Transcript MULTIPLYING AND DIVIDING DECIMALS

Math 7
MULTIPLYING DECIMALS
 Multiplying Decimals to get a precise
answer is a relatively simple
task…assuming you know how to
multiply
 You don’t have to line up the decimal
points like in addition and subtraction
MULTIPLYING DECIMALS
 Multiply the numbers as if no decimal
points existed
 When the product is reached, it is time to
place the decimal point in your answer
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Count up the number of places after the decimal in
each of the numbers
From the end of the product, move in that many
places to the left and put the point in
Eliminate any “unnecessary zeros” on the end of the
answer
EXAMPLES OF MULTIPLYING
DECIMALS
7.29 · 2.1
14.319 · 3.18
11.2 · 0.7
Does this answer make sense? Why?
WORD PROBLEMS
 If your speed is 3.5 miles per hour, how
far will you bike in 1.2 hours?
 A cubic foot of water weighs 62.4 lbs. A
water storage tank can hold 89.5 cubic
feet of water. How much will the water
in tank weigh when the tank is full?
MORE WORD PROBLEMS
 You have 17 pennies, 31 nickels, 22
dimes, and 14 quarters. How much
money will you have left if you lend
your friend $6.50?
PROPERTIES OF
MULTIPLICATION
 Identity Property of Multiplication
6 · 1 = 6 OR
x·1=x
-The Identity Property of Multiplication
states that any number times 1 will
always get you the number back in
return
-Thus, the number 1 is called the
Identity Element of multiplication
PROPERTIES OF
MULTIPLICATION
 Zero Property of Multiplication
6·0=0
OR x · 0 = 0
-The Zero Property of Multiplication states that any
number times zero (0) is always going to equal zero
(0)
 Commutative Property of Multiplication
6 · 3 = 3 · 6 OR xy = yx
-The Commutative Property of Multiplication states
that when you multiply two numbers together, the
order they are listed does not matter
PROPERTIES OF
MULTIPLICATION
 Associative Property of Multiplication
6 · (3 · 2) = (6 · 3) · 2 OR a(bc) = (ab)c
-The Associative Property of Multiplication
states that if you have three or more numbers
being multiplied together, you can multiply
any two at a time, and then multiply the result
by the remaining number(s)
DIVIDING DECIMALS
 Dividing decimals is also relatively easy, so long
as you can perform long division. However,
steps must be taken to simplify the process at
the beginning of the problem.
 The divisor (denominator, second number,
bottom number, or the number on the
“outside of the house”) must be adjusted so
that no decimals are present.
DIVIDING DECIMALS
 In order to get the divisor to be decimal free, simply move
the decimal point to the right end of the number, counting
how many places it moved.
 Since you adjusted the divisor, the dividend (numerator,
first number, number on top, or the number “inside the
house”) has to be adjusted the same way.
 Thus, move the decimal point just as many times as you did
in the divisor.
 If a decimal point still exists in the dividend, bring it up on
top of the “house” directly where it is in the “house”.
Divide, keeping your place values according to the point.
EXAMPLES OF DIVIDING
DECIMALS
 4.32 ÷ 1.2
 16.5 ÷ 1.5
Write it in “house form”
MORE EXAMPLES OF
DIVIDING DECIMALS
2.064 ÷ 0.24
144.06 ÷ 9.8
67 .84
0.64
WORD PROBLEMS
 You use 0.6 lb of bananas in each smoothie.
How many smoothies can you make with 3.12
lb of bananas?
 A car travels 360.25 mi. It uses 13.1 gal of gas.
How many miles per gallon of gas does the car
travel?
WORD PROBLEMS
 You spend $13.92 on fabric. Each yard costs
$4.35. How many yards of fabric did you buy?
 You buy 5 movie tickets for a total of $23.75.
Your friend gives you $5 for one ticket. How
much change should you give your friend?