Number & Operations for Teachers 

Copyright David & Cynthia Thomas, 2009

Arithmetic Operations with Decimals – Addition and Subtraction

Addition and subtraction of decimals may be represented using concept models and expanded algorithms similar to those used in representing addition and subtraction of whole numbers. Figure 6.3 presents concept models and an expanded algorithm for the sum 0.46 + 0.37. In Figure 6.3, a different convention is used relative to the value of the large square. In this case, the large square represents a one. Consequently, each column of the large square represents a tenth and each small square a hundredth. Using this representation, the number 0.46 is shaded as four columns plus six small squares. This approach has the advantage that the relationship between tenths and hundredths is strengthened and the disadvantage that there is no model for thousandths. Note also the manner in which the expanded algorithm separates the values associated with each column.

0.40 + 0.06 + 0.30 + 0.07 0.80 + 0.03 = 0.83

Figure 6.3: Concept Models and Expanded Algorithm for the Sum 0.46 + 0.37

Subtraction of decimals is represented using a similar approach. Figure 6.4 presents a concept model and expanded algorithm for the difference 0.96 – 0.28.

0.80 0.10 0.90 + 0.06 - 0.20 - 0.08 0.60 + 0.08 = 0.68

Figure 6.3: Concept Model and Expanded Algorithm for the Difference 0.96 – 0.28

For elementary school students, one of the most natural contexts for applying decimal operations is everyday questions about money. In general, questions of this sort should represent all monies in terms of dollars. Using both dollars and cents in the same problem can be distracting and possibly confusing.

§ Original Problem: Carl has $0.96. He then buys a piece of candy for $0.28. How much money does Carl have left after buying the candy?

Inverse Problem: Carl has $0.68 after buying a piece of candy for $0.28. How much money did Carl have before he bought the piece of candy?