Adding Decimals with Different Signs
Adding decimals with different signs is a Grade 7 rational numbers skill in Big Ideas Math, Course 2. When one decimal is positive and another is negative, the operation follows the same rules as adding integers with different signs: subtract the smaller absolute value from the larger absolute value, then keep the sign of the number with the greater absolute value. For example, 3.7 + (−1.2) = 2.5, and −4.6 + 2.1 = −2.5. If both decimals are negative, add their absolute values and make the result negative. Aligning decimal points ensures place-value accuracy throughout the calculation.
Key Concepts
To add decimals with different signs, we apply the same rules as adding integers, then align decimal points for computation: 1. If the signs are the same, add the absolute values and keep the common sign. 2. If the signs are different, subtract the smaller absolute value from the larger absolute value and use the sign of the number with the larger absolute value. 3. Line up the decimal points vertically and 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.
Common Questions
How do you add a positive decimal and a negative decimal?
Find the absolute values of both numbers, subtract the smaller from the larger, then assign the sign of the number with the greater absolute value to the result.
What is 3.7 + (−1.2)?
The absolute values are 3.7 and 1.2. Subtract: 3.7 − 1.2 = 2.5. Since 3.7 has the greater absolute value and is positive, the answer is 2.5.
What is −4.6 + 2.1?
Subtract absolute values: 4.6 − 2.1 = 2.5. Since 4.6 is greater and its number is negative, the answer is −2.5.
What happens when both decimals are negative?
Add their absolute values and make the result negative. For example, −2.3 + (−1.4) = −3.7.
Why is aligning decimal points important when adding decimals?
Aligning decimal points ensures you add digits of the same place value (tenths to tenths, hundredths to hundredths), preventing calculation errors.
How is adding signed decimals similar to adding signed integers?
The rules are identical: same signs → add absolute values and keep the sign; different signs → subtract absolute values and keep the sign of the larger absolute value.