Saxon Math Course 1 L71-281 Adaptations Lesson 71
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Parallelograms (page 368)
• A parallelogram has two pairs of opposite, parallel sides.
• The opposite angles of a parallelogram have equal measures.
• The adjacent angles of a parallelogram are supplementary (add to 180°).
• A parallelogram can be cut in half and rearranged to form a rectangle:
• You know how to find the area of a rectangle, so you can use this methodto find the area of a parallelogram.
• Imagine cutting the parallelogram on the dashed line.
• Move the part on the left under the part on the right.
• To get the area, multiply the base times the height.
• Do not be fooled by the slanted side.
Example: Find the area of this parallelogram.
A = bh A = (6)(5) A = 30 sq. cm
• When the angles of a parallelogram change the area changes. The perimeter does not change.
Practice Set (page 371)
Refer to parallelogram QRST to answer questions a–d.
a. Which angle is opposite ∠Q? ∠
b. Which angle is opposite ∠T? ∠
c. Name two angles that are supplements of ∠T? ∠ and ∠
d. If the measure of ∠R is 100°, what is the measure of ∠Q?
Teacher Notes:• Review “Geometric Formulas” on
page 29 in the Student Reference Guide.
• The activity in the Student Edition is optional.
A = bh A = (3)(3) A = 9 sq. cm
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Written Practice (page 372)
Find the perimeter and area of each parallelogram:
e. f.
perimeter area perimeter area
g. Here is the same parallelogram in two different positions.The area is the same in both drawings.
A = bh so h = A
__ b
What is the height in the figure to the right? 12 cm × 6 cm = 72 cm2
9 cm × h = 72 cm2
1. LCM of 6 and 10 2. Mt. Everest 29,035 ft =
sea level 0 ft =
Dead Sea –1371 ft
3. 105 minutes = hours minutes
time start 1:15 p.m.
Count forward hours.
Count forward minutes.
6. 3 __
4 ÷
3 __
8
___ ×
___ =
7. 4 1
__ 2
÷ 6
___ ×
___ =
8. 6 =
3 3
__ 4
=
___
+ 2 1 __
2 =
___
9. 5 1 __
8
– 3 1 __
8
Practice Set (continued) (page 371)
4. 2
__ 3
∙ 3 __
8 = 5. 1
1 __
4 ∙ 2
2 __
3
___ ×
___ =
Saxon Math Course 1 L71-283 Adaptations Lesson 71
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10.
11. (3.5)2 = 12. 15 ) _______
$75.00
13. (1 + 0.6) ÷ (1 – 0.6) =
15. name of point (0, 0) on coordinate plane
17. 1.2f = 120 18. 120
____ f = 1.2
19. 64
____ 224
= ∙ ∙ ∙ ∙ ∙ ____________________________ ∙ ∙ ∙ ∙ ∙ =
20. perimeter
each side
area
Written Practice (continued) (page 372)
5 1
__ 4
=
___
– 1 7 __
8 =
___
14. $4.50
a. tax
b. total
c. change
16. • Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
) _____
210 ) _____
210 ) _____
210 ) _____
210 ) _____
210 ) _____
640
) _____
210 ) _____
210 ) _____
210 ) _____
210 ) _____
210 ) _____
224
c.
a.
b.
1.0+ 0.6
1.0– 0.6
f = f =
b.
d. ( , )
a.
c. ( , )
Saxon Math Course 1 L71-284 Adaptations Lesson 71
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21. not shaded
23. How many centimeters long is your little finger?
24.
32°
25. 20% =
is
__ of
___
___
26. Name this geometric solid. 27. perimeter
each side
so, perimeter of triangle
28. area of your state
A square inches
B square yards
C square miles
29. a. perimeter b. A = bh
30. In this figure ∠BMD is a right angle.
Name two angles that are
a. supplementary. supplementary = 180°
b. complementary. complementary = 90°
Written Practice (continued) (page 373)
22. I multiplied the r by to find the diameter.
Then I m the diameter by .
a.
b.
a. ∠ and ∠
b. ∠ and ∠
Saxon Math Course 1 L72-285 Adaptations Lesson 72
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Fractions Chart Multiplying Three Fractions (page 375)
• To use the S.O.S. method in the Fractions Chart:
Step 1. Write the problem in the correct shape.
Step 2. Perform the operation.
Step 3. Simplify the answer.
• To multiply three or more fractions, cancel vertically and diagonally but never horizontally.
Practice Set (page 376)
a. Fill in the fractions chart for this lesson.
b. Describe the three steps for adding fractions.
1. Write the f so that the d are the same.
2. Add the n but not the d .
3. Reduce and/or c the answer if possible.
Write fractions
with common
d .
Write numbers in f form.
Find the r
of the divisor, then cancel.
R fractions. C improper fractions.
Add or subtract the
n .
Saxon Math Course 1 L72-286 Adaptations Lesson 72
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Written Practice (page 377)
1. average 4.2004.200
4.200
2. tablespoons
____________ cups
4 __
1 _ 4
? __
1 3. 130°
0º–110º
==
4. 5. 1 m = cm
6. Write in cents.
nickel
______ dollar
___ =
7. n – 1
__ 2 =
3 __
5
3 __
5 =
___
– 1 __
2 =
___
8. 1 – w = 7 ___
12
1 7 ___
12
– 1 7 ___
12
9. w + 2 1
__ 2 = 3
1 __
3
3 1 __
3 =
___
+ 2 1 __
2 =
___
10. 1 – w = 0.23
1.23– 0.23
c. Describe the steps for dividing fractions.
1. Write any mixed numbers in f form.
2. Find the r of the divisor.
3. C .
4. M the fractions.
5. S the answer if possible.
Practice Set (continued) (page 376)
d. 2 __
3 ∙
4 __
5 ∙
3 __
8 =
Cancel.
e. 2 1
__ 2 × 1
1 ___
10 × 4
___ ∙
___ ∙
___ =
b. a. c. c
n = w =
w =w =
Saxon Math Course 1 L72-287 Adaptations Lesson 72
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11. (6 × 10) + ( 4 × 1 ___
10 ) + ( 3 ×
1 ____
100 )
14. Which of these figures is not a parallelogram?
15. perimeter in.
a. each side
b. area
16. Figure ABCD is a rectangle.
a. complementary = 90°
b. supplementary = 180°
17.
2 sandwiches 1 green salad 1 small juice 2 medium juices
18. 0 0.07
$20.00 $20.00
Written Practice (continued) (page 378)
Menu
Grilled Chicken Sandwich $3.49 Juice: Small $0.89
Green Salad $3.29 Medium $1.09
Pasta Salad $2.89 Large $1.29
12. closest to 1
A –1 B 0.1 C 10
13. Largest prime number less than 100.
19. • List the items for an order.
• Then find the total not including tax.
.
a. ∠
b. ∠
a.
b.
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22. a. K
b. F
• Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
24. Draw a pair of parallel lines perpendicular to the parallel lines below.
Is the quadrilateral a rectangle?
25. 1 __
2 ∙
5 __
6 ∙
3 __
5 = 26. 3 × 1
1 __
2 × 2
2 __
3
___ ∙
___ ∙
___ =
27. 3
__ 4
÷ 2
___ ∙
___ =
28. 1 1
__ 2 ÷ 1
2 __
3
___ ∙
___ =
29. (0.12)(0.24) =
0.12 0.24
30. 0.6 ÷ 0.25 =
) _______
00000
Written Practice (continued) (page 379)
23. a. (3, –4)
b. (–3, 0)
20. A = l × w
l = 2.5 w = 0.4
2.5
0.4
21. 72
____ 120
= ∙ ∙ ∙ ∙ ________________ ∙ ∙ ∙ ∙ =
) ___
00 ) ___
00 ) ___
00 ) ___
00 ) ___
72
) _____
000 ) _____
000 ) _____
000 ) _____
000 ) _____
120
a. ( , ) b. ( , )
a. point
b. point
A =
Use work area.
Saxon Math Course 1 L73-289 Adaptations Lesson 73
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Exponents Writing Decimal Numbers asFractions, Part 2 (page 380)
• The exponent shows how many times the base number ismultiplied by itself.
The exponent 2 is read “squared.”
The exponent 3 is read “cubed.”
Examples: 52 = 5 × 5 = 25(5 squared)
34 = 3 × 3 × 3 × 3 = 81(three to the fourth power)
25 = 2 × 2 × 2 × 2 × 2 = 32(two to the fifth power)
• To write decimal numbers as fractions or mixed numbers:
The denominator (10 or 100 or 1000…) is indicated by the number of decimal places in thedecimal number.
The numerator is the digits to the right of the decimal point.
Examples: 0.5 = 5 ___
10 =
1 __
2
3.75 = 3 75
____ 100
= 3 3 __
4
Practice Set (page 382)
Find the value of each expression:
a. 104 = , b. 23 + 24 = c. 22 ∙ 52 =
d. Write the prime factorization of 72 using exponents.
72 = ∙ ∙ ∙ ∙ = ∙
Write each decimal number as a fraction or mixed number. Reduce.
e. 12.5 = 12 5 ___
10 = f. 1.25 = = g. 0.125 = =
h. 0.05 = = i. 0.24 = = j. 10.2 = =
Teacher Notes:• Introduce Hint #57, “Prime
Factorization of Powers of Ten.”
• Review “Exponents” on page 8 in the Student Reference Guide.
Saxon Math Course 1 L73-290 Adaptations Lesson 73
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1. 102 98.6 = d
102.0× 198.6
2. – 42 = d
180× 142
3. average pages to finish in 3 days
3p =
4. mixed number
2.5 =
5. reduced fraction
0.35 =
6. total plus tax
$12.60× $12.60
$12.60× $12.60
7. 3 __
4 × 2 × 1
1 __
3
___ ∙
___ ∙
___ =
8. (100 – 102) ÷ 52
÷ =
9. 3 =
2 1 __
3 =
00 ___
00
+ 1 3
__ 4 =
00 ___
00
10. 5 1 __
6 =
00 ___
00
– 3 1 __
2 =
00 ___
00
Written Practice (page 382)
Saxon Math Course 1 L73-291 Adaptations Lesson 73
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11. 3 __
4 ÷ 1
1 __
2
___ ∙
___ =
12. 7 ÷ 0.4 =
13. a. 52 25 b. 0.3 0.125
14. a. C = π d
b. radiusdiameter
_____
15. 25m = 0.175 16. 1.2 + y + 4.25 = 7
1.200× 4.250
7.000× 7.000
17. ten-thousands place
123,456.78
18. least to greatest
1,
1 __
2 ,
1 ___
10 ,
1 __
4 ,
0
00
___ 20
00
___ 20
00
___ 20
19. Use exponents.
200 = ∙ ∙ ∙ ∙
20. a. 20% of $18.00
20% =
isof
_____ ______
18.00
b. $18.00× $18.00
Written Practice (continued) (page 383)
0.30.125
a.
b.
a.
b.
m = y =
, , , ,
∙
a.
b.
Saxon Math Course 1 L73-292 Adaptations Lesson 73
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21. 22. Find the area. Then take 1 _ 2 of it.
23. 24. 22 + 23
________ 2 = 25. Before we multiply
fractions, we write any
m numbers
as i fractions.
26. • Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
a. H
b. L
27. a. (–4, 3)
b. (3, 0)
29. See the Student Reference Guide.
Written Practice (continued) (page 383)
28. s = 9
30.
a. What is the measure of ∠X?
b. What is the measure of ∠Y?
Use work area.
a. ( , )
b. ( , )
a. point
b. point
d. b.
c. a.
b. a.
s2 =
Saxon Math Course 1 L74-293 Adaptations Lesson 74
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Writing Fractions as Decimal Numbers
Writing Ratios as Decimal Numbers (page 385)
• To write a fraction as a decimal:
Divide the numerator by the denominator.
Keep any whole number.
Examples: 3 _ 4 0.75
4 ) _____
3.00
2 2 _ 5 0.4
5 ) ____
2.0 2.4
• Ratios (such as probability) are often written as fractions, so they can be converted to decimals in the same way as any fraction.
Practice Set (page 387)
You may use a calculator to convert these fractions to decimals:
a. 3
__ 4
= .
b. 4 1
__ 5
= .
c. 1 __
8 =
.
d. 7 ___
20 =
. e. 3
3 ___
10 =
. f.
7 ___
25 =
.
g. 11
___ 16
= .
h. 31
___ 32
= .
i. 3 24
___ 64
= .
j. In a bag are three red marbles and two blue marbles. If Chad pulls one marble from the bag, whatis the probability that the marble will be blue? Express the probability ratio as a fraction and as a decimal number.
blue
total
_____ fraction decimal
Teacher Note:• Instruct students on calculator
usage. See page 386 in theStudent Edition.
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1. (43) – ( ) = 2. in.
___ mi
1 ___
3 __
? 3. 2
3 __
4 =
4. a. sample space
b. Write the probability as a fraction and a decimal.
greater than 1
_____________ total numbers
___
5. reduced fraction
0.24 =
6. – 400 = d
ydft
1 ___
300 ____
?
7. A = bh b = 12 h = 8 8. 32 3 + 3
9. 1
__ 2 =
___
2 __
3 =
___
+ 1 __
6 =
___
10. 3 1 __
4 =
___
– 1 7 __
8 =
___
Written Practice (page 387)
A =
.
a. { , , , , } b. . b.
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11. 5 __
8 ∙
3 __
5 ∙
4 __
5 = 12. 3
1 __
3 × 3
___ ∙
___ =
13. 3
__ 4 ÷ 1
1 __
2
___ ∙
___ =
14. (4 + 3.2) – 0.01 =
4.2 3.2
4.2 0.01
15. Complete the triangular prism. 16. 12g =
golf balls
$
12
___ 1
__ ?
17. 81
38
50× 50
18. average
424635
57
19. LCM of 6, 8, and 12 20. 24 + c + 96 = 150
24 96
150 906
Written Practice (continued) (page 388)
Use work area.
c =
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21. 40
___ 96
= ∙ ∙ ∙ ________________ ∙ ∙ ∙ ∙ ∙ 22. perimeter 40 cm
each side
23. mountain bikes
all cyclists
___
25. 3
__ 4 26.
27. 28.
29. Name a pair of parallel segments that are not
___ AB and
___ DC .
30. 60% =
is
of
___ ____
300
Written Practice (continued) (page 388)
24. All f sides of a square are the same
l . Some rectangles are longer than they
are w , so not all the s are the
same l .
a.
b.
and
a.
b.
a.
b.
a. ( , )
b. ( , )
Use work area.
Saxon Math Course 1 L75-297 Adaptations Lesson 75
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Teacher Note:• Review “Fraction Decimal
Percent” on page 13 in the Student Reference Guide.
Writing Fractions and Decimals as Percents, Part 1 (page 390)
• Percent means “per hundred.”
Examples: 23
____ 100
= 23% 3 ___
10 =
30 _____
100 = 30%
15
___ 30
= 1
__ 2 =
50 ____
100 = 50%
• To change a decimal to a percent, shift the decimal point two places to the right.
Examples: 0.08 = 8% 0.40 = 40%
Practice Set (page 392)
Write each fraction as a percent:
a. 31
____ 100
= b. 1 ____
100 = c.
1 ___
10 = ____
100 =
d. 3 ___
50 = ____
100 = e.
7 ___
25 =
____
100 = f.
2 __
5 = ____
100 =
g. Twelve of the 30 students earned a B on the test. What percent of the students earned a B?
12 ___
30 = ___
10 =
____
100 =
h. Jorge correctly answered 18 of the 20 questions on the test. What percent of the questions did he answer correctly?
18 ___
20 = ___
10 = ____
100 =
Write each decimal number as a percent:shift
i. 0.25 = j. 0.3 = k. 0.05 =
l. 1.0 = m. 0.7 = n. 0.15 =
Saxon Math Course 1 L75-298 Adaptations Lesson 75
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Round 94¢ to $ and $6.35 to $ .
Add the items to get $ . Tax is 8¢ per
dollar, so the tax is about ¢. This is
close to my answer.
4. $4.000$4.000
$4.000
4.00
4.08
Written Practice (page 392)
1. reciprocal
2 3 __
5 = __
5
2. time start
Count forward hours.
Count forward minutes.
3. 1 pound = 16 ounces
oz
___ $z
_____ 4.00
1
__ ?
5. part 50%
part
whole 100%
6. Connect the correct corners.
7. 3 __
4 = 8.
3 ___
20 =
9. Write 12% as a reduced fraction and a decimal.
10. 7 ___
10 =
n ____
100
a. .
b.
a.
b.
____
100
. n =
Saxon Math Course 1 L75-299 Adaptations Lesson 75
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11. 5 – m = 3 1 __
8
5 1 __
x
3 1 __
8
12. 1 – w = 0.95
1.00 0.95
13. m + 1 2
__ 3
= 3 1 __
6
3 1
__ 6 =
___
1 2
__ 3 =
___
14. ( 1 __ 2
+ 1
__ 3
) – 1 __
6 =
1
__ 2
=
___
1 __
3 =
___
15. 3 1 __
2 × 1
1 __
3 × 1
1 __
3
___ ∙
___ ∙
___ =
16. (0.43)(2.6)
0.43 2.6
17. 0.26 ÷ 5 Add zeros.
) _________
0000000
18. 17
___ 20
= ____ 100
= %
19. Round to the nearest foot. 20. 4.870.195
21. 18
___ 30
= ∙ ∙ ___________ ∙ ∙ =
) _____
000 ) _____
000 )
_____ 000 )
_____ 000
) _____
180 ) _____
300
Written Practice (continued) (page 393)
m = w =
m =
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Written Practice (continued) (page 393)
22. GCF of 18 and 30
1 , , , , , 18
23. product of 2 numbers is 1
A equal B reciprocals
C opposites D prime
24. A q is a four-sided
p , and every r
has four s .
25. b = 8 h = 6
bh
___ 2 =
26. Use exponents.
28. a. perimeter
b. area
29. a. perimeter
b. A = bh
30. Connect the endpoints to form a quadrilateral.
Is it a rectangle?
Use work area.
.
27. • Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
(3, 1), (3, –1), (–1, 1), (–1, –1)
Use work area.
a.
b.
a.
b. Use work area.
Saxon Math Course 1 L76-301 Adaptations Lesson 76
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Comparing Fractionsby Converting toDecimal Form (page 395)
• To compare two fractions:
1. Cross-multiply.
2. Compare the numbers above the fractions.
18 > 12 6 < 16
Examples: 2 __
3
4 __
9
2 __
8
2 __
3
• Convert to decimals if the problem is mixed (fraction and decimal).
Example: 0.7 3
__ 4
0.7 0.75
Practice Set (page 396)
Compare by cross-multiplying.
24
a. 3 ___
20
1 __
8 b.
3 __
8
2 __
5 c.
15 ___
25
3 __
5
Convert; then compare.
d. 0.7 4
__ 5
e. 2 __
5 0.5 f.
3 __
8 0.325
5 ) ____
4.0 5 ) ____
2.0 8 ) ________
3. 0 0 0
Teacher Note:• Review Hint #47, “Comparing
Fractions.”
<
Written Practice (page 396)
1. 102 23
( )( ) = 2. halfway: Add; then divide by 2.
4.5 6.7
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3. 13 × = y
humandog
7 __
1
? ___
4. 2 __
5
1 __
4
5. shaded
6. circumference of a juice glass
A centimeters
B meters
C kilometers
7. a. 2 1
__ 2 =
b. 3.75 =
8. a. 0.04 = ____
100 =
b. 0.04 =
9. Answer with a mixed number.
halfofeach
200
18
_____ =
10. 6 1 __
3 =
00 ___
00
3 1 __
4 =
00 ___
00
+ 2 1 __
2 =
00 ___
00
11. 4 __
5 =
? ____
100 12. ( 2
1 __
2 ) ( 3
1 __
3 ) ( 1
1 __
5 )
___ ∙ ___ ∙ ___ =
{
Written Practice (continued) (page 396)
a. .
b.
a.
b.
b. .
c.
a.
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13. 5 ÷ 2 1 __
2
___ ∙
___ =
14. 6.7 + 0.48 + n = 8
6.70× 0.48
8.48× 0.48
15. 12 – d = 4.75
12.75× 4.75
16. 0.35× 0.45
17. shift
102
4.3 ÷ =
18. median First, put the numbers in order.
0.3, 0.25, 0.313, 0.2, 0.27
19. 3926 5184
5000× 5000
20. prime numbers between 40 and 50
21. 12
___ 25
= ____
100 = 22. perimeter
Written Practice (continued) (page 397)
n =
d =
, ,
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23. complementary = 90° 24. millimeters
25. two congruent triangles
a. A = bh
b. area of one of the triangles
26.
bottom layer
all layers
27.
• Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
30. Draw a fourth line that intersects but is NOT
perpendicular to the parallel lines. Is the
quadrilateral a rectangle?
Written Practice (continued) (page 397)
A (1, 2)
B (–3, –2)
C (1, –2)
28. a. perpendicular to ___
AC
b. right angle
29. b = 12 h = 9
bh
___ 2
=
a.
b. cubes
a.
b. ∠
Use work area.
Saxon Math Course 1 L77-305 Adaptations Lesson 77
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Finding Unstated Informationin Fraction Problems (page 399)
• Work through the Practice Set.
Practice Set (page 401)
3
__ 8
of the 40 little engines could.
parts that could total parts
parts that could not total parts
The face of a spinner is divided into 12 equal sectors. part red 1 _ 4
part not red
whole 1
1
__ 4
of 12 =
The probability of spinning red on one spin is 1 _ 4 .
g. How many sectors are red?
h. How many sectors are not red?
i. What is the probability of spinning not red in one spin?
j. What is the sum of the probabilities of spinning red and not red?
How are the events related? The events are c .
Teacher Note:• Review Hint #35, “Fraction of a
Group, Part 2.”
3 __
8
5 __
8
a. Into how many parts was the group divided?
c. How many parts could climb the hill?
e. How many parts could not climb the hill?
b. How many engines were in each part?
d. How many engines could climb the hill?
f. How many engines could not climb the hill?
Written Practice (page 401)
1. 1 __
6 of 114
is
__ of
1 __
6
___
2. A desk might weigh about 24 pounds.
is
__ of
1 __
6
___
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Written Practice (continued) (page 401)
3. hitstimes
___ = 4. 3
__ 5
of 30 students are boys
5. shaded 6. 3.6 =
7. 3.6 + a = 4.15
4.15 3.60
8. 2 __
5 x = 1
9.
There is a g chance that it
will rain because % is greater
than %.
10. 3
__ 5
= ____
100 = %
11. Water freezes at °F.
0° = –3° =
12. a. 20 7 ___
20
b. 32 23
part 60%partwhole 100%
a.
b.
a.
b.
c.
d.
a.
b. .
c.
a = x =
Use work area.
a.
b.
0.35
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Written Practice (continued) (page 402)
13. 1 __
2 =
___
+ 2
__ 3
=
___
14. 3 1 __
5 =
___
– 1 3
__ 5
=
___
15. 1
__ 2
=
___
3 __
4 =
___
+ 7
__ 8
=
___
16. 3 × 1 1
__ 3
___ ∙
___ =
17. 3 ÷ 1 1
__ 3
___ ∙
___ =
18. 1 1 __
3 ÷ 3
___ ∙
___ =
19. perimeter
20. area
21. Use exponents.
) ______
1000 )
______ 1000
) ______
1000 )
______ 1000
) ______
1000 )
______ 1000
22. a. 40% =
is
__ of
___ ____
$80
b. $80 $80
b.
a.
∙
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23. a. $38.80 $38.80
b. $38.80 $38.80
24. A polygon is a straight-sided closed figure.
Is every quadrilateral a polygon?
25. time start 12:00 p.m.
Count back hours.
Count back minutes.
26. What percent appears to be shaded?
A 20% B 40%
C 60% D 80%
27. W(2, 3), X(1, 0), Y(–3, 0), Z(–2, 3)
• Always begin at the origin.
• Next, move on the x-axis.
• Last, move on the y-axis.
28. a. parallel to ____
WX
b. parallel to ___
XY
30. a. What shape?
Written Practice (continued) (page 403)
29. 210
____ 350
= ∙ ∙ ∙ _____________ ∙ ∙ ∙ =
) _____
210 ) _____
350 )
_____ 210 )
_____ 350
) _____
210 ) _____
350 )
_____ 210 )
_____ 350
b. Round the circumference to the nearest ten miles.
b.
a.
a.
b.
a. b. Use work area.
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Capacity (page 404)
• Measuring liquids:
U.S. Customary System: ounces, cups, pints, quarts, gallons Metric system: milliliters, liters
• One liter is a little more than one quart.
Practice Set (page 405)
a. What fraction of a gallon is a quart?
gallon
quarts
___
b. A 2-liter bottle has a capacity of how many milliliters? mL
L
mL
1 ___
2 __
?
c. A half gallon of orange juice will fill how many 8-ounce cups? cups
d. The entire contents of a full 2-liter bottle are poured into an empty half-gallon carton. Will the half-gallon container overflow? Why or why not?
The half-gallon c will o because 2 liters is a little m than
half a gallon.
Teacher Notes:• Introduce Hint #58, “Measuring
Liquids and Capacities of Containers.”
• Refer students to “Liquids” and “Equivalence Table for Units” onpage 1 in the Student Reference Guide.
• Post reference chart, “Liquids.”Liquids
U.S. Customary System Metric System
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup = 8 ounces
1 liter = 1000 milliliters
Equivalence Table for Units of Liquid Measure
Half&Half
Milk
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1. ( ) – ( ) = 2. cm
mm 1 ___
___
?
3. Go down the 3s and 4s columns. 4. 4 __
5 of the 60 lights were on.
5. not prime, not composite 6. 4 __
5 m = 1
7. 4 __
5 + w = 1
1
4 __
5
4 __
5
8. 4
__ 5
÷ x = 1
9. y – 4 __
5 = 1
1 4 __
5
4 __
5
10. shaded
Written Practice (page 406)
m =
x =w =
y =
a.
b. .
c.
a.
b.
c.
d.
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11. 1.15 = 12. a. 3 __
5
0.35
b. √_____
100 14 + 23
13. 5
__ 6
=
___
1
__ 2
=
___
14. 4 1
__ 4
=
___
– 3 1 __
3 =
___
15. 1
__ 2
=
___
2 __
3 =
___
+ 5
__ 6
=
___
16. 1 1
__ 2 × 2
2 __
3
___ ∙
___ =
17. 1 1
__ 2 ÷ 2
2 __
3
___ ∙
___ =
18. 2 2
__ 3 ÷ 1
1 __
2
___ ∙
___ =
19. 20. “The opposite sides of a rectangle are parallel.” True or false?
Written Practice (continued) (page 406)
a.
b.
a.
b.
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21. average
33 52
22. ) ______
22.00
23. ft.
in.
1 ___
2 1 _ 2 ___
? 24. 0.1
25. Draw a quadrilateral that is NOT a rectangle.
See the Student Reference Guide.
26.
27. (5, 3), (5, –1), (–1, –1)
29. A liter is like a:
A pint B quart C 1 __
2 gallon D gallon
30. one pint = ounces
Written Practice (continued) (page 407)
28. 3 teaspoons = 1 tablespoon16 tablespoons = 1 cup
2 cups = 1 pint2 pints = 1 quart
4 quarts = 1 gallon
.
a.
b. ( , )
Use work area. ∙ ∙
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Area of a Triangle (page 408)
• Notice that the area of any triangle is:
1 __
2 the area of a parallelogram with the same base and height
• So the formula for the area of a triangle is:
A = 1
__ 2
bh or A = bh
___ 2
• The height must be perpendicular to the base.
• Area must be expressed in square units (16 cm2).
Practice Set (page 410)
Find the area of each triangle:
a. b.
c. d.
e. If the height of the triangle in c is doubled to 30 mm, would the area double?
1 __
2 (56)(30) = ÷ 2 = 420
Teacher Notes:• Review “Geometric Formulas” on
page 29 in the Student Reference Guide.
• The activity in the Student Edition is optional.
Written Practice (page 410)
1. Divide the p by 2 and
s the length from the quotient.
2. 2 liters = 2 quarts + 3.6 ounces
1 liter 1 quart
A = 1 __
2 (8 cm)(4 cm)
A = 16 cm2
Use work area.
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Written Practice (continued) (page 410)
3. 38 33
4. See the Student Reference Guide.
5. 90% =
a. isof
10
___ 03
___ 30
b. birchall others
___ 30
6. a. 18
___ 24
=
b.
7. A = 1 __
2 bh
8. 103
___ 102
_____
9. 6.42 + 12.7 + 8 =
6.426.42
× 6.42
10. 1.2(0.12) =
1.2
11. 64 ÷ 0.08 = 12. 3 1
__ 3 ×
1 __
5 × 3 __
4
____ ∙
____ ∙
____ =
a.
b.
a.
b.
a.
b.
c.
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Written Practice (continued) (page 411)
13. 2 1 __
2 ÷ 3
____ ∙
____ =
14. 10 – q = 9.87
10.00× 19.87
15. 24m = 0.288 16. n – 2 3 __
4 = 3
1 __
3
3 1
__ 3
= 00
___ 00
+ 2 3
__ 4
= 00
___ 00
17. w + 1 __
4 =
5 __
6
5 __
6 =
___
1 __
4 =
___
18. perimeter
each side
area
19. (9 × 10) + (6 × 1) + ( 3 × 1 ____
100 ) 20. circumference
21. closest to zero
A –2 B 0.2
C 1 D 1 __
2
22. 6.7 7.3
500× 500
Round 6.7 to and 7.3 to .
Then m .
m = n =
.
q =
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23. 34 = 3 ∙ 3 ∙ 3 ∙ 3 = 24. halfway
0.2 0.3
25. 26. only one pair of parallel sides
27. (–5, 5), (1, 5), (3, 1), (–3, 1) 28. a. area of square 100 cm2
each side
b. perimeter of square
29. a. each side of hexagon
b. perimeter of hexagon
30. 32
___ 48
= ∙ ∙ ∙ ∙ _____________ ∙ ∙ ∙ ∙ =
) ___
32 ) ___
32 ) ___
32 ) ___
32 ) ___
32
) ___
32 ) ___
32 ) ___
32 ) ___
32 ) ___
48
Written Practice (continued) (page 411)
a.
b.
a.
b.
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Using a Constant Factor to Solve Ratio Problems (page 413)
• Ratio can be used to express an actual count.
• Ratios and actual counts are related by a constant factor. Multiply the terms of a ratio by the constant factor to find the actual count.
• A ratio box can help to sort the numbers out.
• To find the constant factor ask: What did they multiply by to get the actual count? That number is your constant factor.
You will multiply the other ratio term by the same thing.
Example: To make green paint, the ratio of blue paint to yellow paint is 3 to 2. For 6 ounces of yellow paint, how much blue paint is needed? Draw a ratio box.
A ratio term and an actual count are given for yellow paint. What number times 2 (ratio term) equals 6 (actual count)? 33 is the constant factor.Multiply the ratio term for blue paint by the constant factor. 3 × 3 = 99 ounces of blue paint are needed.
Practice Set (page 414)
Draw a ratio box and use a constant factor to illustrate and solve these ratio problems.
a. The ratio of boys to girls in the cafeteria was 6 to 5.
If there were 60 girls, how many boys were there?
b. The ratio of ants to flies at the picnic was 8 to 3. If there
were 24 flies, how many ants were there?
Blue Paint
Yellow Paint
Ratio Actual Count
3
2 6
Blue Paint
Yellow Paint
Ratio
3 × constant factor
2 × constant factor
Actual Count
6
?
Written Practice (page 414)
1. mean range
) ______
0000
964968
75
96 75
2. 2 1
__ 2 = 2.5
mi
___ ft
1 ___
2.5 ___
?
Use work area.
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Written Practice (continued) (page 415)
3. 12p =
players
_______ teams
168
____ ? __
1
4. a. perimeter
b. A = bh
5. a. perimeter
b. A = 1 __
2 bh
6. one pair of parallel sides
7. See the Student Reference Guide. 8. 4
__ 5
of 30 present
___ 5
of 30 absent
is
__ of
___
___ 30
9. 10. a. 19
___ 20
= ____
100 =
b. 0.6 =
11. square
_______ sides
1 ___ 12. a.
3 __
4
0.5
b. 3 qt 1 gal
a.
b.
a.
b.
a.
b.
b. .
a.
b. a.
b.
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Written Practice (continued) (page 415)
13. 4.4 = 14. 8 ) ________
1. 0 0 0
15. 5 __
6 =
___
+ 1 __
2 =
___
16. 5
__ 8 =
___
– 1
__ 4 =
___
17. 2 1 __
2 × 1
1 __
3 ×
3 __
5
___ ∙
___ ∙
___ =
18. 4 – a = 2.6
4.6+ 2.6
19. 3n = 1 1
__ 2
20. 5x = 0.36
21. 0.9y = 63 22. 0.4287
.
a =
n = x =
y =
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23. Frosted Rice 24. Coco Flakes
sugar
______ cereal
____
100
? ___
50
25. How many f grams of sugar
does have than Coco Flakes?
Answer:
26. one quart = cups
27. (3, 0), (3, 3), (0, 3) 28. complement = 90°
A
B
C
29. b = 6 h = 8
A = 1 __
2 bh
Written Practice (continued) (page 416)
30. Connect the endpoints. Is the quadrilateral a parallelogram?
Use work area.
a. ( , )
b.
A = Use work area.
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