Dividing a Decimal by a Decimal

Lesson 2-5

Dividing a Decimal by a Decimal

• We NEVER want a decimal in the divisor.

– If you have a decimal in the divisor, you need to bump it over until it is all the way over to the right of the number.

– Move it the same number of places in the dividend.

Remember… no remainders!

• If you solve a problem and you see a remainder at the end, you are NOT done!– Add a decimal and a zero– If you already have a decimal point, just

add a zero• Do not put 2 decimal points in one problem!

Let’s try one together…

) 13 21 62

We cannot have a decimal point in the divisor!

Let’s fix it!

We need to bounce this decimal point

until it is all the way to the right of the

divisor.

Since we bounced the decimal point in the divisor, we have

to bounce it the same number of places in

the dividend.

We bounced more places than there were numbers. This blank represents the extra spot we bounced.

Turn it into a zero.

0

) 1320162

When you do long division, it is easiest to solve the problem when you estimate using your divisor.

After you have bounced the decimal point in both

the divisor and the dividend, you can

eliminate the new decimal point in the divisor.

Is this divisor, 162, closest to 100? 150? or 200?

162 is closest to 150. I am going to use 150 to

estimate how many times 162 will go into my

dividend.

Does 150 go into 132?

No, 150 is too big. I need to use one more digit of

the dividend then. Instead of 132, I will use

1320.

150

) 1320162150

Remember that we are only using the 150 to estimate!

Use your fingers to cover over the last

digit of both the dividend and the

divisor.

Now ask yourself: “how many times does 15 go into

132?”

15 x 2 = 30If I double that (x4), that

would be 60. If I double that (x 8) would be 120. If I add 15

more to 120, I would have more than 132, so I should

stop at “times 8.”

) 13201628

- 129624

0

0

I know that 162 x 2 is greater than 300. That is too big!

Instead, I will use 1 as the next number in my quotient.

1

- 16 278

) 13201628

- 129624

0

0

1

- 16 278

0150

0

4I am going to use 150 again…

150 x 2 = 300If I double that (x 4), I have

600.If I add another 150 (that would be x5), then I have 750. I will

try that first.

162 x 5 = 810.

Nope! That is too big! Let me try one smaller…

162 x 4 = 648I will use this one.

- 64 8 132

) 13201628

- 129624

0

0

1

- 16 278

0150

0

4

I see that my new difference is the same three numbers as in

my dividend. I will use 8 again…

- 64 8 13 2

0

0- 12 9 6

2 4

8

) 13201628

01

04

My division problem seems to go on and on. I am going to

stop.

Instead, I am going to round my quotient to the hundredths

place.

08

8.148

I am rounding to the hundredths place so I

underlined the four. I look at the number to the right of my underline: the 8. Since 8 is

bigger than 4, I will add one to my underlined number.

8.15

Things to remember…

• You can never have a decimal point outside the division sign– Bounce the outside decimal all the way to the

right– Count up the number of places you bounced– Bounce the inside decimal as many times as

you did the outside.• If you do not have a decimal point, add one to the

end of the number• If you do not have enough places, then add zeros to

the end of a decimal to make more places

• After the decimal point has been bounced in both places, divide as usual.