Download Review Multiplying and Dividing Decimals

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Review Multiplying and Dividing Decimals
Multiplying and dividing decimals follows different rules from adding and subtracting.
Multiplying Decimals
Usually, students learn this rule for multiplication: To multiply decimals, multiply them while
ignoring the decimal point. Then count the number of digits to the right of the decimal in
each factor and add them. Place the decimal that many digits to the left.
Here is an example:
Multiply the numbers as if they were whole numbers.  0.2:0.07 2:7 = 14
Add the decimal places in 0.2 and 0.07.  2 + 1 = 3
Give the answer this many decimal places. 
Add zeros to the left if needed.  0.014
The reason this works is that decimals are really fractions. Read them aloud, and you’ll see.
To multiply two tenths and seven hundredths as fractions, multiply the numerators. This is
the same as ignoring the decimal points and multiplying. Then multiply the denominators.
2
7
14
10 : 100 = 1000
Because of the rules for multiplying powers of 10, the number of zeros in the denominator
of the answer is the sum of the zeros in the original factors. When you convert this fraction
to a decimal, you count over three decimal places to write the decimal point.
?
1. Multiply 4.231 by 0.12.
Multiply the numbers.  4.231:0.12 4231:12 = 50772
Find the correct number of decimal places.  3 + 2 = 5
Add the decimal point.  0.50772
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Essential Math Skills
Dividing Decimals
To divide decimals, use long division. You need to convert the divisor to a whole number.
Set Up the Division Problem and Move the Decimal
To divide decimals, use long division. Shift the decimal points of both the dividend and the
divisor to the right until you are dividing by a whole number. Why can you do this? A division
problem is the same as a fraction.
3 .2
3.2 ' 4.1 = 4.1
10 100
1000
Moving the decimal place is the same as multiplying by 10 , 100 , or 1000 . Since you’re
multiplying by one, you don’t change the value.
3.2 a 10 k 32
4.1 10 = 41
?
1. Set up the division problem and move the decimal: 23.562 ÷ 4.2
Set up long division, and then move the decimal one place so that you are dividing by 42.
Divide and Place the Decimal
g
4.2 23.562 " 42g 235.62
Divide the same way you would divide whole numbers. After dividing, write the decimal
point in the same location as in the revised dividend.
?
2. Divide. 42g 235.62
First, divide 42 into 235. Then bring down the next digit
and continue dividing. If you need to, add zeros to the
end of the dividend to divide until you get a remainder of
zero. If you don’t get a remainder of zero, you may need
to round you answer.
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Bring up the decimal point.
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