Here are the solutions for the "Adding and Subtracting Decimals" exercises shown on the worksheet. I have calculated each problem step-by-step to ensure accuracy.
1. $0.6 + 5.8$
- Align the decimals: $0.6 + 5.8$
- Add tenths: $6 + 8 = 14$ (write 4, carry 1)
- Add ones: $0 + 5 + 1 \text{ (carry)} = 6$
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Answer: 6.4 (Color: Blue)
2. $2.1 + 3.4$
- Add tenths: $1 + 4 = 5$
- Add ones: $2 + 3 = 5$
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Answer: 5.5 (Color: Green)
3. $3.1 - 0.972$
- Add zeros to make lengths equal: $3.100 - 0.972$
- Subtract thousandths: $10 - 2 = 8$
- Subtract hundredths: $9 - 7 = 2$
- Subtract tenths: $10 - 9 = 1$
- Subtract ones: $2 - 0 = 2$
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Answer: 2.128 (Color: Purple)
4. $3.1 - 2.076$
- Add zeros: $3.100 - 2.076$
- Subtract thousandths: $10 - 6 = 4$
- Subtract hundredths: $9 - 7 = 2$
- Subtract tenths: $0 - 0 = 0$
- Subtract ones: $3 - 2 = 1$
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Answer: 1.024 (Color: Yellow)
5. $8.13 - 2.736$
- Add zero: $8.130 - 2.736$
- Subtract thousandths: $10 - 6 = 4$
- Subtract hundredths: $12 - 3 = 9$
- Subtract tenths: $10 - 7 = 3$
- Subtract ones: $7 - 2 = 5$
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Answer: 5.394 (Color: Black)
6. $5.91 + 2.38$
- Add hundredths: $1 + 8 = 9$
- Add tenths: $9 + 3 = 12$ (write 2, carry 1)
- Add ones: $5 + 2 + 1 \text{ (carry)} = 8$
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Answer: 8.29 (Color: Blue)
7. $3.086 + 6.152$
- Add thousandths: $6 + 2 = 8$
- Add hundredths: $8 + 5 = 13$ (write 3, carry 1)
- Add tenths: $0 + 1 + 1 \text{ (carry)} = 2$
- Add ones: $3 + 6 = 9$
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Answer: 9.238 (Color: Green)
8. $4.7 - 1.9$
- Subtract tenths: $17 - 9 = 8$ (borrow from ones)
- Subtract ones: $3 - 1 = 2$
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Answer: 2.8 (Color: Purple)
9. $9.3 - 3.9$
- Subtract tenths: $13 - 9 = 4$ (borrow from ones)
- Subtract ones: $8 - 3 = 5$
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Answer: 5.4 (Color: Yellow)
10. $5.2 - 1.86$
- Add zero: $5.20 - 1.86$
- Subtract hundredths: $10 - 6 = 4$
- Subtract tenths: $11 - 8 = 3$ (borrowed from ones)
- Subtract ones: $4 - 1 = 3$
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Answer: 3.34 (Color: Black)
11. $15.90 + 26.37$
- Add hundredths: $0 + 7 = 7$
- Add tenths: $9 + 3 = 12$ (write 2, carry 1)
- Add ones: $5 + 6 + 1 \text{ (carry)} = 12$ (write 2, carry 1)
- Add tens: $1 + 2 + 1 \text{ (carry)} = 4$
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Answer: 42.27 (Color: Blue)
12. $9.27 + 15.066$
- Add zero: $9.270 + 15.066$
- Add thousandths: $0 + 6 = 6$
- Add hundredths: $7 + 6 = 13$ (write 3, carry 1)
- Add tenths: $2 + 0 + 1 \text{ (carry)} = 3$
- Add ones: $9 + 5 = 14$ (write 4, carry 1)
- Add tens: $1 + 1 \text{ (carry)} = 2$
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Answer: 24.336 (Color: Green)
Final Answer:
1. 6.4
2. 5.5
3. 2.128
4. 1.024
5. 5.394
6. 8.29
7. 9.238
8. 2.8
9. 5.4
10. 3.34
11. 42.27
12. 24.336
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting decimals worksheet fall.
