1. CONFIDENTIALCONFIDENTIAL
Let us warm up with some practiceLet us warm up with some practice
101055
==
2 x 14 + 2 x 6 =2 x 14 + 2 x 6 =
2 x 1 + 2 x 1 =2 x 1 + 2 x 1 =
6.8 + 6.8 + 10.2 + 10.2 =6.8 + 6.8 + 10.2 + 10.2 =

2. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
When multiplying a decimal by a wholeWhen multiplying a decimal by a whole
number, multiply as with whole numbersnumber, multiply as with whole numbers
Then use estimation to place the decimalThen use estimation to place the decimal
point in the product.point in the product.
You can also count the number of decimalYou can also count the number of decimal
placesplaces

3. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
Method 1:Method 1:
– Use estimationUse estimation
Round 14.2 to 14Round 14.2 to 14
14.2 x 6 ->14x6 or 8414.2 x 6 ->14x6 or 84
14.214.2
x 6x 6
85.285.2
(Since the estimate is 84, place the(Since the estimate is 84, place the
decimal point after the 5)decimal point after the 5)
Example: Find 14.2 x 6Example: Find 14.2 x 6

4. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
Example: Find 14.2 x 6Example: Find 14.2 x 6
Method 2:Method 2:
– Count decimal placesCount decimal places
14.214.2
x 6x 6
85.285.2
There is one place to the
right of the decimal point.
Count the same number of
places from right to left.

5. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
Your turn! Find 11.4 x 8Your turn! Find 11.4 x 8

6. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
If there are not enough decimal places in the product, youIf there are not enough decimal places in the product, you
need to add zero to the left.need to add zero to the left.
For example:For example:
– Find 2 x 0.018Find 2 x 0.018
0.0180.018
x 2x 2
0.0360.036 Annex a zero to the left of 36 to make
three decimal places.
There are three decimal places.

7. CONFIDENTIALCONFIDENTIAL
Multiplying Decimals by Whole NumbersMultiplying Decimals by Whole Numbers
Your turn! Multiply 3 x 0.02Your turn! Multiply 3 x 0.02

8. CONFIDENTIALCONFIDENTIAL
Multiplying DecimalsMultiplying Decimals
When multiplying a decimal by a decimal, multiplyWhen multiplying a decimal by a decimal, multiply
as with whole numbers.as with whole numbers.
To place the decimal point, find the sum of theTo place the decimal point, find the sum of the
number of decimal places in each factor.number of decimal places in each factor.
The product has the same number of decimal places.The product has the same number of decimal places.

9. CONFIDENTIALCONFIDENTIAL
Multiplying DecimalsMultiplying Decimals
For example: Find 4.2 x 6.7For example: Find 4.2 x 6.7
4.24.2
x 6.7x 6.7
294294
252252
28.1428.14
One decimal place
One decimal place
Two decimal places
The product is 28.14. Compared to the estimate, the product is reasonable.
Estimate 4.2 x 6.7 ->4x7 or 28

10. CONFIDENTIALCONFIDENTIAL
Multiplying DecimalsMultiplying Decimals
Your turn! Multiply 0.014 x 3.7Your turn! Multiply 0.014 x 3.7

11. CONFIDENTIALCONFIDENTIAL
Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Dividing a decimal by a whole number is similarDividing a decimal by a whole number is similar
to dividing whole numbersto dividing whole numbers

12. CONFIDENTIALCONFIDENTIAL
Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Divide a decimal by a 1-Digit NumberDivide a decimal by a 1-Digit Number
– Find 6.8 ÷ 2. Estimate 6 ÷ 3 = 3Find 6.8 ÷ 2. Estimate 6 ÷ 3 = 3
4.3
00
8
08
6
8.62
−6.8 ÷ 2 = 3.46.8 ÷ 2 = 3.4 Compared to theCompared to the
estimate, the quotient is reasonable.estimate, the quotient is reasonable.

13. CONFIDENTIALCONFIDENTIAL
Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Your turn! Find 3.49 ÷ 4Your turn! Find 3.49 ÷ 4

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Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Divide a decimal by a 2-Digit NumberDivide a decimal by a 2-Digit Number
– Find 7.49 ÷ 14. Estimate 10 ÷ 10 = 1Find 7.49 ÷ 14. Estimate 10 ÷ 10 = 1
535.0
000
070
070
42
049
70
490.714
−
7.49 ÷ 14 = 0.5357.49 ÷ 14 = 0.535 Compared toCompared to
the estimate, the quotient is reasonable.the estimate, the quotient is reasonable.
Place the decimal point
Annex a zero and continue dividing

15. CONFIDENTIALCONFIDENTIAL
Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Your turn! Find 1087.9 ÷ 46Your turn! Find 1087.9 ÷ 46

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Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Round a Quotient:Round a Quotient:
– Usually, when you divide decimalsUsually, when you divide decimals
the answer does not come outthe answer does not come out
evenly.evenly.
– You need to round the quotient to aYou need to round the quotient to a
specified place-value position.specified place-value position.
– Always divide to one more place-Always divide to one more place-
value position than the place tovalue position than the place to
which you are rounding.which you are rounding.

17. CONFIDENTIALCONFIDENTIAL
Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Round a Quotient:Round a Quotient:
– Example: Seth purchased 3 video games for $51.79,Example: Seth purchased 3 video games for $51.79,
including tax. If each game costs the same amount, whatincluding tax. If each game costs the same amount, what
was the price of each game in dollars?was the price of each game in dollars?
263.17
0001
009
00010
018
0019
006
007
21
21
3
790.513
−
−
Place the decimal point
Divide as with whole numbers
Divide until you place a digit in the
thousandths place.
To the
nearest cent,
the cost in
dollars is
17.26

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Dividing Decimals by Whole NumbersDividing Decimals by Whole Numbers
Your turn!Your turn!
– The table shows how much money Halley made in oneThe table shows how much money Halley made in one
week for a variety of jobs. To the nearest cent, what wasweek for a variety of jobs. To the nearest cent, what was
her average pay for these three jobs?her average pay for these three jobs?
JobsJobs Pay in a weekPay in a week
Baby-sittingBaby-sitting $50.00$50.00
Pet-sittingPet-sitting $10.50$10.50
Lawn workLawn work $22.50$22.50

19. CONFIDENTIALCONFIDENTIAL
Dividing by DecimalsDividing by Decimals
When dividing by decimals, changeWhen dividing by decimals, change
the divisor into a whole number.the divisor into a whole number.
To do this, multiply both the divisorTo do this, multiply both the divisor
and the dividend by the sameand the dividend by the same
power of 10.power of 10.
Then divide as with whole numbers.Then divide as with whole numbers.

20. CONFIDENTIALCONFIDENTIAL
Dividing by DecimalsDividing by Decimals
Example: Find 14.19 ÷ 2.2Example: Find 14.19 ÷ 2.2
19.142.2
Multiply by 10 to
make a whole
number
Multiply by the
same number, 10
45.6
00000
0110
00110
088
0099
132
90.14122
−
−
Place the decimal point
Divide as with whole
numbers
Annex a zero to continue

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Dividing by DecimalsDividing by Decimals
Your turn!Your turn!
– Divide 0.4 ÷ 0.0025Divide 0.4 ÷ 0.0025

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Let us take a short break!Let us take a short break!

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How about a jig-saw puzzle?!How about a jig-saw puzzle?!
Let us see how fast you can do this…Let us see how fast you can do this…
http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-ji

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Let us practice!Let us practice!
Find 12.9 x 7Find 12.9 x 7
Find 0.82 x 4Find 0.82 x 4

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Let us practice!Let us practice!
Find 0.04 x 5.1Find 0.04 x 5.1
Find 0.04 x 0.0063Find 0.04 x 0.0063

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Let us practice!Let us practice!
Find 203.84 ÷ 32Find 203.84 ÷ 32
Find 136.5 ÷ 35Find 136.5 ÷ 35

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Let us practice!Let us practice!
DivideDivide
DivideDivide
2.508.0
155.025.0

28. CONFIDENTIALCONFIDENTIAL
Let us practice!Let us practice!
Choose the correct term to completeChoose the correct term to complete
each sentence.each sentence.
To check your answer for a divisionTo check your answer for a division
problem, you can multiply the quotientproblem, you can multiply the quotient
by the (dividend, divisor)by the (dividend, divisor)
When dividing a decimal by a wholeWhen dividing a decimal by a whole
number, place the decimal point in thenumber, place the decimal point in the
quotient directly (below, above) thequotient directly (below, above) the
decimal point found in the dividend.decimal point found in the dividend.

29. CONFIDENTIALCONFIDENTIAL
Good Job!Good Job!