13
Subtracting Mixed Measures
When you subtract mixed measures, you sometimes need to borrow from the larger unit before
you can subtract. Borrow 1 pound to make 16 more ounces, 1 foot to make 12 more inches, or 1
hour to make 60 more minutes. Add these to the amount of the smaller unit already there.
7
19
11
8 lb 3 oz
– 3 lb 5 oz
4 lb 14 oz
The pound I borrow
is 16 ounces.
1. a. –
2. a. –
5¬
4¬
11¬
b. – 8¬
3 oz
15 oz
10 hr
b. – 8 hr
83
The hour I borrow
is 60 minutes.
12 + 10 = 22
1¬¬
6¬¬
2 lb
5
6 hr 23 min
– 4 hr 46 min
1 hr 37 min
The foot I borrow
is 12 inches.
16 + 3 = 19
Solve.
22
12¬ 10¬¬
– 9¬ 11¬¬
2¬ 11¬¬
60 + 23 = 83
3 80
4:20 p.m.
–1:30
2:50 p.m.
The hour I borrow
is 60 minutes.
60 + 20 = 80
25 lb
c. – 18 lb
3¬¬
15 min
30 min
6 oz
14 oz
11 : 2 0 a.m.
c. – 1 : 4 5
We R e m e m b e r
Round to the nearest 100 to estimate. Then copy and solve.
3. 4,630 – 79.41 =
–
=
53
Lesson 13
Do this activity using the map scale for the section of Virginia shown. Measure to the
nearest mile.
4. How many miles is it
from Dayton to
Bridgewater?
5. How far is it from
Pleasant Valley to
Mt. Crawford if you take
704 to 81, then 257, and
Route 11?
6. Traveling south on
Route 11, how far is
it from Route 726 to
Route 257?
M astery D rill
7. a. 1 liter =
8. a. A pentagon has
9. a. An octagon has
cubic centimeters
10. a. A quadrilateral has
11. 1 metric ton =
sides.
sides.
sides.
kilograms
12. The short version of the percent proportion is
13. The three dimensions of a solid are
Multiply to find the number.
14. a. 163 =
54
b. 124 =
b. 1 cubic meter =
liters
b. A hexagon has
b. A triangle has
b. 1 ton =
,
.
sides.
sides.
pounds
, and
c. 85 =
.
Lesson 13
+ -x S k i l l B u i l d e r s
÷
5:15
15. a. + 3 : 5 0
Match.
a.m.
b. +
4 lb
3 lb
2 oz
15 oz
13 oz
c. +
2¬
8¬
5¬
16.
a•b=b•a
a. Distributive property
18.
a(b + c) = ab + ac
c. Associative property of multiplication
17.
(a • b) • c = a • (b • c)
9¬¬
11¬¬
8¬¬
b. Commutative property of multiplication
Use the formula to find the area of each parallelogram.
11 in
18 cm
14 in
19. a.
b.
13 cm
55
Lesson 13
Today you will complete your graph. Follow these steps. Refer to your tally chart or
table on page 24, and the graph question on page 29.
20. If you are drawing a bar graph or
line graph, follow these steps.
a. Check your number scale and the
label.
b. Decide how far apart to make your
bars or points. Draw and name each one.
Color your bars or connect your points.
c. Label the names for the bars or points.
d. Write a title for your graph.
56
If you are drawing a pictograph,
follow these steps.
a. Check your symbol and the
number it represents.
b. Fill in the information for the
number scale and label it.
c. Draw your symbols for each item.
d. Write a title for your graph.
Lesson 13
Use the perimeter formula to find the width.
This diagram shows a small parking area for four cars.
12 meters
P = 34 m
21. The parking area is
wide.
22. On March 15, Miss Yoder’s class began their Mother’s Day
planter projects. They finished them on May 10, just in time
for Mother’s Day. How many weeks did the project take?
Round to the nearest whole week.
23. Sharon had $25.00 in her savings account on January 1.
The bank pays 4% interest for children’s accounts. How much
money did she have in her account at the end of the year?
Use the area formula to find
the missing dimension.
24. The width is
A = 48 m2
.
8m
Solve.
25. a. –
9¬
1¬
3¬¬
6¬¬
b. –
8 lb
5 lb
8 oz
9 oz
1 0 : 2 5 p.m.
c. – 7 : 3 0
57
14
Decimal Equivalents of Thirds and Sixths
In Math 500, you memorized the decimal equivalents of these common fractions:
1
2
1
4
= 0.5
3
4
= 0.25
= 0.75
Now you will memorize the decimal equivalents for thirds and sixths. You can see from
the number lines below that you already know some of these equivalents.
1
4
0
1
2
3
4
1
3
0
0
1
6
0
–
0.16
0.25
4
4
2
3
2
6
3
6
4
6
–
0.3
0.5
–
0.6
3
3
0.75
5
6
6
6
–
0.83
1.0
The only decimal equivalents you need to memorize for thirds and sixths are the decimals
1 2 1
5
for 3 , 3 , 6 , and 6 .
To change these four fractions to decimals, we divide the numerators by the denominators.
Notice that each of these fractions results
1
2 in a repeating decimal.
1
5
0.166
0.666
0.333
0.833
3
3
6
6
)
)
)
)
6 1.000
3 1.000
3 2.000
6 5.000
6
9
18
48
2
0
40
10
20
18
36
9
18
2
0
40
10
20
18
3
6
9
18
2
4
1
2
Memorize these four decimal equivalents for thirds and sixths.
1
3
58
–
= 0.3
2
3
–
= 0.6
1
6
–
= 0.16
5
6
–
= 0.83
Write the decimal equivalent for each fraction.
1. a.
2. a.
1
4
1
2
b.
=
b.
=
2
3
2
10
=
Lesson 14
c.
c.
=
1
6
5
6
=
=
Write the fraction in simplest form for each decimal.
–
–
3. a. 0.5 =
b. 0.6 =
c. 0.3 =
–
–
4. a. 0.16 =
b. 0.75 =
c. 0.83 =
d.
d.
3
4
1
3
=
=
d. 0.25 =
d. 0.4 =
We R e m e m b e r
Solve.
5. a. –
8 hr
2 hr
5 min
15 min
24¬
b. – 8¬
50 lb
c. – 9 lb
2¬¬
3¬¬
8 oz
Look back at the map on page 54. Answer the questions. Measure to the nearest mile.
6. How many miles is it from Bridgewater to Massanetta Springs using Routes 257,
81 north, 726, 659, and 689?
7. How many miles is it from Timber Ridge to Pleasant Valley using the shortest route by
road?
Write an expression for each using an exponent.
8. a. Sixteen cubed
b. 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
59
Lesson 14
M astery D rill
9. a. A right triangle has one
10. a. A circle has
11. a. 1 cubic centimeter =
12. 1 meter =
°.
millimeters
° angle.
milliliter
13. The formula for the area of a circle is
14. An acute angle measures between
b. 1 yard3 =
feet3
b. A half circle has
°.
b. A straight angle measures
° and
.
°.
°.
Follow the directions and answer the questions.
15. Use your compass to draw a circle with a
radius of 3.5 cm from center point U.
16. What is the diameter of this circle in cm?
17. Use the formula to find the circumference
22
of this circle. Use 7 for pi.
U
Divide to show each fraction as a decimal to the nearest hundredth. Then write the
percent.
1
18. a. 2 8 ≈
60
=
b.
11
12
≈
=
Lesson 14
+ -x S k i l l B u i l d e r s
÷
1
3
1.3
b. × 0 . 0 0 4
19. a. 0 . 4 7 ) 0 . 0 3 9 9 5
c. +
1
6
1
9
Names for the days of the
week are derived from names
of the Roman gods. The
original names were Sun’s
day, Moon’s day, and
Saturn’s day. Tuesday,
Wednesday, Thursday and
Friday are named after the
Norse gods Tyr, Woden,
Thor, and Frigg.
20. Sharon’s school has spring break from March 21
to March 25. School is scheduled to let out on May
27. How many weeks is it from the last day of
spring break to the last day of school?
21. Dr. McNett can see 15 patients from noon to 5 p.m.
a. How many hours is this?
b. Change the hours to minutes.
c. What is the average amount of time he spends with each
patient?
Write the equivalent decimal for each fraction.
22. a.
1
3
=
b.
2
3
=
c.
1
6
=
d.
5
6
=
61