# Adding and Subtracting Decimals with Two Decimal Digits

This is a complete lesson with instruction and exercises about adding and subtracting decimals with two decimal digits (hundredths). It first compares decimal addition with fraction addition, and uses number lines to help students understand how to add decimals mentally. The lesson contains exercises, word problems, and pattern exercises.

1. Try to solve these
the lesson! Each time, write
the corresponding fractions
below the decimals.
 a. 0.05 + 0.04 = 5 100 + 4 100 =
 b. 0.07 + 0.04 = 100 + 100 =
 c. 0.37 – 0.06 = 100 – 100 =
 d. 0.45 + 0.65 = 100 + 100 =
 e. 3.25 – 1.08 = 3 100 – 1 100 =

You can add or subtract the hundredths and whole numbers separately. Examples:

 0.11 + 0.09 = 0.20 11 hundredths + 9 hundredths = 20 hundredths
 2.90 – 1.07 = 1.83 2 and 90 hundredths – 1 and 7 hundredths = 1 and 83 hundredths

2. Add and subtract mentally. Think how many hundredths there are in each number.

 a.  0.03 + 0.09 = ______ 2.03 + 2.09 = ______ b. 0.52  +  0.43 = ______ 1.55  +  1.25 = ______ c. 1.03  –  0.03 = ______ 4.03  –  2.01 = ______ d. 0.10 – 0.08 = ______ 20.06 – 1.03 = ______

Often you need to use the fact that 100 hundredths makes one whole. Notice carefully:

 0.90 + 0.11 = 1.01 90 hundredths + 11 hundredths = 101 hundredths
 1.12 – 0.20 = 0.92 112 hundredths – 20 hundredths = 92 hundredths

Shortcut: when all of the numbers in the problem all have hundredths, add or subtract as if there was
no decimal point. Then put the decimal point in the answer so it has two decimals (hundredths).

3. Add and subtract. Be careful and remember that 100 hundredths makes one whole.

 a.  0.97 + 0.04 = ______ 2.96 + 0.06 = ______ b.  0.95 + 0.11 = ______ 8.91 + 0.11 = ______ c.  1.03  –  0.04 = ______ 7.01  –  0.05 = ______ d.  1.12  –  0.16 = ______ 4.01  –  0.50 = ______

 0.2  +  0.05  = _______ 0.7  +  0.04  = _______ 0.12  +  0.5  = _______

0.2 + 0.05 = _____ What do you think?  If you are at 0.2 and go five hundredths (0.05) further, where will you end up?

 2 10 + 5 100 ↓ ↓ 20 100 + 5 100 = 25 100 0.2 + 0.05 ↓ ↓ 0.20 + 0.05 = 0.25

Let's write 0.2 and 0.05 as fractions. They have
different denominators (10 and 100).

Before adding, we can convert the first one into hundredth parts. Then they both have a denominator 100 and you can add easily.

When you add them as decimals (0.2 and 0.05), you can tag a zero on the end of 0.2 (two tenths), so it becomes 0.20 (twenty hundredths).
This is the same process as writing 2/10 as 20/100.

Let's check the other two problems you tried earlier. We will write them so that the addends have the same amount of decimals. 0.7 + 0.04 If you are at 0.7 and go four hundredths further, where do you end up? ↓ ↓ 0.70 + 0.04 = ______ 0.12 + 0.5 If you are at 0.5 and go twelve hundredths further, where do you end up? ↓ ↓ 0.12 + 0.50 = ______

 0 .  2 = 0 .  2 0 ones tenths ones tenths hund- redths
0.2 has zero ones and two tenths.
0.20 has zero ones, two tenths and zero hundredths.
So both have the same amount of ones, tenths, and hundredths.
They are equal!

4. Add mentally. Before adding, tag a zero to the number with only one decimal so that the addends
will have the same amount of decimals. Write the problems using fractions also.

 a. 0.10 + 0.05 = 0.15 = 10 100 + 5 100 = 15 100
 b. 0.04 + 0.4 = ______ = 100 + 100 = 100
 c. 0.6 + 0.09 = ______ = 100 + 100 = 100

5. Add mentally. Before adding, you can tag a zero to the number with only one decimal.

 a. 0.11  +  0.5  = _______ b. 0.24  +  0.2  = _______ c. 0.3  +  0.39  = _______ d. 0.22  +  0.7  = _______ e. 0.2  +  0.41  = _______ f. 0.27  +  0.8  = _______

6. Continue the patterns.

 a.  0.91 + 0.02  = _____ + 0.02  = _____ + 0.02  = _____ + 0.02  = _____ + 0.02  = _____ + 0.02  = _____ b.  0.80 – 0.05  = _____ – 0.05  = _____ – 0.05  = _____ – 0.05  = _____ – 0.05  = _____ – 0.05  = _____ c.  2.90 + 0.03  = _____ + 0.03  = _____ + 0.03  = _____ + 0.03  = _____ + 0.03  = _____ + 0.03  = _____ d.  1.77 + 0.11  = _____ + 0.11  = _____ + 0.11  = _____ + 0.11  = _____ + 0.11  = _____ + 0.11  = _____

7. Add enough hundredths to make the next whole tenth. Remember, 0.5 = 0.50.

 a.  0.47  + _____ = 0.5b.  0.55  + _____ = 0.6
 c.  0.06 + _____ = 0.1d.  0.32  + _____ = 0.4
 e.  0.88 + _____ = ______f.  0.97 + _____ = ______

8. Explain why the following additions are wrong.

 a.  0.99 + 0.1 = 1 b.  0.43 + 0.59 = 0.102

9. Subtract from a whole number.

 a. 1  –  0.6  = _____1  –  0.67  =  _____
 b. 2  –  0.6  = _____2  –  0.57  =  _____
 c. 4  –  0.23  = _____4  –  0.13  =  _____

 Remember? 100 cm makes one meter. Therefore, 1 cm is one-hundredth part of 1 meter. In other words, 1 cm = 0.01 m. 5 cm = 0.05 m 64 cm = 0.64 m 2 m 12 cm = 2.12 m

10. Convert between meters and centimeters, and solve the problems.

 a.   0.73 m = __________ cm b.   2.82 m = __________ cm c.   _________ m = 9 m 80 cm d.   _________ m = 306 cm e.  A boy is 1.15 m tall and a bush is 156 cm     tall. Which is taller? How much taller? f.  A table is 2.40 m long and 0.90 m wide.     Find its perimeter in meters. g. A door that is 90 cm wide will have a     decorative board above it. The decorative     board is now 1.25 m long. How much needs     to be cut off from the board so that it fits? h.  The height of a room is 2.25 m. How much    space is left above a person's head who is    186 cm tall?

11. Add and subtract mentally. You can tag a zero to the decimal with only tenths.

 a. 0.04  +  0.1  = _______    0.14  +  0.1  = _______ b. 0.28  +  0.1   = _______    0.25  +  0.5   = _______ c. 2.04  +  0.1   = _______   3.08  +  0.6   = _______ d. 13.53  +  0.4   = _______    5.03  +  2.25   = _______ e. 0.3  +  0.05  = _______    0.03  +  0.5   = _______ f. 0.8  –  0.09   = _______    0.9  –  0.08   = _______ g. 1.3  –  0.07   = _______     1.3  –  0.7    = _______ h. 6.2  –  1.2   = _______    6.2  –  1.25  = _______ i. 2   –  0.1    = _______    3   –  0.08  = _______

 + + + + + + + + 1.00

1.06

1.11

1.19 1.2 1.37 1.44 1.5 1.65

This lesson is taken from Maria Miller's book Math Mammoth Decimals 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Decimals 1

A self-teaching worktext for 4th grade that gives a solid foundation for decimals. It covers tenths and hundredths, comparing decimals, adding and subtracting decimals both mentally and in columns, multiplying decimals by whole numbers, rounding, estimating, and money problems.