Lesson 6: Operations with Decimals and Whole Numbers

Property

To add or subtract decimals, we line up the decimal points. By lining up the decimal points this way, we can add or subtract the corresponding place values. The steps are:

1. Determine the sign of the sum or difference.
2. Write the numbers so the decimal points line up vertically.
3. Use zeros as placeholders, as needed.
4. Add or subtract the numbers as if they were whole numbers. Then place the decimal point in the answer under the decimal points.

Examples

• Add $19.45 + 7.8$. We line up the decimal points: $19.45 + 7.80 = 27.25$.

• Subtract $8.15 - 12$. The result will be negative. We subtract the smaller value from the larger: $12.00 - 8.15 = 3.85$. So, the answer is $-3.85$.

Property

To solve real-world problems involving decimals, translate the words into a mathematical expression.
Use addition to find a total or combine quantities.
Use subtraction to find a difference, how much is left, or how much more is needed.

Examples

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.