1. PRE-ALGEBRA

2. Lesson 6-9 Warm-Up

3. PRE-ALGEBRA How do you solve a word problem involving rational numbers in more than one form (i.e. a mixture of fractions, decimals, and percents) To solve a problem involving a combination of decimals, fractions, and / or percents, write all of the numbers in the same form before doing anything else. This way, the numbers can be accurately compared to one another. Example: A family drove 800 mi. from Oakland, Ca. to Seattle, Wash. They drove of the trip on the first day, 0.2 of the trip the second day, 30% of the trip the third day, and 150 mi. on the last day. On which day did they drive the farthest? Method 1: Compare the distance traveled each day. 800 mi. = = 250 mi. First Day 0.2 800 mi. = 1600 = 160 mi. Second Day 0.30 800 mi. = 2400 = 240 mi. Third Day (30% = 0.30) = 240 mi. Fourth Day They drove the furthest, 250 mi., on the first day 5 16 5 16 5 16 800 1 1 50 Applications of Rational Numbers (6-9)

4. PRE-ALGEBRA Method 2: Compare the four parts of the trip in the same form, like decimals. = 5  16 = 0.3125 First Day = 0.2 Second Day 30% = 0.30 = 0.3. Third Day = 150  800 = 0.1875 Fourth Day 0.3125  0.30  0.20  0.1875 or First  Third  Second  Fourth They drove the furthest on the first day. 5 16 150 800 Applications of Rational Numbers (6-9)

5. PRE-ALGEBRA Janice spent $75.00 at the store. She spent 0.25 of the money on a sweater, 22% on shoes, of the money on a jacket, and the rest on a shirt. Which item cost the most? 2525 Method 1: Find the cost of each item. Compare. 0.25 $75.00 = $18.75 Janice spent 0.25 of $75.00 on a sweater. 0.22 $75.00 = $16.50 Janice spent 22%, or 0.22, of $75.00 on shoes. 2525 2525 $75.00 = $30.00 Janice spent of $75.00 on a jacket. $75.00 – $18.75 – $16.50 – $30.00 = $9.75 Janice spent the remaining amount on a shirt. Janice spent the most, $30.00, on the jacket. Applications of Rational Numbers LESSON 6-9 Additional Examples

6. PRE-ALGEBRA (continued) Method 2: Write the portions spent on the four items in the same form. Compare. 0.25 The portion spent on the sweater is a decimal. 22% = 0.22 Write the percent spent on the shoes as a decimal. 2525 = 0.4 Write the fraction spent on the jacket as a decimal. 9.75 75 = 0.13 Divide 9.75, the amount spent on the shirt, by 75 to find the portion spent on the shirt. Compare the decimals: 0.4 > 0.25 > 0.22 > 0.13. Janice spent the most on the jacket. Applications of Rational Numbers LESSON 6-9 Additional Examples

7. PRE-ALGEBRA How do you compare rates in different forms? To compare two or more rates written in different forms, write the rates in the same form (same units) so they can be compared. Example: One printer print 300 pages in 10 min. A second printer prints 40% more pages in 12 min. Which printer prints faster? Step 1: Find the unit rate of the first printer. = 300  10 = 30 pages / min.Unit rate of 1 st printer Step 2: Find the unit rate of the second printer. 40% of 300 = 0.40 x 300 = 12000 = 120 pagesFind 40% of 300 300 pages + 120 pages = 420 pages Number of pages 2 nd printer prints in 12 min. = 420  12 = 35 pages / min. The second printer prints 5 pages more per minute, so it’s faster. 300 10 420 pages 12 min. Applications of Rational Numbers (6-9)

8. PRE-ALGEBRA Gavin read 40 pages of a book in 32 minutes. Brian read 20% more pages of the same book in 40 minutes. Who read faster? Step 1: Find Gavin’s rate. 40 32 = 1.25 Divide the number of pages by the number of minutes reading. Gavin read 1.25 pages/min. Step 2: To find Brian’s rate, first find the number of pages read in 40 minutes. 20% of 40 = 0.20 40 Write 20% as a decimal. = 8 Multiply. Applications of Rational Numbers LESSON 6-9 Additional Examples

9. PRE-ALGEBRA (continued) Step 3: Brian read 20% more pages. Add. 40 + 8 = 48 Brian read 48 pages in 40 minutes. Step 4: Find Brian’s rate. 48 40 = 1.2 Divide the number of pages by the number of minutes reading. Brian read 1.2 pages/min. Gavin read more pages per minute than Brian, so Gavin's rate is faster. Applications of Rational Numbers LESSON 6-9 Additional Examples

10. PRE-ALGEBRA How can you use estimation percent problems that don’t require an exact answer.? To estimate a percent, change it to a fraction or decimal that’s close to its value. You can use the table below for common percent, fraction, and decimal equivalents. Example: A jacket is on sale for 35% off of $49.95. After the discount, 7.75% sales tax is added. Is $30.00 enough money to buy the jacket? Step 1: Estimate the discount on the jacket. 35%   0.4Round percent up to the closest fraction or decimal equivalent 49.95  50Round the price of the jacket. 35% of 49.95  0.4 50  20Estimate 35% of $49.95 The discount is about $20. 1313 Applications of Rational Numbers (6-9)

11. PRE-ALGEBRA Step 2: Estimate the sale price of the jacket. 50 – 20  30Estimate the sale price The sale price of the jacket is about $30. Step 3: Estimate the sales tax 7.75%   0.1Round percent up to the closest fraction or decimal equivalent 7.75% of 30  0.1 30  3Estimate 35% of $49.95 The sale’s tax is about $3. Step 4: Add the tax to the sales price. $30 + $3 = $33. The total cost is about $33. $30 is not enough to buy the jacket. 1 10 Applications of Rational Numbers (6-9)

12. PRE-ALGEBRA The RDI for iron is 18 mg. If a serving of cereal has 25% of the RDI for iron, about how many milligrams of iron are in one serving? 18 20 Round up to a compatible number close to 18. 1414 25% of 18 20 Estimate. = 5 Multiply. There are about 5 milligrams of iron in one serving of cereal. Applications of Rational Numbers LESSON 6-9 Additional Examples

13. PRE-ALGEBRA A pair of shoes is 25% off of $29.95. After the discount, 6.5% sales tax is added. Is $20 enough money to buy the shoes? Step 1: Estimate the discount on the shoes. 25% = 0.25 Use the decimal equivalent of 25%. 29.95 ≈ 30 Round the regular price. 25% of 29.95 ≈ 0.25 30 Estimate. = 7.5 Multiply. The discount is about $7.50. Step 2: Subtract to find the sale price of the shoes. $30 – $7.50 = $22.50 The sale price of the shoes is about $22.50. Applications of Rational Numbers LESSON 6-9 Additional Examples

14. PRE-ALGEBRA (continued) Step 3: Estimate the amount of tax. 6.5% ≈ 0.1 Use a decimal close to 6.5%. 6.5% of 22.50 ≈ 0.1 22.50 Estimate = 2.25 The amount of tax is about $2.25. Step 4: Add the tax to the sale price: $22.50 + $2.25 = $24.75. The total cost is about $24.75, so $20 is not enough. Applications of Rational Numbers LESSON 6-9 Additional Examples

15. PRE-ALGEBRA 1. Marissa spent exactly 2 hours studying. She spent 0.35 of the time on math, of the time on history, and the rest of the time on literature. Which subject did she spend the most time studying? 2. Two families are traveling in cars. The Baker family travels 60 miles in 70 minutes. The Doyan family travels 25% farther in 100 minutes. Which family travels at the faster rate? 3. Cole mixes different types of soil. The total mass of the mixture is 2,050 grams. Sand makes up 18% of the mixture’s mass. About what is the mass of the sand? 4. A shirt normally sells for $14.95. It is on sale for 25% off plus 8.00% sales tax. Is $12.00 enough to buy the shirt? history about 400 grams the Baker family 3 8 no Lesson Quiz Applications of Rational Numbers LESSON 6-9