6
Flash Cards ÷6 and ×8
Speed Drill 6, page 63
Adding and Subtracting Fractions Vertically
You can add and subtract fractions horizontally.
3 + 6 = 9
11 11 11
7 – 5 = 2
11 11 11
You can also add and subtract fractions vertically. Follow this rule.
Add or subtract just the numerators. The denominator stays the same.
vertical
vertical
3
11
6
+ 11
9
11
7
11
5
– 11
2
11
Add or subtract these fractions vertically.
1. a. +
1
12
3
12
5
12
b. +
Add or subtract.
2. a.
7
9
–
4
9
=
1
4
1
4
b.
c. +
2
12
+
3
12
=
Go back to Numbers 1 and 2.
Circle the answers that equal one.
20
2
10
3
10
1
10
d. +
c. +
3
8
5
8
3
12
5
12
e. +
d. –
8
10
5
10
4
5
1
5
Lesson 6
Division With a Remainder
Sometimes when we divide into equal groups, there are some left over.
If we divide 16 walnuts into groups of 5, we have 1 left over.
3R1
5)1 6
number of walnuts
in each group
number of groups
and how many left
over
number of walnuts
all together
Draw circles to divide into equal groups. Write the division problem with the
remainder.
3. a. groups of 3
b. groups of 4
)13
) 11
c. groups of 2
)7
W e R emember
Flowing
lava is hot.
By the time it
rises to the surface
from 25 or more
miles beneath the
soil, it can still
be 1,832°F.
Use letters and symbols to name these.
4. Ray
C
G
E
G
5. Line
6. Line segment
F
G
D
G
A
G
B
G
21
Lesson 6
7. Mount Vesuvius is still an active volcano, so
its height changes each time it erupts. If the
mountain grew 42 feet higher in one week,
about how much higher did it grow each day?
(Hint: Think how many days are in a week.)
My Work Space
8. Italy is a boot-shaped peninsula 708 miles
long and 130 miles wide. How many more
miles is the length than the width?
My Work Space
Follow the directions. Use symbols.
G
Z
9. Name the line parallel to GH.
G
Z
R
Z
intersects TU.
M ental M ath . . . ?
12. a. double 71 =
13. a. double 24 =
22
b. double 45 =
b. double 16 =
H
G
10. Name the ray perpendicular to GH.
11. Name the line that
F
G
U
T
c. double 36 =
c. double 48 =
S
Lesson 6
-
S kill B uilders +÷ x
37
25
14. a. + 4 2
48
15. a. × 6
1
2
1
b. + 5
3
7
0
6
9
8
7
7
72
b. × 8
2
3
4
5
c. + 7
c.
Measure. Write the answers.
16. The diameter of the circle is
18. Radius × 2 =
19. Diameter ÷ 2 =
4
7
+
19
16
e. + 8
1,052
2,190
d. + 1 , 3 0 7
=
d.
5
6
32
5
29
8
f. + 1 2
–
2
6
6
1
5
6
2
7.2
10.6
e. + 4 . 5
=
cm.
17. The radius of the circle is
Write radius or diameter.
4
7
1
5
9
8
6
cm.
.
.
Be sure you know how many days are in each month and the measurements below.
You will have them on your speed drills, starting in Lesson 7.
F act F ocus
20. 24 ÷ 6 =
42 ÷ 6 =
22. 18 ÷ 6 =
1L=
21. 54 ÷ 6 =
23. 36 ÷ 6 =
24. 48 ÷ 6 =
1 cm =
1 tbsp =
1m=
January has
mm
mL
tsp
mm
December has
March has
July has
August has
days.
days.
days.
days.
days.
23
7
Flash Cards ÷9 and ÷2
Speed Drill 7, page 64
Factors
2 × 8 = 16
You know that 2 and 8 are factors, and 16 is the product. But there are other factors
that also give the product 16.
1 × 16 = 16
4 × 4 = 16
The factors of 16 are all the numbers that can be multiplied to get 16. The factors of
16 are 1, 16, 2, 8, 4.
Think:
1 × 12 = 12, 2 × 6 = 12, and
3 × 4 = 12, so the factors of 12
are 1, 12, 2, 6, 3, and 4.
Write the factors of 27.
1.
Write the factors of 18.
2.
Write the factors of 8.
3.
24
What are the factors of 12?
1
12
2
6
3
4
Lesson 7
Finding a Fraction of a Number
You can find one-half of a number by dividing by 2.
1
2
of 12 = __
12 ÷ 2 = 6
1
3
of 15 = __
15 ÷ 3 = 5
1
4
of 20 = __
20 ÷ 4 = 5
1
10
of 30 = __
30 ÷ 10 = 3
Here’s a
quick way to
multiply by 50:
Write down the
number that you want
to multiply. Add two
zeros to the end
of it and then
divide by 2.
You can find one-third of a number by dividing by 3.
To find one-fourth of a number, divide it by 4.
To find one-tenth of a number, divide it by 10.
Write division facts to answer these questions. One is done for you.
4. a.
1
5
of 10
6. a.
1
3
of 18
5. a.
1
2
of 16
10 ÷ 5 = 2
b.
b.
b.
1
6
of 6
1
4
of 12
1
10
of 20
W e R emember
Circle equal groups. Write the division problem with the remainder.
7. a. groups of 6
)15
b. groups of 5
)13
c. groups of 8
)20
25
Lesson 7
8. Italians are famous for their delicious,
crusty bread. It takes 3 cups of flour to
make each loaf. How many loaves could
be made from 21 cups of flour?
My Work Space
9. Many ancient homes in Rome did not have
ovens. Julia made 18 loaves and took them
to Quartus the baker to have them baked.
Quartus could bake 6 loaves at a time in his
oven. How many times did Quartus need to
fill his oven to bake all of Julia’s loaves?
My Work Space
-
S kill B uilders +÷ x
460
10. a. – 1 8 2
13
11. a. × 7
637
b. – 5 9 2
18.3
b. + 4 2 . 6
502
c. – 1 9 5
c. +
3
8
5
8
Go back to Number 11.
Circle the fraction answer that equals one.
26
d. –
1,008
99
d. –
8
10
5
10
e.
2
12
f.
7
9
700
e. – 1 3 6
+
+
3
12
4
9
=
=
Lesson 7
M ental M ath . . . ?
12. a. double 28 =
b. double 95 =
c. double 18 =
14. a. double 34 =
b. double 9 =
c. double 82 =
13. a. 19 + 2 =
b. 48 + 5 =
Name the commas.
15. 25,303,495
16. 11,685
25
c. 72 + 8 =
, 303
11
, 495
, 685
Answer the questions.
17. If the radius of a circle is 12 inches, what is the diameter?
18. If the diameter of a circle is 14 inches, what is the radius?
Write the correct word.
19. Radius × 2 =
.
20. Diameter ÷ 2 =
inches
inches
.
The division facts below will be on your Speed Drill in Lesson 8.
Study any you do not know.
F act F ocus
21. 12 ÷ 6 =
24 ÷ 6 =
February has
23. 42 ÷ 6 =
60 ÷ 6 =
July has
days.
April has
days.
22. 54 ÷ 6 =
24. 30 ÷ 6 =
25. 18 ÷ 6 =
36 ÷ 6 =
48 ÷ 6 =
6÷6=
January has
October has
days in leap year.
days.
days.
27