Dividing decimals by decimals
This is a complete lesson with a video, instruction, and exercises about dividing decimals by decimals, meant for 5th grade. The lesson concentrates on the idea that we can transform any division with a decimal divisor into a wholenumber division by multiplying BOTH the dividend and the divisor by 10, 100, 1000, or some other power of ten.
So, why do we move the decimal point in both the dividend and the divisor the same number of steps? This is just a shortcut, and it comes from the idea above; actually the dividend and the divisor are MULTIPLIED by some same number. In the video, I aim to make sense of this "rule". The actual lesson continues below the video.
You can make worksheets for decimal division here.
You have learned:

2.04 ÷ 2 = ________ 0.24 ÷ 6 = ________ 5.2 ÷ 10 = ________ 5.2 ÷ 100 = ________ 



Solve. 2.5 ÷ 0.5 = _______ 0.021 ÷ 0.003 = _______ 

But how can we solve divisions where the divisor is a decimal, yet the divisor does not fit an even number of times into the dividend? For example: 4.6 ÷ 0.029 or 0.23 ÷ 0.07 ?  
That is based on the following principle:

1. Solve, thinking how many times the divisor “fits into” the dividend. What can you notice?
a. 60 ÷ 20 = _______ b. 6 ÷ 2 = _______ c. 0.6 ÷ 0.2 = _______ d. 0.06 ÷ 0.02 = _______ 
e. 350 ÷ 50 = _______ f. 35 ÷ 5 = _______ g. 3.5 ÷ 0.5 = _______ h. 0.35 ÷ 0.05 = _______ 
i. 2,000 ÷ 10 = _______ j. 200 ÷ 1 = _______ k. 20 ÷ 0.1 = _______ l. 2 ÷ 0.01 = _______ 
What did you notice?
It is no wonder: 0.02 fits
into 0.06 as many times as 2 fits into 6, as many 
2. Solve the easier of the two problems in each box. The answers to both are the same.
a. 5 ÷ 0.2 = _______ 50 ÷ 2 = ________ 
b. 7 ÷ 0.35 = ________ 700 ÷ 35 = ________ 
c. 36.9 ÷ 3 = __________ 0.369 ÷ 0.03 = _______ 
The way to transform a more difficult decimal division problem, such as 3.439 ÷ 5.6, into a problem with the same answer, but with a wholenumber divisor, is this:


The last problem, 60 ÷ 3, is easy to solve. The answer is 20. So, the answer to 0.6 ÷ 0.03 is also 20. Check by multiplying: 20 × 0.03 is 20 times 3 hundredths = 60 hundredths = 0.60 = 0.6. It checks. 


3. Multiply both the dividend and the divisor by 10, repeatedly, until you
get a wholenumber divisor.
Then, divide using long division. The first one is partially done for you.
a. 0.445 ÷ 0.05 4.45 ÷ 0.5 44.5 ÷ 5

b. 2.394 ÷ 0.7 
4. Multiply both the dividend and the divisor by 10, repeatedly, until you
get a wholenumber divisor.
Then, divide using long division.
a. 0.832 ÷ 0.4

b. 0.477 ÷ 0.09 
c. 9.735 ÷ 0.003

d. 1.764 ÷ 0.006 
e. 2.805 ÷ 0.11

f. 546.6 ÷ 1.2 
You can make worksheets for decimal division here.
This lesson is taken from Maria Miller's book Math Mammoth Decimals 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Decimals 2
A selfteaching worktext for 5th6th grade that covers the four operations with decimals up to three decimal digits, concentrating on decimal multiplication and division. The book also covers place value, comparing, rounding, addition and subtraction of decimals. There are a lot of mental math problems.
Download ($6.25). Also available as a printed copy.