Comparing Decimals and Operations with Decimals

Decimal Order, Addtion, and Subtraction

Justify Decimal Addition with Fractions

We rewrite decimals in expanded common fraction form to justify the "line up decimal points" for the addition of decimals. The decimal expanded notation helps us see how place value with decimal addition is important.

Example: Find the sum 4.8 + 5.24.

First note that and .

We add these two values by place-value

The addition of the fractions with common denominators justifies that lining up the decimal points to add fractions is just the addition of the corresponding place-value. Below, we complete the problem without changing to common fractions.

With common denominators , which justifies line up decimal points .

Self-Check Problem

Yesterday, we received 1.3 inches of rain and today we received 1.83 inches of rain. How much rain did we receive over the two days?

Solution

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