Transcript Multiplying Decimals

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Adding and Subtracting
Decimals
Solve problems involving addition
and subtraction of decimals.
To add decimals
Line up the decimal points and add the
columns from right to left.
Place a decimal point in the answer
directly below the other decimal points.
Example 1
0.64 + 0.39
Line up the decimal points.
0.64
+ 0.39
__________________________
Add the columns.
0.64
+ 0.39
__________________________
1.03
Example 2
5.74 + 3.3
Line up the decimal points.
5.74
+ 3.3
_____________________________
Add the columns.
5.74
+ 3.3
_____________________________
9.04
Try this one on your own!
39.66
+22.7
Remember,
line up the decimals,
Place the decimal point in the answer
under the ones in the problem,
Add like whole numbers.
11
39.66
+22.7
62.36
To subtract decimals
Line up the decimal points.
Subtract the columns from right to left,
regrouping if necessary.
Place a decimal point in the answer
directly below the other decimal points.
Example 1
0.86 – 0.49
Line up the decimal points
0.86
- 0.49
__________________________
Regroup the tenths. Subtract the columns.
7 16
0.86
- 0.49
__________________________
0.37
Multiplying Decimals
0.7
You can use graph paper to model
decimal multiplication. Here is a
model of the product of 0.7 and 0.3.
0.3
1
Because 21 of the 100 squares are
shaded, 0.7  0.3 = 0.21.
1
Multiplying Decimals
Words
Multiply decimals as you would whole
numbers. Then place the decimal point in the product.
The number of decimal places in the product is equal to
the sum of the number of decimal places in the factors.
Numbers 0.7  0.3 = 0.21
Multiplying Decimals
EXAMPLE
1
Multiplying Decimals
5.82
0.41

––––––
582
2 328
–––––––
2.3 8 6 2
1234
2 decimal places
2 decimal places
+
–––
4 decimal places
Multiplying Decimals
Checking Reasonableness To check that the product in Example 1 is
reasonable, round each factor to the place value of the leading digit, then
multiply. The leading digit of a number is the first nonzero digit.
5.82
6
Round to the nearest whole number.
0.41
0.4
Round to the nearest tenth.
Because 6  0.4 = 2.4, the product of the previous example is reasonable.
Multiplying Decimals
EXAMPLE
2
Multiplying Decimals
6.45
 18
––––––
5160
645
––––––
116.10
2 decimal places
+ 0 decimal places
–––
2 decimal places
After you place the decimal
point, you can drop any zeros
at the end of an answer.
ANSWER 6.45  18 = 116.1
CHECK
Because 6  20 = 120, the
product is reasonable.
Multiplying Decimals
EXAMPLE
2
Multiplying Decimals
6.45
 18
––––––
5160
645
––––––
116.10
2 decimal places
1.273
+ 0 decimal places
0.06

–––––––
–––
0.07638
2 decimal places
+ 2 decimal places
–––
5 decimal places
Write a zero before the 7 as a
placeholder so that the number
has 5 decimal places.
After you place the decimal
point, you can drop any zeros
at the end of an answer.
ANSWER 6.45  18 = 116.1
3 decimal places
ANSWER 1.273  0.06 = 0.07638
CHECK
CHECK
Because 6  20 = 120, the
product is reasonable.
Because 1  0.06 = 0.06,
the product is reasonable.
Multiplying Decimals
EXAMPLE
3
Multiplying Decimals to Find Area
Central Park Central Park is a rectangular park about 2.5 miles long and
about 0.5 mile wide. What is the area of Central Park?
SOLUTION
A = lw
Write formula for area of a rectangle.
= 2.5(0.5)
l w
Substitute 2.5 for l and 0.5 for w.
= 1.25
Multiply.
ANSWER
The area of Central Park is about 1.25 square miles.
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Diana Lenartiene, IRSC ABE Instructor