This document provides instructions for multiplying, dividing, and converting between decimals and fractions. It explains the basic steps: 1) Count the decimal places and line up the numbers accordingly. 2) Ignore the decimal point and multiply or divide the numbers as whole numbers. 3) Place the decimal point by counting places left or right from the original decimal. Several examples are worked through, such as multiplying 5.8 x 7 and dividing 21.086 by 3. Then readers are prompted to try problems themselves, like dividing 0.4 by 0.0025.

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