# Adding and Subtracting Decimals (one decimal digit)

This is a complete lesson with instruction and a variety of exercises, teaching how to add and subtract decimals with one decimal digit (tenths). The lesson also strives to counteract the common misconception where student adds the decimal parts as if they were whole numbers living on the right side of decimal point.

subtract decimals with tenths, because they are
just fractions with a denominator of 10.

Compare these problems that are
written with decimals or fractions.

 0.1 + 0.5 = 0.6 1 10 + 5 10 = 6 10
 8.4 − 2.3 = 6.1
 8 4 10 − 2 3 10 = 6 1 10

There is one tricky part though:
0.6 + 0.7 is NOT  0.13 !!

To see why, add the fractions. Notice
that six tenths and seven tenths
makes more than one whole!

 0.6 + 0.7 = ? =  1.3 6 10 + 7 10 = 13 10 =  1 3 10
 1.5 + 0.9 =  2.4 1 5 10 + 9 10 =  2 4 10

1. Write an addition or subtraction sentence for each “number line jump”. a. You're at 0.7, and you jump five tenths to the right.  _____________________________________

b. You're at 0.6, and you jump eight tenths to the right.  _____________________________________

c. You're at 1.1, and you jump eight tenths to the left.  _____________________________________

d. You're at 1.3, and you jump four tenths to the left.  _____________________________________

 a.  0.9 + 0.2 = _____    1.9 + 0.2 = _____ b.  0.5 + 0.7 = _____    3.5 + 0.7 = _____ c.  0.8 + 0.7 = _____    0.8 + 2.7 = _____ d.  1.8 − 0.9 = _____    5.8 − 0.9 = _____

3. Add a decimal so the sum is the next whole number.

 a. 2.1 + ______ = 3 b. 4.5 + ______ = ____ c. 8.9 + ______ = ____ d. 5.3 + ______ = ____

 a. _____ + 0.5 = 3 b. 0.2 + _____ = 8 c. 0.4 + _____ = 1.2 d. 0.7 + _____ = 1.4

 a.  2.3 + 0.9 =       2.3 + 0.8 = b.  1.5 + 0.7 =      1.8 + 0.4 = c.  2.2 + 3.4 =      2.2 + 5.6 = d.  4.7 − 0.7 =      6.6 − 0.5 =

6. Write the numbers.

 a. 3 tenths, 5 ones b.  7 tens, 8 ones, 4 tenthsc. 4 tenths, 3 ones, 6 tens d.  Write the numbers in order. 9   8.9   9.1   9.0   9.9   1.9

7. Continue the patterns by adding or subtracting the same number repeatedly.

 a.  0.1 + 0.2  = _____ + 0.2  = _____ + 0.2  = _____ + 0.2  = _____ + 0.2  = _____ + 0.2  = _____ b.  1.1 + 0.5  = _____ + 0.5  = _____ + 0.5  = _____ + 0.5  = _____ + 0.5  = _____ + 0.5  = _____ c.  2.5 + 0.3  = _____ + 0.3  = _____ + 0.3  = _____ + 0.3  = _____ + 0.3  = _____ + 0.3  = _____ d.  3.6 − 0.4  = _____ − 0.4  = _____ − 0.4  = _____ − 0.4  = _____ − 0.4  = _____ − 0.4  = _____

8. Remember? 1 millimeter is one-tenth of a centimeter. Or, 1 mm = 0.1 cm.

a. Draw a line that is 4.7 cm long. b. Measure the line in centimeters.
Use a decimal. a. 0.5 cm  = ______ mm     1.2 cm  = ______ mm b.  7 mm  = ______ cm      35 mm  = ______ cm c.  5 mm + 0.9 cm = ______ cm      4 cm + 3.4 cm = ______ cm

10. The two sides of a rectangle
measure 6.5 cm and 3.6 cm.
Draw the rectangle.
What is its perimeter?

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.