Lesson 8: Decimal Subtraction: Sense Making and Estimation

Property

To subtract decimals, align the numbers by their decimal points. Subtract as you would with whole numbers, starting from the rightmost place value, and regroup (borrow) when necessary. Place the decimal point in the difference directly below the decimal points in the numbers being subtracted.

Examples

• $5.432 - 2.156$

• $12.5 - 3.481$

Property

To estimate the difference between two decimals, first round each number to the same, convenient place value (such as the nearest whole number or tenth). Then, subtract the rounded numbers to find the estimated difference. If $a \approx a_{rounded}$ and $b \approx b_{rounded}$, then $a - b \approx a_{rounded} - b_{rounded}$.

Examples

To estimate the value of $12.82 - 4.19$ by rounding to the nearest whole number:

• The estimated difference is $13 - 4 = 9$.

To estimate the value of $7.58 - 3.91$ by rounding to the nearest tenth:

• The estimated difference is $7.6 - 3.9 = 3.7$.

Explanation

Estimating differences helps you quickly check if an answer is reasonable without performing a complex calculation. By rounding the numbers in a subtraction problem first, you can work with simpler, whole numbers or tenths. This mental math strategy is useful for everyday situations, like calculating change or comparing prices. The closer your rounding is to the original numbers (e.g., rounding to tenths vs. whole numbers), the more precise your estimate will be.