6-1 Study Guide and Intervention - Loudoun County Public ...

Lesson 6-1

NAME ________________________________________________ DATE ____________ PERIOD _____

6-1 Study Guide and Intervention

Ratios and Rates

Ratios written as 7 to 12, 7:12, and 7 are different ways to write the same ratio. Ratios should be

written in simplest form.

12

Example 1

6 fe et 15 inches

Express the ratio 6 feet to 15 inches as a fraction in simplest form.

Write the ratio as a fraction.

7125 iinn cchheess

Convert feet to inches.

7224 in ches

155 inches

24

5

Divide the numerator and denominator by the GCF, 3.

Written as a fraction in simplest form, the ratio is 24 to 5.

Example 2 Express the ratio $10 for 8 fish as a unit rate. Round to the nearest

tenth, if necessary.

10 do llars 8 fish

8

Write the ratio as a fraction.

10 do llars 1.25 d ollars

8 fish

1 fish

Divide the numerator and denominator by 8 to get a denominator of 1.

8 The unit rate is $1.25 per fish.

Exercises

Express each ratio as a fraction in simplest form.

1. 4 weeks to plan 2 events 2 1

2. 9 inches to 2 feet 3 8

3. 8 teaspoons to 12 forks 2 3

4. 16 cups to 10 servings 8 5

5. 7 shelves to 84 books

1 12

6. 6 teachers to 165 students

2 55

Express each ratio as a unit rate. Round to the nearest tenth, if necessary.

7. $58 for 5 tickets $11.60 per 1 ticket 8. $4.19 for 4 cans of soup $1.05 per can

9. $274.90 for 6 people

$45.82 per person

10. 565 miles in 12 hours

47.1 miles per hour

? Glencoe/McGraw-Hill

299

Glencoe Pre-Algebra

NAME ________________________________________________ DATE ____________ PERIOD _____

6-1 Skills Practice

Ratios and Rates

Express each ratio as a fraction in simplest form.

1. 8 pencils out of 12 pens 2 3

3. 27 rooms to 48 windows 9 16

5. 75 cats to 100 dogs 3 4

7. 3 gallons to 15 quarts 45

2. 42 textbooks to 28 students 3 2

4. 15 angel fish to 75 fish 1 5

6. 6 aces out of 24 serves 1 4

8. 30 feet to 11 yards 1101

Express each ratio as a unit rate. Round to the nearest tenth, if necessary.

9. $9 for 6 cans of soup

10. $39 for a case of 75 bananas

$1.50 per can

$0.52 per banana

11. 108 miles in 6 days

12. 51 meters in 8 seconds

18 miles per day

6.4 meters per second

13. 21 new pairs of sneakers in 7 years

14. 52 feet for 8 costumes

3 new pairs of sneakers per year 6.5 feet per costume

15. 40 sneezes in 20 minutes

16. $2702 from 28 people

2 sneezes per minute

$96.50 per person

Convert each rate using dimensional analysis.

17. 12 m /min = ? cm /s

18. 8 qt/min = ? gal/ h

20

120

19. 44 yd/s = ? mi/h

20. 10 c/min = ? qt /h

90

150

21. 32 ft /h = ? yd/day

22. 56 mi /h = ? ft /min

256

4928

23. 40 cm /s = ? m/min

24. 180 in./min = ? yd/h

24

300

? Glencoe/McGraw-Hill

300

Glencoe Pre-Algebra

Lesson 6-1

NAME ________________________________________________ DATE ____________ PERIOD _____

6-1 Enrichment

Comparison Shopping

Rates are useful and meaningful when expressed as a unit rate. For example, which is the better buy--one orange for $0.50 or 8 oranges for $3.49? To find the unit rate for 8 oranges, divide $3.49 by 8. The result is $0.44 per orange. If a shopper needs to buy at least 8 oranges, then 8 oranges for $3.49 is the better buy.

For each exercise below, rates are given in Column A and Column B. In the blank next to each exercise number, write the letter of the column that contains the better buy.

Column A

___A___ 1. 1 apple for $0.19

___A___ 2. 20 pounds of pet food for

$14.99

Column B 3 apples for $0.59

50 pounds of pet food for $37.99

___B___ 3. A car that travels 308 miles

on 11 gallons of gasoline

___B___ 4. 10 floppy discs for $8.99

A car that travels 406 miles on 14 gallons of gasoline

25 floppy discs for $19.75

___B___ 5. 1-gallon can of paint for

$13.99

___A___ 6. 84 ounces of liquid detergent

for $10.64

5-gallon can of paint for $67.45 48 ounces of liquid detergent for $6.19

___A___ 7. 5000 square feet of lawn food

for $11.99

___A___ 8. 2 compact discs for $26.50

12,500 square feet of lawn food for $29.99

3 compact discs for $40.00

___A___ 9. 8 pencils for $0.99

12 pencils for $1.49

___B___ 10. 1000 sheets of computer

paper for $8.95

5000 sheets of computer paper for $41.99

? Glencoe/McGraw-Hill

303

Glencoe Pre-Algebra

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