Decimals represent numbers between whole numbers, such as 0.1 being between 0 and 1. When adding, subtracting, multiplying, or dividing decimals, it is important to line up the decimal points before performing the calculation. For multiplication and division, the number of decimal places in the answer should match the total number from the numbers in the problem. Dividing decimals requires moving the decimal points in the divisor and dividend to properly set up the calculation.

1.  Decimals are numbers that are less than 1 but greater than 0
0 < 0.1 < 1 (0.1 is between 0 and 1, so it is a decimal)
 They appear to the right of the decimal point
whole number decimal
39.1
“39” is the whole number part
“.1” is the decimal part
 “39.1” is read…
“Thirty-nine and one tenth”
 “0.1” is the same thing as
“.1”. “.1” is just a lazy way of
writing the number.
15 Minute Math – Decimals
Lesson # 1 – What Are Decimals?

2. 1 2 3 4 5 6 7 8 9
10,000.
+ 2,000.
+ 300.
+ 40.
+ 5.
+ .6
+ .07
+ .008
+ .0009
12,345.6789
The “3” is in the hundreds column,
so there are “3 hundreds”.
If all the other numbers were
a 0, then the number would be
00300.0000, which is 300 (three hundred.)
The “7” is in the hundredths column,
so there are “7 hundredths.”
If every other number were a 0, then the number
would be 00000.0700, which is 0.07 (seven hundredths.)
 Remember, decimals
have a “th” at the end
of their names.
15 Minute Math – Decimals
Lesson # 1 – What Are Decimals?

3. 15 Minute Math – Decimals
Lesson # 1 – What Are Decimals?
To read a number…
For example: 20.045 is read, “Twenty and forty-five thousandths.”
0.2 = 0.20 = 0.200 but…
0.2 = “two tenths”
0.20 = “twenty hundredths”
0.200 = “two hundred thousandths“
 Extra zeroes to the far right of a
decimal don’t change the value, but
they do change how you pronounce
the number.

4. Try it yourself
What numbers are these?
Three and two hundredths = 3.02
Forty and two thousandth =
Twelve and twelve hundredths =
Eighty and eighty ten-thousands =
How do you say these numbers?
37.03 = Thirty-seven and three hundredths
9.04 =
20.040 =
100.01 =
Which of these are true:
A) 2.01 = 2.010 B) 2.01 = 2.001
C) 2.001 = 2.100 D) 2.10 = 2.010
E) 2.10 = 2.100 F) 2.0010 = 2.001
Forty and two thousandth = 40.002
Twelve and twelve hundredths = 12.12
Eighty and eighty ten-thousands = 80.0080
9.04 = nine and four hundredths
20.040 = twenty and forty thousands
100.01 = one hundred and one hundredth
A, E, and F are true
End of Lesson 1
15 Minute Math – Decimals
Lesson # 1 – What Are Decimals?
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5. 15 Minute Math – Decimals
Lesson # 2 – Addition & Subtraction
This lesson explains how to add and subtract
numbers that have a decimal point.
Problem: You need to take 3 grams of pain medication. You’ve already
taken 0.75 grams of pain medication from a multi-purpose formula. How
much more medication do you need?
3.00
-0.75
2.25
When adding and subtracting numbers with decimal points, ALWAYS line up
the decimal points!

6.  Line up the decimals points
 Put zeroes in the blank spaces to help you see what you’re
adding
24.3 + 18.45  24.30 18.62 – 3.8  18.62
+18.45 - 3.80
42.75 14.82
 When adding, don’t forget to carry when numbers add
up to more than 10.
 When subtracting, don’t forget to borrow if the top
number is smaller than the bottom number.
1
1
7
/
15 Minute Math – Decimals
Lesson # 2 – Addition & Subtraction

7.  All numbers have a decimal point, even if you can’t see it.
For example, $15 can also be written as $15.00
20 + 4.02  20.00 100 – 25.783  100.000
+ 4.02 - 25.783
24.02 74.217
 Even if you don’t
see the decimal point,
it’s actually at the end.
100 = 100. = 100.00
1
9
15 Minute Math – Decimals
Lesson # 2 – Addition & Subtraction
9
9 9
/// //
Remember when you’re borrowing, you
can’t borrow from nothing (zero). Make
sure you borrow all the way over to the
first non-zero number you find.

8. Try it yourself
2.89 + 1.5 = 20.6 + 10.9 = 3.13 + 9 =
20 + 8.2 = 9.373 + 3.34 = 9 + 2.8 =
12.99 – 8.1 = 19 – 3.2 = 2.933 – 1.2 =
8.4 – 5.555 = 20 – 2.5 = 100 – 2.66 =
2.89 + 1.5 = 4.39 20.6 + 10.9 = 31.5 3.13 + 9 = 12.13
20 + 8.2 = 28.2 9.373 + 3.34 = 12.713 9 + 2.8 = 11.8
12.99 – 8.1 = 4.89 19 – 3.2 = 15.8 2.933 – 1.2 = 1.733
8.4 – 5.555 = 2.845 20 – 2.5 = 17.5 100 – 2.66 = 97.34
End of Lesson 2
15 Minute Math – Decimals
Lesson # 2 – Addition & Subtraction
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9. 15 Minute Math – Decimals
Lesson # 3 – Multiplication
This lesson explains how to multiply numbers that
have a decimal point.
Problem: You need to buy 12 cans of paint costing $5.29 each. How much
will you pay?
5.29
× 12
63.48
When multiplying numbers with decimal points, count the total number of
numbers to the right of the decimal point in the problem and make sure
the answer has the same number!

10.  Don’t worry about the decimal until you’re done multiplying
everything
 First multiply, and then count up the places to the right of the
decimal point and put the decimal in the answer.
3.51 x 1.4  351
×14
1404
+3510
4914
3 decimal
places
 first, multiply 351 by 4
 then, multiply 351 by 10
 then, add up the numbers
 last, since there are a total of 3
decimal places in the problem,
start from the right and move the
decimal 3 places to the left in the
answer (the problem has 3
decimal places and so does the
answer)
 4.914
So, 3.51 x 1.4 = 4.914!
15 Minute Math – Decimals
Lesson # 3 – Multiplication

11.  Remember to only count numbers to the RIGHT of the decimal
point.
2.3 × 0.0002  23
× 2
46
5 decimal
places
 Sometimes you may see
.00046 instead of
0.00046. Both are
right, but it’s more
common to put a 0 in
the ones place.
 0.00046
So, 2.3 x 0.0002 = 0.00046!
15 Minute Math – Decimals
Lesson # 3 – Multiplication
5 decimal
places

12.  There are some shortcuts you can take if you’re multiplying by a
multiple of 10. Multiples of 10 are things like 10, 100, 1000 and
also things like 0.1, 0.01, 0.001, etc.
shift the decimal left 4 places (if you move the decimal point right
(don’t see the decimal point it’s at the end) 2 spaces (100 has 2 0’s)
297 × 0.0001 = 0.0297 2.309 × 100 = 230.9
4 decimal
places
Try not to think about if you’re moving the
decimal to the right or the left. Think if you need
to make the number larger (because you’re
multiplying by a number bigger than 1) or if you
need to make the number smaller (because you’re
multiplying by a number between 0 and 1). Then
move the decimal point in the direction that will
make the number bigger or smaller.
15 Minute Math – Decimals
Lesson # 3 – Multiplication

13. 15 Minute Math – Decimals
Lesson # 3 – Multiplication
Try it yourself
27.2 × 9.2 = 3.2904 × 0.22 = 62.5 × 12.8 =
38 × 0.25 = 0.034 × 0.026 = 8.02 × 2.1 =
2.04 × 0.001 = 589 × 100 = 10.2 × 1.2 =
0.34 × 0.5 = 5.89 × 100 = 9.9999 × 0.01 =
27.2 × 9.2 = 250.24 3.2904 × 0.22 = 0.723888 62.5 × 12.8 = 800
38 × 0.25 = 9.5 0.034 × 0.026 = 0.000884 8.02 × 2.1 = 16.842
2.04 × 0.001 = 0.00204 589 × 100 = 58,900 10.2 × 1.2 = 12.24
0.34 × 0.5 = 0.17 5.89 × 100 = 589 9.9999 × 0.01 = 0.099999
End of Lesson 3
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14. 15 Minute Math – Decimals
Lesson # 4 – Division
This lesson explains how to divide numbers that
have a decimal point.
Problem: A wall measures 96.5 inches tall. You need to install 3.25 inch tall
siding panels. How many panels do you need?
26.5
3.25|96.5
When dividing numbers with decimal points, decimal point placement is key.

15. 15 Minute Math – Decimals
Lesson # 4 – Division
 Remind yourself of the steps you need to take when dividing
1. Divide
2. Multiply
3. Subtract
4. Bring down one
more number
and do it again
8
21|172263
8
21|172263
-168
8
21|172263
-168
4
8
21|172263
-168
42
8203
21|172263
-168
42
-42
06
- 0
63
-63
0

16. Step 1 - Move the decimal of the divisor (outside the house) as far to
the right as you can
Step 2 - Move the decimal of the dividend (inside the house) by the
same number of spaces
Step 3 - Move the decimal straight up onto the answer line
Step 4 - Divide like normal
Problem
8.91 ÷ 3.3
Steps 1 & 2
 3.3 |8.91  33 |89.1
Step 3
.
 33 |89.1
Step 4
2.7
 33 |89.1
- 66
231
- 231
0
 Think of the division sign, | , like a house. With all division
problems, the first number goes inside the house (the 8.91) and the
second goes outside the house (3.3).
 If you forget, think about a problem you know. 10 ÷ 2 = 5. You
wouldn’t say 10 | 2. To work it out you’d say 2 |10 (2 goes into 10.)
15 Minute Math – Decimals
Lesson # 4 – Division

17. Problem
8.91 ÷ 0.0033
Steps 1 & 2
 0.0033 |8.91  33 |89100.
Step 3
.
 33 |89100.
Step 4
2700.
 33 |89100.
- 66
231
- 231
0
Problem
8.91 ÷ 0.33
Steps 1 & 2
 0.33 |8.91  33 |891.
Step 3
.
 33 |891.
Step 4
27.
 33 |891.
- 66
231
- 231
0
Move the decimal 2 places to the right
Move the decimal 2 places to the right
Fill in the empty spaces with zeroes
15 Minute Math – Decimals
Lesson # 4 – Division

18. 15 Minute Math – Decimals
Lesson # 4 – Division
Try it yourself
3.2 ÷ 64 = 60.8 ÷ 19 = 187.53 ÷ 3 =
3.2 ÷ 6.4 = 60.8 ÷ 0.19 = 187.53 ÷ 0.03 =
32 ÷ 6.4 = 0.608 ÷ 0.19 = 18753 ÷ 0.3 =
32 ÷ 0.00064 = 608 ÷ 1.9 = 0.0018753 ÷ 0.3 =
3.2 ÷ 64 = 0.05 60.8 ÷ 19 = 3.2 187.53 ÷ 3 = 62.51
3.2 ÷ 6.4 = 0.5 60.8 ÷ 0.19 = 320 187.53 ÷ 0.03 = 6251
32 ÷ 6.4 = 5 0.608 ÷ 0.19 = 3.2 18753 ÷ 0.3 = 62510
32 ÷ 0.00064 = 50000 608 ÷ 1.9 = 320 0.0018753 ÷ 0.3 = 0.006251
End of Lesson 4
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