2. 5.3 Adding and Subtracting Signed Decimal Numbers
Chapter 5 Rational Numbers: Positive and
Negative Decimals

3. 5.3 Adding and Subtracting Signed Decimal Numbers
Objectives
Add and subtract positive decimals.
Add and subtract negative decimals.
Estimate the answer when adding or subtracting decimals.
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4. Objective 1: Add and subtract positive decimals.
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5. Objective 1: Add and subtract positive decimals.
Example
Find the sum of and
Step 1
Write the numbers in columns with the decimal points lined up.
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6. Objective 1: Add and subtract positive decimals.
Example
(continued)
Step 2
Add as if these were whole numbers.
Step 3
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7. Objective 1: Add and subtract positive decimals.
Example
Find the sum
Write the numbers in columns with the decimal points lined up. Then add.
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8. Objective 1: Add and subtract positive decimals.
Example
Find the sum
Write a 0 in the hundredths place in 7.3, so it has two decimal places also.
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9. Objective 1: Add and subtract positive decimals.
Example
Find the sum
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10. Objective 1: Add and subtract positive decimals.
Example
Find the difference of and
Step 1
Step 2
Step 3
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11. Objective 1: Add and subtract positive decimals.
Example
Find minus
Regrouping is needed in this problem.
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12. Objective 1: Add and subtract positive decimals.
Example
Subtract 16.5 from
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13. Objective 1: Add and subtract positive decimals.
Example
Find 12 less 5.83.
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14. Objective 2: Add and subtract negative decimals.
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15. Objective 2: Add and subtract negative decimals.
Example
Find the sum of –3.7 + (–16).
Both addends are negative, so the sum will be negative.
Add the absolute values.
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16. Objective 2: Add and subtract negative decimals.
Example
Find the sum of –
The addends have different signs.
Find absolute values of each and subtract the smaller absolute value from the larger.
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17. Objective 2: Add and subtract negative decimals.
Example
Find the difference of 4.3 –
–12.73 has the larger absolute value and is negative, so the answer will be negative.
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18. Objective 2: Add and subtract negative decimals.
Example
Find the difference of –4.3 – (–4.8).
4.8 has the larger absolute value and is positive, so the answer will be positive.
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19. Objective 2: Add and subtract negative decimals.
Example
Find the difference 14.2 – ( ).
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20. Objective 3: Estimate the answer when adding or subtracting decimals.
Estimate the sum of and using front end rounding. Then find the exact answer.
Example
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21. Objective 3: Estimate the answer when adding or subtracting decimals.
Subtract $13.78 from $69.42 using front end rounding. Then find the exact answer.
Example
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22. Objective 3: Estimate the answer when adding or subtracting decimals.
Subtract –1.861 – 7.3 using front end rounding. Then find the exact answer.
Example
Estimate:
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23. Objective 3: Estimate the answer when adding or subtracting decimals.
Subtract –1.861 – 7.3 using front end rounding. Then find the exact answer.
Example
Exact:
The answer will be negative because both numbers are negative.
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