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7.2B Solve problems (Decimals & Fractions)
Adding decimals
Ex1: 7 + 3.08 + 4.9
 Pay attention to place value. You can
give all decimal numbers the same place
value by placing zeros to the right of the
decimal point (by filling in zeros).
 Line up the numbers using the ones digits
and the decimal points.
 Add in each place value position.
 Regroup when needed.
7.00
3.08
+4.90
14.98
Subtracting decimals
Ex 2: 40-2.07
 Place the larger decimal number on top.
 Pay attention to place value.
 Line up the numbers using the ones digits
and the decimal points.
 Subtract in each place value position.
 Regroup when needed.
40.00
- 2.07
37.93
Multiply decimals
 To multiply decimals, first multiply the
numbers as if they were whole numbers.
(place the larger number of digits, not
including zeros, on top)
 Then place the decimal point correctly in
the product. To place the decimal point
correctly in the product, count the total
number of decimal places to the right of
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7.2B Solve problems (Decimals & Fractions)
the decimal point in the factors. The same
number of decimal places should be to
the right of the decimal in the product as
is the total number of decimal places to
the right of the decimal in the factors.
Decimal points are not lined up in
multiplication as you do in addition and
subtraction.
 Before you multiply decimals, you should
round to the nearest whole number and
estimate the answer. This is a good way
to be certain the decimal point has been
correctly placed in the product.
Ex 3: 2.8 x 0.785
Whole
Number
Multiplication
785
x 28
6280
+15700
21980
Divide decimals
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Decimal
Number
Multiplication
0.785 3 decimals
x 2.8 1 decimal
6280 4 decimals
+15700
21980 = 2.1980
Estimate of
Decimal
Multiplication
2.8 ≈ 3
0.785 ≈ 1
3x1=3
Since I
rounded up,
my actual
answer is less
than 3.
 To divide a number by a decimal, count
7.2B Solve problems (Decimals & Fractions)
the number of decimal places to the right
of the decimal point in the divisor. Then
move the decimal point to the right that
many places in both the divisor and the
dividend.
 Divide as you would for whole numbers.
Then place the decimal point in the
correct place in the quotient (i.e. over the
decimal point in the dividend).
 Before you divide decimals, you should
round to the nearest whole number and
estimate the answer. This is a good way
to be certain the decimal point has been
placed in the correct place in the quotient.
Decimal point in answer
Ex 4:
2.7 9.18
1
1
2.7 9.18 =
3.4
2.7 9.18

81
0108
 108
0
The answer is 3.4.
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7.2B Solve problems (Decimals & Fractions)
Add /Subtract Fractions
 If the fractions have the same
denominator, add or subtract the
numerators and use the same
denominator.
 If the fractions have unlike denominators,
rewrite them as equivalent fractions with
a common denominator.
 Then add or subtract the numerators and
3
3
Ex 5:  2
4
8
use the common denominator.
Since the Least Common Multiple of 4 and 8 is
8, the common denominator will be 8.
For 4: 4, 8, 12, 16
For 8: 8, 16, 24
3 2 6
  
4 2 8
3 ?

4 8
3
?
2 2
8
8
3
3
6
3
2 = 2
4
8
8
8
3 1
3
 2    2
8 1
8
3
3
6
3
9
2 = 2 2
4
8
8
8
8
9
2 =?
8
1
8
9 8 1
1
8 9 or    1
8 8 8
8
1
2
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9
1
1
 2 1  3
8
8
8
7.2B Solve problems (Decimals & Fractions)
1
8
The answer is 3 .
1 7
5 15
Ex 6: 6 
Since the Least Common Multiple of 5 and 15
is 15, the common denominator will be 15.
For 5: 5, 10, 15, 20
For 15: 15. 30, 45
6

1  3
3
6    6
5  3
15
1

5 15
7

15 15

7 1
7
   
15  1 
15
You can’t subtract
3 from 7, so
regroup.
6
3
15 3
18
5 
5
15
15 15
15
7

15
The answer is 5
Multiply Fractions
11
.
15
 Convert mixed numbers to a fraction by
multiplying whole # with the denominator
& add numerator, then the answer is put
over the denominator.
 Convert whole numbers to a fraction by
putting the # of 1.
 Simplify a numerator & a denominator if
possible.
 When you multiply fractions, first multiply
the numerators to get the numerator of
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7.2B Solve problems (Decimals & Fractions)
the product. Then multiply the
denominators to get the denominator of
the product. The fractions do not need a
common denominator.
Ex 7:
2
3
6 5
5
4
Since 6(5) + 2= 32, then 6
2 32
5

;5=
5 5
1
32 5 3
 
5 1 4
Simplify both the numerator 5 & denominator 5
to 1 by dividing each by 5.
Simplify both the 32 & 4 by dividing each by 4;
then 32 becomes 8 & 4 becomes 1.
32 5 3
8 1 3 24
  =
  
 24
5 1 4
1 1 1 1
The answer is 24.
Divide Fractions
 To divide a number by a fraction, multiply
the number by the reciprocal of the
divisor (i.e. the second fraction).
Ex8:
3 33

and
5 5
1
2
the reciprocal of is ,
2
1
13
1
33 2 66
then    5 66 = 13
5
5 1 5
-5
16
-15
1
1
The answer is 13 .
5
3 1
6 
5 2
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Since 6(5)+3 = 33, then 6
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7.2B Solve problems (Decimals & Fractions)
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