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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