Multiplying and Dividing with Decimals by Allison Hendley

Multiplying and Dividing with Decimals by Allison Hendley

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: 5.8 X 7

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

Step 2 Just ignore the decimal point! Multiply just as if they were normal whole numbers 5 5 5.8 8 X 7 406

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

That’s It! Our final answer is: 5.8 X 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. 58 5.8 X 7 x 10

What are we Really Doing? Now you multiply the numbers without decimals 58 X 7 406 BUT DON’T FORGET WE MULTIPLIED BY 10 EARLIER!

What are we Really Doing? So now we divide by 10 58 X / 10 7 406 / 10 4 0. 6 . Moving the decimal to the left one place is the same as dividing by 10!

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

What was Step 1? Count the digits to the right of the decimal point From 0.024, how many digits? 3 What about from 0.61? 2 That gives a total of: 5

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

Now we just multiply that out 2 24 X 61 24 144 0 1464

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 0.024 X 0.61 1 4 6 4. But wait! There are only 4 numbers!

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 .

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

Why It Works All we are really doing is multiplying and dividing by powers of 10 as needed to make the problem easier When we turned 0.024 into 24, we multiplied it by 10 three times 1.) 0.024 x 10 0.24 2.) 0.24 x 10 2.4 3.) 2.4 x 10 24

Also, 0.61 becomes 61 by multiplying by 10 twice Each time we move the decimal to the right on place we are multiplying by 10 That’s why we count, so we can divide by 10 the same number of times later

Everybody think of a number Multiply that number by 10 Divide that number by 10 What do you have now?

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

Remember the 3 steps: Count the number of digits to the right of the decimals Ignore the decimals and multiply Place the decimal in the answer by moving it back to the left by the same number of digits as before

Dividing When we divide numbers with decimal points, we use the same idea as multiplying them Keeping everything lined up is key! 6.2 21.08

Step 1 Multiply both the divisor and dividend by whatever power of 10 we need so that the divisor is a whole number 6.2 21.08 62 210.8

Step 2 Divide just like normal Ignore the decimal point 62 34 1 1 0 10 210.8 186 248 248 0

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 3 .4 62keeping210.8 This is why numbers aligned is so important!

Why It Works Just like before, when we multiply and divide by the same number, we don’t change what we started with Look at the division like this: 21.08 21.08 x 10 210.8 6.2 6.2 x 10 62

Notice that by multiplying both the divisor and the dividend by 10, all we really did is multiply by a special form of 1 21.08 x 6.2 10 10 21.08 x 1 6.2

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

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