Dividing Decimals—Mental Math
This is a complete lesson for 5th/6th grade with instruction and exercises, teaching students how to divide decimals using mental math (based on number sense). It starts out with some sharing divisions, then explains the basic strategy for those. Students also divide decimals with "measurement division", such as 0.45 ÷ 0.05, where we think how many times the divisor goes into the dividend. The lesson has pattern exercises, word problems, a crossnumber puzzle, and more.
You can make worksheets for decimal division here.
1. First shade the parts. Then divide and write a division sentence.








A decimal divided by a whole number

2. Write the division problems with numbers, and solve.
a. 9 tenths divided by 3 equals ...  _______ ÷ ____ = _______ 
b. 72 thousandths divided by 9 equals ...  _______ ÷ ____ = _______ 
c. 54 hundredths divided by 6 equals ...  _______ ÷ ____ = _______ 
d. 240 thousandths divided by 60 equals ...  _______ ÷ ____ = _______ 
e. 122 hundredths divided by 2 equals ...  _______ ÷ ____ = _______ 
3. Divide. Think of dividing “bananas”: how
many tenths, hundredths, or thousandths you are dividing.
Or, think of multiplication backwards.
a. 0.024 ÷ 6 = ______ b. 0.24 ÷ 6 = _______ c. 2.4 ÷ 6 = ________ 
d. 0.49 ÷ 7 = _______ e. 1.2 ÷ 3 = ________ f. 0.056 ÷ 7 = _______ 
g. 5.40 ÷ 9 = _______ h. 0.20 ÷ 4 = ________ i. 0.050 ÷ 10 = _______ 
Trick! Remember how 0.40 = 0.4? We can omit the decimal zero, but we can also write it. When dividing a decimal by a whole number, it often helps to “tag” a zero on the number before dividing. 

0.8 ÷ 100 (tag two zeros) → 0.800 ÷ 100 = 0.008
(800 thousandths divided
by 100 
0.7 ÷ 10 (tag one zero) → 0.70 ÷ 10 = 0.07
(70 hundredths divided by 10 
4 ÷ 8 (tag one zero) → 4.0 ÷ 8 = 0.5
(40 tenths divided by 8 
4. Divide. Tag a zero or zeros on the dividend.
a. 0.3 ÷ 5 = ________ b. 0.3 ÷ 10 = ________ c. 3 ÷ 5 = ________ 
d. 0.06 ÷ 12 = _______ e. 0.2 ÷ 40 = _______ f. 2 ÷ 5 = _______ 
g. 0.3 ÷ 50 = ________ h. 0.7 ÷ 100 = ________ i. 0.02 ÷ 10 = ________ 
5. Jane shared $2.00 equally
among five friends.
How much did each one get?
6. If each heartbeat takes 0.8 seconds, how long do five heartbeats take?
Ten heartbeats?
7. Write two division problems and two multiplication problems with the same numbers—a fact family!
a. 8 × 0.04 =
0.32
_____ × _____ = ______ _____ ÷ _____ = ______ _____ ÷ _____ = ______ 
b. ____ ×
____ = _____ ____ × ____ = _____ 2 ÷ 0.4 = 5 ____ ÷ ____ = _____ 
c. ______ ×
______ = _______ ______ × ______ = _______ ______ ÷ ______ = _______ 0.025 ÷ 5 = 0.005 
Sometimes it helps to think how many times the divisor “goes” or “fits” into the dividend. 
Example 1. 0.24 ÷ 0.03 = ? Think: “How
many times will 3
hundredths go into 24 hundredths?” Just as 3 goes into 24 eight times, 3 hundredths goes into 24 hundredths 8 times. 
Example 2. Mom cut 0.4meter pieces from
a 1.2meter piece of material.
Think, “How many times does 0.4 go into 1.2?” The
answer is of course easy: 3 times. 
8. Divide. Think: how many times does the divisor go into the dividend?
a. 4.5 ÷ 0.5 = _______ b. 0.45 ÷ 0.05 = _______ c. 0.450 ÷ 0.005 = _______ 
d. 0.12 ÷ 0.06 = _______ e. 0.006 ÷ 0.002 = ______ f. 0.63 ÷ 0.07 = ________ 
g. 2.1 ÷ 0.7 = ________ h. 1.5 ÷ 0.3 = ________ i. 0.09 ÷ 0.01 = _______ 
9. Write a division sentence for each problem, and solve.
a. How many 0.3 m pieces do you get from 1.8 m of cloth? _______ ÷ _____ = ________
b. How many 0.7 m pieces do you get from 4.2 m of wood? _______ ÷ _____ = ________
c. How many 0.05 m pieces do you get from 0.25 m of string? _______ ÷ _____ = ________
Example 3. 0.72 ÷ 0.008 = ? First, tag a
zero on 0.72 so that it also has three decimals, just
like 0.008 has three decimals. Now think, “How
many times does 8 thousandths fit into 720 thousandths?” The answer: 90 times. So, 0.720 ÷ 0.008 = 90 (not 0.90 or 0.090; just plain 90). 
10. Divide. You may need to tag a zero
or zeros on the dividend so that both numbers have the same
amount of decimal digits. Then think: How many times does the divisor go into the dividend?
a. 0.20 ÷ 0.05 = _______ d. 0.3 ÷ 0.05 = _______ 
b. 1 ÷ 0.2 = _______ e. 5 ÷ 0.2 = _______ 
c. 0.4 ÷ 0.02 = _______ f. 0.05 ÷ 0.001 = _______ 
g. 0.6 ÷ 0.05 = _______ j. 1 ÷ 0.02 = _______ 
h. 0.9 ÷ 0.01 = _______ k. 1 ÷ 0.01 = _______ 
i. 0.1 ÷ 0.01 = _______ l. 0.03 ÷ 0.002 = _______ 
11. The asphalt crew does a 1.2mile stretch of road each day.
a. How many days does it take for them to cover a distance of 6 miles?
b. How many days does it take for them to cover a distance of 60 miles?
12. Jack has $1.45 in nickels in his pocket.
a. How many nickels does Jack have?
b. If you have not already, write a decimal
division to match the problem.
13. How many 0.04meter sticks can you cut from a 0.20meter board?
Write a decimal division to match the problem.
14.
Which expressions match the
problem? There are two. (You do not have to calculate anything.) One book
that is 3 cm thick is lying in a box that 
8 × 1.5 cm + 3 cm = 15 cm 15 × 3 cm + 1.5 cm = 46.5 cm (15 cm − 3 cm) ÷ 1.5 cm = 8 (15 cm − 1.5 cm) ÷ 3 cm = 4.5 15 cm + 3 cm + 1.5 cm = 19.5 cm (15 cm ÷ 3 cm) + 1.5 cm = 6.5 (15 cm ÷ 1.5) + 3 cm = 13 
15. Write a single expression (number sentence with several operations) to match this problem. Solve.
How much is left from 5 meters of material
after you cut off four 0.6 meter pieces?
16. Joe has 0.85 kg of meat. How many 0.3 kg servings can he get from that?
Also, “convert” this problem into grams, remembering that 1 kg has 1,000 grams.
17. Divide and place the answers in the crossnumber puzzle.
Across: a. 1 ÷ 0.04 b. 0.018 ÷ 9 c. 0.044 ÷ 0.004 d. 5 ÷ 10 e. 0.9 ÷ 0.09 
Down: a. 0.9 ÷ 0.06 b. 0.09 ÷ 3 c. 8.4 ÷ 0.7 d. 1 ÷ 100 e. 0.32 ÷ 8 
18. Figure out the pattern and continue it for at least two more problems.
a. 0.025 ÷ 0.005 = 0.25 ÷ 0.05 = 2.5 ÷ 0.5 =

b. 1000 ÷ 20 = 100 ÷ 2 = 10 ÷ 0.2 = 
c. 4,200 ÷ 40 = 420 ÷ 4 = 42 ÷ 0.4 = 
Based on what you observed in
the previous
exercise, change

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. It addresses the Common Core Standard for 5th grade 5.NBT.7.
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.