NAME ________________________________________________ DATE ____________ PERIOD _____
6-1
Study Guide and Intervention
Ratios and Rates
7
Ratios written as 7 to 12, 7:12, and are different ways to write the same ratio. Ratios should be
12
written in simplest form.
Example 1
Express the ratio 6 feet to 15 inches as a fraction in simplest form.
6 feet
15 inches
72 inches
15 inches
Convert feet to inches.
7224 inches
155 inches
Divide the numerator and denominator by the GCF, 3.
Lesson 6-1
Write the ratio as a fraction.
24
5
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 dollars
8 fish
Write the ratio as a fraction.
8
10 dollars
1.25 dollars
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
3
1
5. 7 shelves to 84 books 12
3. 8 teaspoons to 12 forks
2. 9 inches to 2 feet
3
8
4. 16 cups to 10 servings
8
5
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
9. $274.90 for 6 people
8. $4.19 for 4 cans of soup $1.05 per can
10. 565 miles in 12 hours
$45.82 per person
©
Glencoe/McGraw-Hill
47.1 miles per hour
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. 42 textbooks to 28 students
2
3
3. 27 rooms to 48 windows
3
2
4. 15 angel fish to 75 fish
9
16
5. 75 cats to 100 dogs
1
5
6. 6 aces out of 24 serves
3
4
7. 3 gallons to 15 quarts
1
4
8. 30 feet to 11 yards
4
5
10
11
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
11. 108 miles in 6 days
$0.52 per banana
12. 51 meters in 8 seconds
18 miles per day
13. 21 new pairs of sneakers in 7 years
6.4 meters per second
14. 52 feet for 8 costumes
3 new pairs of sneakers per year
15. 40 sneezes in 20 minutes
6.5 feet per costume
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
19. 44 yd/s = ? mi/h
120
20. 10 c/min = ? qt /h
90
21. 32 ft /h = ? yd/day
150
22. 56 mi /h = ? ft /min
256
23. 40 cm /s = ? m/min
4928
24. 180 in./min = ? yd/h
24
©
Glencoe/McGraw-Hill
300
300
Glencoe Pre-Algebra
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?
Lesson 6-1
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 B
Column A
A
______
1. 1 apple for $0.19
3 apples for $0.59
A
______
2. 20 pounds of pet food for
$14.99
50 pounds of pet food for $37.99
B
______
3. A car that travels 308 miles
on 11 gallons of gasoline
A car that travels 406 miles on
14 gallons of gasoline
B
______
4. 10 floppy discs for $8.99
25 floppy discs for $19.75
B
______
5. 1-gallon can of paint for
$13.99
5-gallon can of paint for $67.45
A
______
6. 84 ounces of liquid detergent
for $10.64
48 ounces of liquid detergent for $6.19
A
______
7. 5000 square feet of lawn food
for $11.99
12,500 square feet of lawn food for
$29.99
A
______
8. 2 compact discs for $26.50
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
©
Glencoe/McGraw-Hill
5000 sheets of computer paper for $41.99
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Glencoe Pre-Algebra