Name: ________________________________________________ Date:________________________
LESSON 51: MENTALLY DIVIDING DECIMAL NUMBERS BY 10 AND BY 100
Saxon 7/6 page 251
*When we divide, numbers get ______________________!
Ex:
12.5 ÷ 10 = 1.25
12.5 ÷ 100 = 0.3
*When divide decimals by 10 and 100, count the ____________________ and move the decimal that
many places to the LEFT.
Ex:
37.5 ÷ 10 =
37.5 ÷ 100 =
**moving the decimal to the left will make the number ___________________________.
*Where is the decimal in a whole number? All the way to the _________________. All numbers have a
decimal even if it is not written.
Ex: 34 = 34.
8=
390=
1004=
PRACTICE:
Mentally divide and write your answer as a decimal.
a. 2.5 ÷ 10 =
b. 2.5 ÷ 100 =
c. 87.5 ÷ 10 =
d. 87.5 ÷ 100 =
e. 0.5 ÷ 10 =
f. 0.5 ÷ 100 =
g. 25 ÷ 10 =
h. 25 ÷ 100 =
Name: ________________________________________________ Date:________________________
LESSON 52: DECIMALS CHART ■ SIMPLIFYING FRACTIONS
Saxon 7/6 page 254
DECIMALS CHART
+ Line up the decimal points.
x
÷ by whole number
Multiply. Then count
Decimal point moves up.
decimal places.
1. Place a decimal point to the right of a whole number.
2. Fill empty places with zeros.
÷ by decimal
Over, over, up.
Simplifying Fractions Means:
a.) Reducing to lowest terms
b.) Changing improper fractions to mixed numbers
2
Example:
3
+
5
2
6
3
+
x
2
2
=
4
6
5
5
6
6
9
6
REDUCE =
3
2
CONVERT = 2) 3
PRACTICE:
a. Discuss how the rules in the decimals chart apply to each of these problems. Solve each problem.
5 - 4.2
.04 x 0.2
0.12 ÷ 3
5 ÷ 0.4
b. Fill in the decimal chart.
+ -
x
÷ by whole number
÷ by decimal
1. Place a decimal point _______________________________________________________.
2. Fill empty places ___________________________.
Add then simplify:
c.
5
6
+
5
12
d.
9
10
+
3
5
e.
2
3
+
7
12
Name: ________________________________________________ Date:________________________
LESSON 53: MORE ON REDUCING ■ DIVIDING FRACTIONS
Saxon 7/6 page 258
**Reduce by crossing off numbers that are the same in the numerator and denominator.
2∙2∙3∙5
Example:
2∙2∙3
5
=
2
2∙2∙2∙5
Example:
Example:
=
2 ∙ 2 ∙ 3∙ 5
How many
3
4
÷
=5
1
3
1
3
’s are in 4 ?
2
1
3
2
4
x
**This is a ____________________ problem.
1
3
2
4
Change
multiplication
to division
Example:
How many
3
x
2
1
=
6
4
=
3
2) 3
2
Multiply
and
reduce
Reciprocal
of the 2nd
fraction
1
’s are in 2 ?
4
Practice:
a.
2∙2∙3∙5
b.
2∙2∙5
c. How many
3
1
’s are in 2 ?
8
2∙2∙3∙3∙5
2∙2∙3∙5∙5
d. How many
1
3
’s are in 8 ?
2
Name: ________________________________________________ Date:________________________
LESSON 54: COMMON DENOMINATORS, PART 1
Saxon 7/6 page 265
*When the denominators of two or more fractions are the ___________, we say the fractions have
COMMON DENOMINATORS.
1
Examples:
8
1
8
and
+
3
8
3
2
8
5
2
=
5
and
3
4
5
9
3
=
4
+
5
9
and
-
3
9
3
?
=
*When _________________________ and ___________________________ fractions, you must have
COMMON DENOMINATORS.
Example:
1
2
+
3
1
4
2
+
x
2
2
=
2
**Rename
4
3
3
4
4
5
1
2
by multiplying by
CONVERT = 4) 5 = 1
4
Example:
1
2
-
1
1
6
2
-
x
=
3
6
1
1
6
6
2
6
**Rename
1
2
REDUCE =
Practice:
a.
1
+
3
d.
1
-
1
2
8
2
4
b.
3
+
1
e.
5
-
1
8
4
8
4
c.
3
+
1
4
8
f.
3
-
3
4
8
1
4
2
2
Name: ________________________________________________ Date:________________________
LESSON 55: COMMON DENOMINATORS, PART 2
Saxon 7/6 page 270
*Sometimes we need to rename both fractions before we can add or subtract.
Example:
1
2
+
1
1
3
3
3
2
3
6
1
2
2
3
2
6
x =
+ x =
1
3
1
2
**Rename 2 by multiplying by 3
**Rename 3 by multiplying by 2
5
6
Example:
3
4
-
2
3
3
4
x
=
- x
=
2
3
9
12
8
12
**Rename
**Rename
3
4
2
3
1
12
Practice:
a.
2
+
1
d.
2
-
1
3
2
3
4
b.
1
+
2
e.
1
-
1
4
5
3
4
c.
3
+
1
4
3
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
_____
N. Taylor