.80 $0.08 $0.96 Total Cost $108 $10.80 $1.08 $12.96 Use a percent bar. For a percent decrease, to find the sale price of a $12.80 item with a 25% discount: $0 $9.60 $12.80 discount 25% 0% 75% 100% For a percent increase, to find this year s profit increased 25% from last year s profit of $12,800: $0 $12,800 $16,000 increase 25% 0% 100% 125% 32

9 Use a double number line. For a percent decrease, to find the length of a 20-cm photo reduced to 80%: 0 cm 4 cm 16 cm 20 cm 0% 20% 80% 100% Use arrow language. For a percent increase, to find the total cost of an item with a 19% sales tax included: Price 1.19 Total, tax included Brenda and Kim are writing an article for the school newspaper. They need to reduce a photo with dimensions 12 cm by 18 cm. 1. a. What are the new dimensions of the picture if it is reduced to 50%? b. If the original picture is reduced to 75%? Afterward, the layout editor informs them that she allotted a blank space of 5 cm by 10 cm for their photo. 2. What reduction can Brenda and Kim use to fit their photo in the allotted blank space? Ron and Ben are designing a poster for the school band concert. They have a picture they want to make 5 times as long and wide as it is now. 3. a. What enlargement would they have to make to have all measurements 5 times as big? Section : 33

10 The copier they are using enlarges to only 200%. They will need to make several enlargements. b. How can they do this? Use arrow language to describe the enlargements they might use. 4. Which multiplication calculation can you use to find the total cost of an item that has a 12% sales tax? Salali buys the following items. (Prices do not include tax.) Envelopes $2.05 A set of 12 pens $5.99 A birthday card $1.80 A magazine $ Find Salali s total bill including 12% tax. You have used percent bars, double number lines, arrow language, and multiplications to describe increases and decreases. Which one do you prefer? Why? 34

11 Additional Practice Section arnel must make a poster for a presentation in his history class. He plans to enlarge a small drawing that is 28 cm by 40 cm. 1. a. How big is the poster if arnel enlarges the drawing to 115%? 125%? b. arnel enlarges the drawing to 150%. It is too small. He decides he would like to enlarge it another 150%. How large is the resulting poster? uring his presentation, arnel plans to hand out two pictures. The pictures are both 21 cm by 27 cm. The photocopier can reduce pictures only to 75%, 70%, or 60%. 2. Explain what arnel can do to reduce his two pictures so they both fit onto one sheet of paper that is 21.5 cm by 28 cm and the pictures are as large as possible. Laura s grandparents started a college fund for her on her twelfth birthday. They put $500 in a savings account that earns 4% interest every year. 3. a. How much is in the account after one year? What percent of the original amount is this? b. When Laura enters college in six years, how much money will she have in her account? Additional Practice 37

12 Answers to Check Your Work Section 1. a. The new measurements are 6 cm by 9 cm. Sample calculations: 50% of 12 cm is 1 2 of 12 cm or 6 cm. 50% of 18 cm is half of 18 cm or 9 cm. b. The new measurements are 9 cm by 13.5 cm. Sample calculations: Reduced to 75%, new measurements are 3 4 of old measurements. 1 4 of 12 cm is 3 cm, and 3 4 is 3 times as much, so 3 3 cm 9 cm. 1 4 of 18 cm is cm, and 3 4 is 3 times as much, so cm 13.5 cm. 2. Reductions must be close to and a little less than reducing to 42%. Here is one strategy. Using 1a, reducing the picture to 50% is too wide, but not too long. Reducing to 40%, I need to check only the width. 40% of 12 cm: 10% of 12 cm is 1.2 cm, so 40% is 4.8 cm (4 1.2 cm). So the width (4.8 cm) is less than 5 cm, so reducing to 40% will fit. 46

13 Answers to Check Your Work 3. a. 5 times as big is an enlargement to 500%. b. measurement new measurement There are different ways to solve this problem. One way is the following. They need to make several enlargements. Start with 200% or 2. Then use this 200% or 2 enlargement again. This means the result is now 400%, or 4. This is still too small. An enlargement of the enlarged picture to 125% will result in an enlargement of the original picture to 500%. Another way to solve this problem is to choose a measurement (for example, 100 cm) and then use the arrows to find the final amount ? 500 To get from 400 to 500, you need to multiply by (1 1 4 ) 400 (1.25) 4. Multiply by Total including tax is $ You can calculate the tax on each item and find the price and add all prices, but it is easier to add the prices first and calculate the tax for the total. Total without tax is $ Including tax: $ $15.44 Answers to Check Your Work 47