LESSON
Name
96
Teacher Notes:
page 627
• Introduce Hint #57 “Canceling
Fractions.”
• Using Reciprocals
to Divide Fractions
• Review Hint #56 “Reciprocal.”
• Review “Fraction Terms” on page
19 in the Student Reference Guide.
• For additional practice, students
may complete Targeted Practice 96.
New Concept
• To use reciprocals to divide fractions:
1.
2.
3.
4.
5.
Copy the first fraction.
Change the ÷ to a ×.
Flip the second fraction.
Cross cancel (if possible).
Multiply across.
Example
2 ÷ __
2=
__
1 3
1
3 __
2 × __
__
=3=3
2
1
1
1
• Cross cancel fractions to make multiplying and dividing
fractions easier.
Canceling fractions is another way to reduce.
Example
3
÷ __
4 8
© 2008 Saxon
1
__
2
1
__
4
×
8
__
3
2 (Cancel the 8 and the 4.)
= __
3
1
Saxon Math Intermediate 5
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Adaptations Lesson 96
11/3/07 11:53:25 AM
Lesson Practice
Copy, change, and flip. If necessary, convert.
1 =
1 ÷ __
a. __
3 2
2 ÷ __
3 =
b. __
3 4
2 ÷ __
1 =
c. __
3 4
1 × ___ =
__
3
2 × ___ =
__
3
2 × ___ =
__
3
1
1 ÷ __
d. __
2 3
___
3 ÷ __
2
e. __
4 3
=
× ___ =
___
=
f. Cross cancel.
3
3 ÷ __
4
× ___ =
___
1
g. 2 ÷ __
3
___
2
h. 3 ÷ __
3
=
× ___ =
___
i. Cross cancel.
× ___ =
5
10 ÷ __ =
6
j. How many 3_1 s are in 4_3 ?
3 ___
__
÷
=
4
k. How much of 4_3 is in 1_3 ?
1 ÷ ___ =
__
3
× ___ =
page 629
Written Practice
1.
Shade __
2
× ___ =
=
___
1.
=
1 of __
1=
2. __
2 2
2.
Shade __
3
© 2008 Saxon
What percent is that?
Use work area.
Saxon Math Intermediate 5
SM_H5_AD_L096_FF.indd 626
626
Use work area.
Adaptations Lesson 96
11/3/07 11:53:27 AM
Written Practice, continued
page 629
3. Cross cancel.
4. Estimate the product.
2 of ___ =
__
3
712
490
5. digits
ninety-three million, eight hundred fourteen thousand, two hundred
,
,
1=
7. __
4
6. How many one tenths are there
in three?
1 ÷3
A ___
10
1
B 3 ÷ ___
10
1 ÷ ___
3
C ___
10 10
D
___
20
1 = + ___
__
20
5
3 ÷ ___
1
___
10 10
Use work area.
9. Multiples: Think multiplication table.
8. Copy, change, and flip.
1 × ___ =
a. __
3 × ___ =
b. __
© 2008 Saxon
a.
b.
,
,
,
10. Cross cancel.
_3
4
of 10 tons
Saxon Math Intermediate 5
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627
Adaptations Lesson 96
11/3/07 11:53:28 AM
page 630
Written Practice, continued
11. Label the figure.
A
B
?
C
12. decimal, reduced fraction, and percent
D
13. Copy, change, and flip.
1 =
÷ __
4
3
1
__
___
× ___ =
.
14. Copy, change, and flip.
1 =
1 ÷ __
__
3
4
___
× ___ =
15. Copy, change, and flip.
16. m + 1.4 = 3.75
1 =
3 ÷ __
2
___ × ___
=
17. m − 1.4 = 3.75
10
1 × ___ = ____
18. ___
100
10
19. Write your answer
with a dollar sign.
20 × 47¢ =
© 2008 Saxon
m=
m=
Saxon Math Intermediate 5
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628
Adaptations Lesson 96
11/3/07 11:53:30 AM
page 630
Written Practice, continued
0
R
_________
21. 30 ) 4 2 7
20. 568 ÷ 15
=
________
22. 6m = $30.24
Think 20 ) 6 0 0
Use work area.
2 × __
1 =
23. 5 × __
3 2
m=
Use work area.
____
25. √ 100
1+2 =
24. 5 − 1 __
4
52
Cross cancel.
1 =
2 × __
__
2
3
5
__
× ___ =
Use work area.
26. 20, 18, 30, 20, 22, 28, 31, 20, 27, 30, 26, 31, 20, 24, 28
In order: 18,
,
,
,
,
a. mode
Mode
,
,
,
,
most
Range
,
,
,
, 31
b. range
a.
© 2008 Saxon
,
c. median
span
Median
b.
27. a. Classify triangle ABD by sides.
middle
c.
A
b. What single transformation
would move triangle ABC to
triangle ADC?
D
C
B
a.
b.
Saxon Math Intermediate 5
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629
Adaptations Lesson 96
11/3/07 11:53:31 AM
page 631
Written Practice, continued
28. Michelle’s birthday
July 4
July 4 + 14 days = July
Mio’s birthday
Mio’s birthday + 6 days =
Rusita’s birthday
Use work area.
29. Tyrone
21 miles per gallon
Trina
500 ÷ 21 =
500 ÷
26 miles per gallon
500 ÷ 26 =
=
500 ÷
gallons
=
gallons
gallons Tyrone purchased
gallons Trina purchased
fewer gallons
I used
numbers. Tyrone purchased
about
gallons. Trina purchased about
−
gallons.
=
Use work area.
30. a. Range
span
b. metal that melts at coldest temperature
melting temperature of gold:
1064.43°C
© 2008 Saxon
c. melting temperature of ruthenium:
−
I rounded the numbers.
–
=
Use work area.
Saxon Math Intermediate 5
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630
Adaptations Lesson 96
11/3/07 11:53:33 AM
LESSON
Name
97
Teacher Note:
page 633
• Refer students to “Ratio” on page
21 in the Student Reference
Guide.
• Ratios
New Concept
• Ratios can be written as fractions.
Math Language
Ratio – a way of
comparing numbers
by division
12
__
“12 to 18” is written 18
.
12 ÷ 6 = _2_
• Reduce ratios like fractions: _______
18 ÷ 6 3
• Do not convert ratios. Leave them as improper fractions.
Example
There were 12 girls and 16 boys in the class. What was the ratio
of boys to girls?
boys ___
16
_____
1. Write the ratio:
girls 12
2. Reduce but don’t convert:
4
16 ÷ 4 = __
_______
12 ÷ 4 3
The ratio of boys to girls is 3_4.
Lesson Practice
There were 20 prairie dogs and 30 jackrabbits in a section of the Texas high plains.
a. What was the ratio of jackrabbits to prairie dogs?
jackrabbits
___________
© 2008 Saxon
114 = ____
114 Reduce but don’t convert.
____
prairie dogs 114 114
b. What was the ratio of prairie dogs to jackrabbits?
prairie dogs
___________
jackrabbits
114 = ____
114 Reduce.
____
114 114
Saxon Math Intermediate 5
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631
Adaptations Lesson 97
11/3/07 11:55:46 AM
Lesson Practice, continued
There were 8 red socks and 10 blue socks in George’s drawer.
c. What was the ratio of red socks to blue socks?
red socks ____
114
__________
114 Reduce.
= ____
blue socks 114 114
d. What was the ratio of blue socks to red socks?
blue socks ____
114
__________
red socks 114
114 Reduce but don’t convert.
= ____
114
page 635
Written Practice
1.
pennies ____
114
_______
nickels 114
114
= ____
114
2. The sum of one fourth and one fourth
is one half.
Reduce but don’t convert.
$4.00
3.
$0.00
____
)
$0.00
00 $0.00
$
left.
I
divided by
Saxon Math Intermediate 5
SM_H5_AD_L097_FF.indd 632
to find the total amount of
and
.
632
© 2008 Saxon
She has
Adaptations Lesson 97
11/3/07 11:55:47 AM
page 635
Written Practice, continued
4. How many 8_1 s are in 2_1 ?
5. decimal and reduced mixed number
shaded
1
1 ÷ __
__
2 8
Copy, change, and flip.
Cross cancel.
.
.
6.
−
.
7. a. A quart is what fraction of a gallon?
b. one gallon =
0
gallons
_______
c.
quarts
quarts
4
1 = __
__
?
1
a.
b.
c.
2=
8. __
3
15
___
15
9. decimal number and fraction
15
2 = − ___
__
5
15
© 2008 Saxon
0
10
10
.
Use work area.
Saxon Math Intermediate 5
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633
Adaptations Lesson 97
11/3/07 11:55:48 AM
page 636
Written Practice, continued
10. Copy, change, and flip.
1÷2
__
2
1
2 ÷ __
2
00
1 × ___
__
2 00
00 × ___
00
___
00 00
Use work area.
11. Label the figure.
A
12. Copy, change, and flip.
2 =
3 ÷ __
3
__
B
?
D
C
2 ÷ 3 =
13. __
3
__
7 =
7 + ___
14. ___
10 10
× __ =
× __ =
Convert and simplify.
15.
43.15
16. ($10 − 19¢) ÷ 9 =
17. 6 × 72¢ =
00.00
© 2008 Saxon
00.00
0000.00
Saxon Math Intermediate 5
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634
Adaptations Lesson 97
11/3/07 11:55:50 AM
page 636
Written Practice, continued
0
_________
19. 24 ) 5
18. 35 =
2
0
R
0
20. Reduce:
50
____
100
=
3 =
3 − 3 − 1__
22. 5 __
4
4
21. 12y = 1224
Simplify.
y=
1 + 1__
1 + 1__
1 + 1__
1=
23. 1__
4
4
4
4
24. Write the missing number as your
answer.
3 = ____
___
10 100
25.
26.
area = 64 sq. in.
inch
1
each side =
2
in.
The opposite of “squared” is “square root.”
© 2008 Saxon
a. length
b. perimeter
a.
b.
Saxon Math Intermediate 5
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635
Adaptations Lesson 97
11/3/07 11:55:54 AM
page 636
Written Practice, continued
1 of 640
27. ___
64
28. What are the next three terms in this Fibonacci sequence?
1, 1, 2, 3, 5, 8, 13, 21,
,
,
,…
1+1=
1+2=
2+3=
Use work area.
29. a. factors of 64:
,
,
,
,
,
,
b. Is the number of factors an odd or even number?
c. What is the median of the factors?
___
d. What is √ 64 ?
Use work area.
stripes
_______
stars
123
____
123
Saxon Math Intermediate 5
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© 2008 Saxon
30.
636
Adaptations Lesson 97
11/3/07 11:55:55 AM
LESSON
Name
98
Teacher Notes:
page 638
• Introduce Hint #58 “Positive and
Negative Numbers.”
• Review “Number Line” on page 12
in the Student Reference Guide.
• Temperature
• Review Reference Chart “Number
Line.”
New Concept
• On a number line there are both positive and negative
numbers.
Math Language
Positive numbers
are greater than
zero.
• Negative numbers are written with a minus sign in front.
Negative numbers
are less than zero.
Ľ5
Zero is neither
negative nor
positive.
Ľ4
Ľ3 Ľ2 Ľ1
negative
0
1
2
3
positive
4
5
• To calculate the difference between a positive temperature
and a negative temperature:
1. Find the difference from the positive temperature
to 0.
2. Find the difference from the negative temperature
to 0.
3. Add the two differences together.
Example
How many degrees are there between 6°C and −2°C?
1. The difference from 6°C to 0°C is 6°.
6
2. The difference from −2°C to 0°C is 2°.
4
3. Add the differences.
6
2
© 2008 Saxon
6° + 2° = 8°
There are 8° between 6°C and −2°C.
0
2
Ľ2
Ľ4
C
Saxon Math Intermediate 5
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637
Adaptations Lesson 98
11/3/07 12:00:52 PM
Lesson Practice
a. Write the temperature that is twelve degrees below zero on the
Fahrenheit scale.
b. What temperature is shown on this thermometer?
10
0
c. If the temperature shown is 14° lower than the
high temperature for the day, then what was the
high temperature?
–10
C
Count up 14°.
d. If the temperature falls 3° from the temperature shown, what will the temperature be?
Count down 3°.
Use the table below to answer problems e and f.
Daily Temperatures ( ˚C)
Day
Sun
Mon
Tues
Wed
Thurs
Fri
Sat
High ( ˚C)
25
20
32
40
45
30
32
Low (˚C)
11
13
15
23
25
15
15
e. What is the median of the low temperatures for the week?
List the temperatures from least to greatest.
,
,
,
,
,
,
f. What is the mean (average) of the high temperatures for the week?
mean:
Saxon Math Intermediate 5
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638
© 2008 Saxon
median:
Adaptations Lesson 98
11/8/07 1:09:03 PM
page 641
Written Practice
cats
1. _____
dogs
____
=
____
2.
a. name
Reduce.
a.
b. How many faces?
b.
3.
1.2 miles
4.
10˚
Start at 2ºF. Count down 5ºF.
.
0
Ľ10˚
F
5.
A
Ľ5
Ľ4
Ľ3
B
Ľ2
C D
Ľ1
0
1
2
3
4
a. Which arrow could be pointing to 2 3_1?
5
a.
b. Which arrow is pointing to negative three?
b.
© 2008 Saxon
6. person
trout (person + 10)
mph
sailfish (trout + 45)
mph
Saxon Math Intermediate 5
SM_H5_AD_L098_FF.indd 639
mph
639
Adaptations Lesson 98
11/3/07 12:00:59 PM
page 641
Written Practice, continued
7.
K
J
6.5
8.
L
M
9.
4.26
.
.
N
A ∠JNK
B ∠KNL
C ∠KNM
D ∠LNM
23.45
10.
–
.
14. 364 ÷ 16 =
+
0.367
11.
–
+
.
12. $1.25 × 7 =
.
13.
608
× 750
17.
8
5 ___
15
7
– 4 ___
15
.
15. $7.20 ÷ 20 =
16.
_____
Think 20 ) 4 0 0 .
1
3 __
2
1
+ 1 __
2
=
6
1
– 1 __
3
Saxon Math Intermediate 5
SM_H5_AD_L098_FF.indd 640
19. Identity Property
of Multiplication
4 of 25 =
20. __
5
Cross cancel.
5
1 × __ =
7
21. Copy, change, and flip.
3 ÷ __
2 =
__
4
3
3 × ___
00 =
__
00
4
640
© 2008 Saxon
18.
Adaptations Lesson 98
11/3/07 12:01:01 PM
Written Practice, continued
page 642
30 =
22. Write the missing number as your answer. 23. Reduce: ____
100
7 = ____
___
100
10
24.
10
a. highest temperature
90
b. lowest temperature
80
0
difference from highest
temperature to 0
70
–10
F
highest
c. range of temperatures
F
lowest
difference from lowest
temperature to 0
+
sum of the differences
a.
b.
c.
___
25. 92 +√81
26. a. List the factors of the smaller number (70).
© 2008 Saxon
Cross out those that are not factors of the larger number (100).
,
,
,
,
,
,
70 ÷ __ =
b. ____
100
,
a.
b.
Saxon Math Intermediate 5
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641
Adaptations Lesson 98
11/3/07 12:01:03 PM
page 642
Written Practice, continued
1
1 × __
27. a. __
3
2
1
__
2
1
1 × __
b. __
3
2
28.
Which transformation moves the first
triangle to the position of the second
triangle?
1
__
3
A translation
B rotation
C reflection
D slide
Use work area.
29. Which of these numbers is a composite number?
A 3
B 5
C 7
D 9
30. least to greatest
0.376
0.037
© 2008 Saxon
0.38
0.367
,
Saxon Math Intermediate 5
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642
,
,
Adaptations Lesson 98
11/3/07 12:01:05 PM
LESSON
Name
99
Teacher Notes:
page 644
• Review “Decimal Arithmetic
Reminders Chart” on page 9 in the
Student Reference Guide.
• Adding and Subtracting
Whole Numbers and
Decimal Numbers
• For additional practice, students
may complete Targeted Practice 99.
New Concept
• Line up the decimal points.
• Fill empty spaces with zeros.
• Put a decimal point on the back of any whole number.
Example
6.2 + 4.25 + 3
6.20
4.25
+ 3.00
13.45
Lesson Practice
Find each sum or difference:
4.3
a.
+
12.0
b.
+
.
6.4
c.
+
.
4.4
d.
.
.
+
56.4
© 2008 Saxon
f.
+
8.2
g.
.
.
+
Saxon Math Intermediate 5
SM_H5_AD_L099_FF.indd 643
9.2 i.
h.
.
.
+
643
5.2
e.
+
.
4.75
–
.
.
j.
.
12.4
–
.
.
Adaptations Lesson 99
11/3/07 12:04:00 PM
Lesson Practice, continued
k. Which digit in 24.7 is in the same place as the 6 in 16?
l.
Compare: 12
12.0
Written Practice
1.
girls
_____
boys
__
=
page 646
__
2.
Cancel the matching zeros.
Don’t convert.
ate
2 =
__
___________
total pieces 2
__
What percent is that?
Simplify.
3.
pens
_____
$
5 = ___
__
?
1
4. “Slower” means more time.
13.8
0013.0
6. 10n = 100
5. decimal and reduced mixed number
3
4
© 2008 Saxon
n=
X
n2 =
.
Saxon Math Intermediate 5
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644
Adaptations Lesson 99
11/3/07 12:04:02 PM
page 647
Written Practice, continued
7. one thousand, six hundred twenty
and three tenths
.
8.
Estimate the area.
2 ft 11 in.
Area = length × width
2 ft 11 in.
6 ft 10 in.
6 ft 10 in.
9.
10. $7.13
7
__
8
3 = − __
__
8
4
Use work area.
11. Label the figure.
R
S
?
T
© 2008 Saxon
Q
Saxon Math Intermediate 5
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645
Adaptations Lesson 99
11/3/07 12:04:03 PM
page 647
Written Practice, continued
___
13.4
12.
+
.
15. 60 =
2
13.
7.25
–
___
14. √ 25 – √ 16
.
0
_________
16. 28 ) 9
5
2
17. $18.27 ÷ 9 =
______
Think 30 ) 1 0 0 0 .
5 + 1 __
7=
18. 4 __
8
8
3−1 =
19. 5 − 2 __
5
1=
3 × __
20. __
4 3
Cross cancel.
Convert and simplify.
3÷ 3 =
__
4
3
__
4
× __ =
22. Write the missing
number as your
answer.
9
___
10
20 =
23. Reduce: ____
100
© 2008 Saxon
21. Copy, change, and flip.
= ____
100
Cross cancel.
Saxon Math Intermediate 5
SM_H5_AD_L099_FF.indd 646
646
Adaptations Lesson 99
11/3/07 12:04:05 PM
page 648
Written Practice, continued
24. Gallons
Fluid Ounces
1
2
3
4
5
128
256
384
512
640
the number of
a. Rule:
by
.
b. How many fluid ounces in 8 gallons?
ounces in each gallon
×
number of gallons
Use work area.
25. Use digits and symbols to write the temperature that is ten degrees below zero
Fahrenheit.
26.
à1
© 2008 Saxon
3,
à3
4,
à?
7,
3, 4, 7, 12, 19,
Saxon Math Intermediate 5
SM_H5_AD_L099_FF.indd 647
à?
12,
à?
19,
,
____,
,
, ...
647
Adaptations Lesson 99
11/3/07 12:04:06 PM
page 648
Written Practice, continued
27. A standard number cube is rolled once.
a. What is the probability that the upturned face is 3 or less?
b. Describe a different event that has the same probability.
The upturned face is an
number.
Use work area.
28. two billion, six hundred million
Expanded notation using powers of 10
See
page 506.
×
(
)+(
×
)
Use work area.
29. Which transformation would position triangle A on triangle B?
y
5
4
3
A translation
B rotation
C reflection
D flip
A
2
1
B
x
1
2
3
4
5
© 2008 Saxon
0
3 = ___
00
3 + __
30. __
8
8
00
Reduce.
Saxon Math Intermediate 5
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648
Adaptations Lesson 99
11/3/07 12:04:07 PM
LESSON
Name
100
page 649
• Simplifying Decimal
Numbers
New Concept
• Get rid of the extra zeros in front and back.
• Keep the zero in front of the decimal.
• Don’t remove zeros in the “middle.”
Example
0 2.0 1 0 0 = 2.0 1
0.4 2 0 0 = 0.4 2
Lesson Practice
Simplify each decimal number:
a. 0 3 . 2 0 =
b. 0.320 =
c. 32.00 =
d. 3.020 =
Simplify each answer.
e.
3.65
+ 6.35
f.
=
23.16
– 19.46
g.
4.23
– 3.18
=
=
© 2008 Saxon
h. Attach a zero to the end of 2.5 without changing its value.
i.
Attach a zero to the end of 6 without changing its value.
Saxon Math Intermediate 5
SM_H5_AD_L100_FF.indd 649
649
.
.
Adaptations Lesson 100
1/3/08 10:17:26 PM
page 651
Written Practice
_______
1. carrots
peas
____
=
____
10 = __
2. rolls ____
3.25
?
$
3×
3. __
4
____
=
Cross cancel.
3=
__
4
percent
Reduce.
4.
5. Attach a zero to the end
of 8 without changing the
value of the number.
Use a decimal.
a. How many pins form the perimeter?
b. How many small squares cover
the rectangle?
a.
b.
3
6. a. 7 __
4
.
A
B
C
D
b. negative 2
0
a.
5=
7. __
6
10
© 2008 Saxon
–10
b.
1 __
m
5
__
8. cm
=
?
___
12
3
__
= – ___
4
12
Use work area.
Saxon Math Intermediate 5
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Adaptations Lesson 100
11/3/07 12:10:14 PM
page 652
Written Practice, continued
1
__
2
6.2 0
10.
9. Find AD.
.0 0
of 40 mm is
A
mm.
+
B
C
.0 0
D
?
11. 103 − 102 =
6.37
12.
−
14. 10 × $1.75 =
13.
234
× 506
.
15. $17.50 ÷ 10 =
16. Write the missing
number as your answer.
1 = _____
___
50 100
___
18. √ 6 4 =
19. 16w = 832
© 2008 Saxon
40 =
17. Reduce: ____
100
w=
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11/3/07 12:10:16 PM
page 652
Written Practice, continued
5 + __
5=
5 + __
20. __
9 9 9
9 =
9 × ___
21. ___
10 10
22. Copy, change, and flip.
2 ÷ __
3=
__
3 4
Convert and reduce.
3
23. 3 ÷ __ =
4
24.
yd
ft
1
__ = 10
___
?
Cross cancel.
25. See page 3 in the Student Reference Guide.
June (start on Jun. 21)
July
August
September
© 2008 Saxon
October
November
December (don’t count Dec. 21)
Saxon Math Intermediate 5
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+
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Written Practice, continued
page 653
26.
a. How many faces?
a.
b. How many edges?
b.
27.
10
0
Ľ10
C
5º colder than 0ºC
28.
have a
brother
7
6
have a
sister
9
© 2008 Saxon
a. How many children have a brother?
b. How many have a sister but not a brother?
c. The numbers in the circles do not add to 30. What does that mean?
children have
siblings.
Use work area.
Saxon Math Intermediate 5
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page 653
Written Practice, continued
29.
Elapsed Time (in minutes)
0
10
20
30
Distance Traveled (in miles)
0
6
14
22
a. line graph
2 = 44
22 × __
___
b. miles ___
2
min 30
2 = 88
miles 44
___
___
× __
2
min
A rate of 22 miles in 30 minutes is equal to a rate of 44 miles
in
minutes and 88 miles in
minutes, which is about
hours.
Use work area.
30. North Canadian River
of North Canadian River
Wisconsin River
Saxon Math Intermediate 5
SM_H5_AD_L100_FF.indd 654
_1
2
© 2008 Saxon
_1
2
of North Canadian River + 30
654
Adaptations Lesson 100
11/3/07 12:10:21 PM