Mutiplication and division of decimal numbers

1. Multiplying and
Dividing with
Decimals

2. 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

3. • While we learn the steps, we
will look at the example:
5.8
X 7

4. Step 1
• Count the number of digits to
the right of the decimal point
5.8
X 7
1 digit

5. Step 2
• Just ignore the decimal point!
• Multiply just as if they were
normal whole numbers
5.8
X 7
5 8
X 7
5
64 0

6. Step 3
• Use the number of digits from
Step 1 to count out where to put
the decimal
• We counted 1 digit
in Step 1, so we
move the decimal
point by 1 place to the left now
5.8
X 7
4 0 6. .

7. That’s It!
• Our final answer is:
5.8
X 7
4 0.6

8. 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 8
X 7
x 10
5.8
X 7

9. What are we Really Doing?
• Now you multiply the numbers
without decimals
• BUT DON’T FORGET WE
MULTIPLIED BY 10 EARLIER!
5 8
X 7
4 0 6

10. 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 8
X 7
4 0 6 . .4 0 6

11. 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
0.018
x 2
0.036
Annex a zero to the left of 36 to make
three decimal places.
There are three decimal places.

12. Multiplying Decimals by Whole
Numbers
Your turn!
• Find 11.4 x 8
• Multiply 3 x 0.02

13. • Let’s try it again with more digits
to the right of the decimal point
this time
0.024
X 0.61
Multiplying Decimals

14. • 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

15. • What was Step 2?
• Ignore the decimal points
• That means that 0.024 becomes:
• In the same way, 0.61 is:
24
61

16. • Now we just multiply that out
2 4
X 6 1
42
04
2
1 4
1 4 6 4

17. • 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!
0.024
X 0.61
1 4 6 4.

18. • 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.
0.024
X 0.61
0 1 4 6 4 ..

19. • Don’t forget, its the same as
dividing by 10, five times
• For our final answer, we have
0.024
X 0.61
0.01464

20. Multiplying Decimals
Your turn!
Multiply 0.014 x 3.7

21. 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

22. 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

23. Dividing Decimals by Whole Numbers
Divide a decimal by a 1-Digit Number
Find 6.8 ÷ 2.
4.3
00
8
08
6
8.62


24. Dividing Decimals by Whole Numbers
Divide a decimal by a 2-Digit Number
Find 7.49 ÷ 14.
535.0
000
070
070
42
049
70
490.714

Place the decimal point
Annex a zero and continue dividing

25. Dividing Decimals by
Whole Numbers
Your turn!
Find 3.49 ÷ 4
Find 1087.9 ÷ 46

26. 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

27. 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

28. Step 2
• Divide just like normal
• Ignore the decimal point
210.862
3
186
0
4
1 1
2 8
10
4
248
0

29. 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
210.862
3 4.
• This is why keeping numbers
aligned is so important!

30. 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
00000
0110
00110
088
0099
132
90.14122


Place the decimal point
Divide as with whole
numbers
Annex a zero to continue

31. Dividing by Decimals
Your turn!
Divide 0.4 ÷ 0.0025
Divide 1087.9 ÷ 4.6

32. 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

33. 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

34. Kilograms
• If 1 lb = 0.45 kg, how many pounds
is each canoer carrying when
every backpack is 5.49 kgs?
12.2 lbs

35. Let us practice!
Find 12.9 x 7 Find 0.82 x 4
Find 0.04 x 5.1 Find 0.04 x 0.0063
Find 203.84 ÷ 32 Find 136.5 ÷ 35
Divide Divide
2.508.0155.025.0