Chapter 2 Review
!
Selected Worked Problems
Page 41
Simplifying Ratios.
Write each comparison as a ratio in fraction form in simplest terms. !
!
1. 68 to 24 !
2. 4.2 to 1.8 !
Ratios require whole numbers.
Move the decimal point 1 place
to the right for each number
68
24
=
6/ 8/ 17
2/ 4/ 6
4.2 42
=
1.8 18
cancel out a 6
!
=
17
6
=
4/ 2/ 7
1/ 8/ 3
=
7
3
!
Simplifying Rates
Write each comparison as a rate in fraction form in simplest terms.
4. 64 boys to 48 girls!
5. 18 centigrams to 45 liters!
64 boys
48 girls
18 cg
45 liter
=
6/ 4/ 4 boys
4/ 8/ 3 girls
4 boys
3 girls
Math 30 !
!
=
18/ 2 cg
4/ 5/ 5 liter
!
!
2 cg
5 liter
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Unit Rates
Convert each rate into a Unit Rate. Be sure to include the units.
7. 42 riders for 14 cars!
8. 84 grams to 12 liters!
3
14 ) 42
42
0
7
12) 84
84
0
!
=
3 riders
1 cars
=
or 3 riders per 1 car
7 grams
1 liter
or 7 grams per 1 liter
Page 42
Find the unit rate for each size of a given product and then decide which is the best buy.
!
!
10. An 8 ounce bottle of shampoo sold for $ 1.20 or a 14 ounce bottle of shampoo sold for $1.68
!
!
!
1.20 dollars
8 ounces
or
1.68 dollars
14 ounces
.15
8 1.20
8
40
40
0
.12
14 1.68
14
$ .15 per ounce
$ .12 per ounce
28
28
0
Buying 8 ounces is the best buy
Math 30 !
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Use the relationships below to convert the given measurements. Show the set up and answer.
1 foot (ft.) = 12 inches (in.)
12. Convert 60 inches to feet!
Use
!
1 yard (yd.) = 3 feet (ft.)!
13. Convert 4 feet to inches
1 ft.
so the inches cancel out
12 in.
Use
60 /in.
/ 1 ft.
•
1
12 /in.
/
12 in.
so the feet cancel out
1 ft.
4 f/t/. 12 in.
•
1
1 f/t/.
!
4 •12 in. = 48 in.
60 ft.
= 5 ft.
12
4 feet = 48 inches
60in. = 5 ft.
Page 43
Use the relationships below to convert the given measurements. Show the set up and answer.
!
16 ounces (oz.) = 1 pound (lb.) ! 4 cups = 1 quart !
4 quarts = 1 gallon
15. Convert 10 pounds to ounces !
Use
16 oz.
so the lb. cancel out
1 yd.
18. Convert 6 quarts to cups
Use
/ 16 oz.
10 /lb.
•
/
1
1 /lb.
4 cup
1 qt.
so the qt. cancel out
6 q/
/ t. • 4 cup
1
1 q/
/ t.
!
10 •16 oz. = 160 oz.
6 • 4 cup
= 24 cups
Math 30 !
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Page 44
Use the relationships below to convert the given measurements. Show the set up and answer.
!
8 fluid ounces (fl. oz.) = 1 cup
2000 pounds (lb.) = 1 ton
21. Convert 5 cups to fluid ounces (fl. oz.)!
Use
8 fl. oz.
so cups cancel out
1 cup
23. Convert 4 tons to pounds
Use
5 c/ u/ p/ 8 fl. oz.
•
1
1 c/ u/ p/
2000 lb.
1 ton
so the tons cancel out
4 ton 2000 lb.
•
1
1 ton
!
4 • 2000 lb. = 8,000 lb.
5 • 8 fl. oz
= 40 fl. oz.
Use the relationships below to convert the given measurements. Show the set up and answer.
1 inch ≈ 2.5 centimeter (cm) !
1 yard ≈ .9 meter (m)!
25. Convert 20 inches to centimeters (cm)!
Use
2.5 cm.
so the in. cancel out
1 in.
28. Convert 90 meters (m) to yards
Use
20 /in.
/ 2.5 cm
•
1
1 /in.
/
1 mile ≈ 1.6 kilometer (km)
1 yd.
so the m cancel out
.9 m
90 m
/ 1 yd.
•
1
.9 m
/
!
20 • 2.5 cm
8 in. ≅ 50 cm
Math 30 !
90 •1 yd.
.9
90 m ≅ 100 yards
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Page 44 continued
Use the relationships below to convert the given measurements. Show the set up and answer.
1 mile ≈ 1.6 kilometer (km)
29. Convert 5 miles to kilometers (km)!
Use
1.6 km.
so the mi. cancel out
1 mi.
30. Convert 14.4 kilometers (km) to miles
Use
1 mile
so the mi. cancel out
1.6 km
14.4 k/ m
/ 1 mile
•
1
1.6 k/ m
/
5 m/
/ i. 1.6 km
•
1
1 m/
/ i.
!
5 •1.6 km
14.4 •1 mile
1.6
5 mi. ≅ 8 km
14.4 km ≅ 9 miles
31. Betty's Fabrics sells fabric for 6 dollars a yard. How much would 5 feet cost? You have 5 feet of fabric and need to know the price.
You need to convert feet to yards and
then find the price of that number of yards.
5 f/e/ e/ t/ 1 y/ a/ r/d/
$6
•
•
3 f/o/ o/ t/ 1 y/ a/ r/d/
=
5• 6 $
3
= $10 for 5 feet
Math 30 !
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Page 45
Solve each proportion for x. Show all steps. Reduce answers with fractions to decimals.
6 54
= !
5 x
Cross multiply and solve for x
x 2
=
!
13 4
Cross multiply and solve for x
33.
35.
6 • x = 5 • 54
4 • x = 2 •13
6x = 270
4 x = 26
!
6x 270
=
6
6
4 x 26
=
4
4
x = 45
x = 6.5
2
inches on the map is equal to 2 miles in the real world. If the
3
actual distance between two cities is 15 miles, how many inches will they be apart on the map?
37. !The scale on a map states that
Solve using proportions.
The ratio of 2/3 inches on the map to 2 miles in real life
2
inches on the map
3
2 miles in real life
The ratio of an unknown inches on the map to 15 miles in real life
The inches on the map must go on top to match the first ratio
x inches on the map
15 miles in real life
2
inches on the map x inches on the map
3
=
2 miles in real life
15 miles in real life
cross multiply and solve for x
2
2 • x = •15
3
2x = 10
x = 5 inches on the map
Math 30 !
Chapter 2 Review pages 41 to 46!
© 2016 Eitel
Page 46
Similar Triangles. Find the missing sides of the similar triangles. Show the set up and work.
38. !
Large Δ → Small Δ
20
12 corresponds to 3
x
y
20 corresponds to x
4
y corresponds to 4
3
12
Solve for x!
!
Solve for y
Large Δ → Small Δ
12 20
=
3
x
Large Δ → Small Δ
12 y
=
3 4
!
12x = 60
3y = 48
y = 16
x=5
39.
Small Δ → Large Δ
5 corresponds to 7
x
8
7
5
9
9 corresponds to y
y
Solve for x!
8 corresponds to x
Solve for y
Small Δ → Large Δ
5 9
=
7 y
Small Δ → Large Δ
5 8
=
7 x
!
5x = 56
x = 11.2
Math 30 !
5y = 63
y = 12.6
Chapter 2 Review pages 41 to 46!
© 2016 Eitel