Multiplying and dividing decimals

Multiplying and Dividing with

Decimals

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

• While we learn the steps, we will look at the example:

5.8X 7

Step 1• Count the number of digits to the right of the decimal point

5.8X 7

1 digit

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

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 . .

That’s It!• Our final answer is:

5.8X 7 4 0.6

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

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

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

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.

Multiplying Decimals by Whole Numbers

Your turn! • Find 11.4 x 8

• Multiply 3 x 0.02

• Let’s try it again with more digits to the right of the decimal point this time

0.024X 0.61

Multiplying Decimals

• 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

• What was Step 2?• Ignore the decimal points

• That means that 0.024 becomes:

• In the same way, 0.61 is:24

61

• Now we just multiply that out

2 4X 6 1

4204

2

1 41 4 6 4

• 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.

• 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 ..

• Don’t forget, its the same as dividing by 10, five times

• For our final answer, we have 0.024

X 0.610.01464

Multiplying Decimals

Your turn! Multiply 0.014 x 3.7

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

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

Dividing Decimals by Whole

NumbersDivide a decimal by a 1-Digit Number

Find 6.8 ÷ 2. 4.3

0080868.62

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

Dividing Decimals by Whole Numbers

Your turn! Find 3.49 ÷ 4

Find 1087.9 ÷ 46

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

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

Step 2• Divide just like normal• Ignore the decimal point

210.8623

186

0

4

1 1

2 8

104

2480

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!

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

Dividing by Decimals

Your turn!Divide 0.4 ÷ 0.0025

Divide 1087.9 ÷ 4.6

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

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

Kilograms• If 1 lb = 0.45 kg, how many

pounds is each canoer carrying when every backpack is 5.49 kgs?

12.2 lbs

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