multiplying and dividing decimals
TRANSCRIPT
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Multiplying and Dividing with
Decimals
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Multiplying• Maybe multiplying with decimal points seems a little scary! BUT…
• There is a simple 3-step trick to multiply decimal point numbers just as if they were whole
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• While we learn the steps, we will look at the example:
5.8X 7
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Step 1• Count the number of digits to the right of the decimal point
5.8X 7
1 digit
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Step 2• Just ignore the decimal point!• Multiply just as if they were normal whole numbers
5.8X 7 5 8X 7
5
64 0
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Step 3• Use the number of digits from Step 1 to count out where to put the decimal
• We counted 1 digitin Step 1, so we move the decimal point by 1 place to the left now
5.8X 74 0 6 . .
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That’s It!• Our final answer is:
5.8X 7 4 0.6
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What are we Really Doing?• When we “ignore” a decimal
point, we are really multiplying by 10 for each digit to the right of the decimal.
5 8X 7
x 10 5.8X 7
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What are we Really Doing?• Now you multiply the numbers
without decimals
• BUT DON’T FORGET WE MULTIPLIED BY 10 EARLIER!
5 8X 74 0 6
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What are we Really Doing?• So now we divide by 10
• Moving the decimal to the left one place is the same as dividing by 10!
/ 10
/ 10
5 8X 74 0 6 . .4 0 6
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Multiplying Decimals by Whole Numbers
If there are not enough decimal places in the product, you need to add zero to the left.
For example:– Find 2 x 0.018
0.018x 20.036 Annex a zero to the left of 36 to make
three decimal places.
There are three decimal places.
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Multiplying Decimals by Whole Numbers
Your turn! • Find 11.4 x 8
• Multiply 3 x 0.02
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• Let’s try it again with more digits to the right of the decimal point this time
0.024X 0.61
Multiplying Decimals
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• What was Step 1?• Count the digits to the right of the decimal point
• From 0.024, how many digits?
• What about from 0.61?
• That gives a total of:
3
2
5
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• What was Step 2?• Ignore the decimal points
• That means that 0.024 becomes:
• In the same way, 0.61 is:24
61
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• Now we just multiply that out
2 4X 6 1
4204
2
1 41 4 6 4
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• What was Step 3? Place the decimal point in our answer. What did we count in Step 1? Now move the decimal that many places to the left
• But wait! There are only 4 numbers!
0.024X 0.611 4 6 4.
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• Since we need to move the decimal point 5 places to the left but only have 4 numbers, we write the 0 out in front.
0.024X 0.61
0 1 4 6 4 ..
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• Don’t forget, its the same as dividing by 10, five times
• For our final answer, we have 0.024
X 0.610.01464
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Multiplying Decimals
Your turn! Multiply 0.014 x 3.7
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Canoeing If a group of people
set out in 14 canoes, and they each canoe for 8.6 miles, how many total miles were traveled by the canoes?
120.4 miles
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Backpacks• The canoers weighed all
their packs before leaving and found that all together they weighed 195.2 lbs. If 1 lb = 0.45 kg, how many kilograms of gear have the canoers brought along?
87.84 kgs
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Dividing Decimals by Whole
NumbersDivide a decimal by a 1-Digit Number
Find 6.8 ÷ 2. 4.3
0080868.62
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Dividing Decimals by Whole NumbersDivide a decimal by a 2-Digit
NumberFind 7.49 ÷ 14. 535.0
0000700704204970490.714
Place the decimal point
Annex a zero and continue dividing
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Dividing Decimals by Whole Numbers
Your turn! Find 3.49 ÷ 4
Find 1087.9 ÷ 46
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Dividing by Decimals
• When we divide numbers with decimal points, we use the same idea as multiplying them
• Keeping everything lined up is key!
21.086.2
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Step 1• Multiply both the divisor and dividend by whatever power of 10 we need so that the divisor is a whole number
21.086.2
210.862
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Step 2• Divide just like normal• Ignore the decimal point
210.8623
186
0
4
1 1
2 8
104
2480
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Step 3• Bring up the decimal point The decimal point in the quotient is placed directly above where it is in the number being divided
210.8623 4.
• This is why keeping numbers aligned is so important!
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Dividing by Decimals
• Example: Find 14.19 ÷ 2.2
19.142.2
Multiply by 10 to make a whole number
Multiply by the same number, 10
45.6
000000110001100880099132
90.14122
Place the decimal point
Divide as with whole numbers
Annex a zero to continue
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Dividing by Decimals
Your turn!Divide 0.4 ÷ 0.0025
Divide 1087.9 ÷ 4.6
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3 Steps of Division:• Multiply both the divisor and the dividend by a power of 10
• Ignore the decimal and divide like normal
• Bring up the decimal from its position in the divisor
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Backpacks, Again• If each canoer carries 5.49
kgs of gear while hiking (out of the total 87.84 kgs), how many canoers are there total? Note: some canoes may have more than one canoer.
16 canoers
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Kilograms• If 1 lb = 0.45 kg, how many
pounds is each canoer carrying when every backpack is 5.49 kgs?
12.2 lbs
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Let us practice!Find 12.9 x 7 Find 0.82 x 4Find 0.04 x 5.1 Find 0.04 x 0.0063Find 203.84 ÷ 32 Find 136.5 ÷ 35
Divide Divide2.508.0155.025.0