However, lining up the ending digits of decimal numbers might not ... We use another method for decimal ... with decimals; add with negative integers;...
California Mathematics Content Standards REFRESHER LESSON
5.NS 2.0, 2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.
20 • Adding and Subtracting Decimal Numbers Refresher Concept
When we add or subtract numbers using pencil and paper, it is important to align digits that have the same place value. For whole numbers this means lining up the ending digits. When we line up the ending digits (which are in the ones place) we automatically align other digits that have the same place value.
23 241 + 317
Lining up the ones place automatically aligns all other digits by their place value.
However, lining up the ending digits of decimal numbers might not properly align all the digits. We use another method for decimal numbers. We line up decimal numbers for addition or subtraction by lining up the decimal points. The decimal point in the answer is aligned with the other decimal points. Empty places are treated as zeros. 2.3 2.41 + 31.7 .
Lining up the decimal points automatically aligns digits that have the same place value.
Example 1 The rainfall over a three-day period was 3.4 inches, 0.26 inches, and 0.3 inches. Altogether, how many inches of rain fell during the three days? We line up the decimal points and add. The decimal point in the sum is placed in line with the other decimal points. In three days 3.96 inches of rain fell.
Example 2 A gallon is about 3.78 liters. If Margaret pours 2.3 liters of milk from a one-gallon bottle, how much milk remains in the bottle? 3.78 – 2.3 1.48
We subtract 2.3 from 3.78. We line up the decimal points to subtract and find that 1.48 liters of milk remains in the bottle.
Refresher Practice
Find each sum or difference. Remember to line up the decimal points. a. 3.46 + 0.2 3.66
b. 8.28 − 6.1 2.18
c. 0.735 + 0.21 0.945
d. 0.543 − 0.21 0.333
e. 0.43 + 0.1 + 0.413 0.943 f. 0.30 − 0.27 0.03 g. 0.6 + 0.7 1.3 i. 0.9 + 0.12 1.02
h. 1.00 − 0.24 0.76 j. 1.23 − 0.4 0.83
k. On a hike the scouts walked 2.7 miles on the first hike and 3.79 miles on the second hike. On the third day they hiked 3 miles and the fourth day they hiked 2.83 miles. Altogether, how many miles did the scouts hike on their four day trip? 12.32 miles
