Decimal Operations

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Decimal Operations · Grade 5 · Worksheet 1

1. Emma is tracking her weekly jogging distances. On Monday she jogged 3.45 kilometers and on Wednesday she jogged 2.85 kilometers. How many total kilometers did Emma jog on these two days? Answer: 6.30 Solution: Identify the distances to add: Monday = 3.45 km, Wednesday = 2.85 km 3.45 + 2.85 Add the hundredths place: 5 + 5 = 10, write 0 and carry over 1 to the tenths place Add the tenths place: 4 + 8 + 1 (carry over) = 13, write 3 and carry over 1 to the ones place Add the ones place: 3 + 2 + 1 (carry…
   Full step-by-step solution

   Step 1: Identify the distances to add: Monday = 3.45 km, Wednesday = 2.85 km Step 2: Write the numbers with decimal points aligned: 3.45 + 2.85 ______ Step 3: Add the hundredths place: 5 + 5 = 10, write 0 and carry over 1 to the tenths place Step 4: Add the tenths place: 4 + 8 + 1 (carry over) = 13, write 3 and carry over 1 to the ones place Step 5: Add the ones place: 3 + 2 + 1 (carry over) = 6 Step 6: The total is 6.30 kilometers The answer is 6.30.

2. Liam is measuring fabric for a school project. He needs a piece that is 2.75 meters long. He already has a piece that is 1.48 meters long. How much more fabric, in meters, does Liam need to add to the piece he already has? Answer: 1.27 Solution: Liam needs 2.75 meters of fabric in total. He already has 1.48 meters. To find how much more he needs, subtract the fabric he already has from the total fabric needed.
   Full step-by-step solution

   Liam needs 2.75 meters of fabric in total. He already has 1.48 meters. To find how much more he needs, subtract the fabric he already has from the total fabric needed. Step 1: Write the subtraction. 2.75 − 1.48 Step 2: Subtract the hundredths place. 5 hundredths − 8 hundredths: We can’t do this directly, so we borrow 1 tenth from the 7 tenths. Now 7 tenths becomes 6 tenths, and 5 hundredths becomes 15 hundredths. 15 hundredths − 8 hundredths = 7 hundredths. Step 3: Subtract the tenths place. 6 tenths − 4 tenths = 2 tenths. Step 4: Subtract the ones place. 2 ones − 1 one = 1 one. So, 2.75 − 1.48 = 1.27. Step 5: Interpret the result. Liam needs 1.27 more meters of fabric. Final answer: 1.27

3. A scientist is measuring the growth of a plant. On Monday, the plant was 587.45 centimeters tall. By Friday, it had grown another 32.78 centimeters. However, a strong wind caused it to bend and lose 15.63 centimeters from its height. What is the plant's final height in centimeters? Answer: 604.60 Solution: The plant started at 587.45 cm. From Monday to Friday, it grew 32.78 cm. So, new height before the wind = 587.45 + 32.78 587.45 + 32.78 = 620.23 cm Wind caused a loss of 15.63 cm.
   Full step-by-step solution

   Let's go step by step. **Step 1: Start with Monday's height** The plant started at 587.45 cm. **Step 2: Add the growth by Friday** From Monday to Friday, it grew 32.78 cm. So, new height before the wind = 587.45 + 32.78 587.45 + 32.78 = 620.23 cm **Step 3: Subtract the loss due to wind** Wind caused a loss of 15.63 cm. So, final height = 620.23 − 15.63 620.23 − 15.63 = 604.60 cm **Step 4: Conclusion** The plant's final height is 604.60 cm.

4. Olivia is helping her grandmother make a quilt. She needs to cut three pieces of ribbon for the border. The first piece needs to be 3.25 meters long, the second piece needs to be 4.50 meters long, and the third piece needs to be 2.75 meters long. What is the total length of ribbon Olivia needs to cut? Answer: 10.50 Solution: Identify the lengths to add: 3.25 m, 4.50 m, and 2.75 m. Write the numbers vertically, aligning the decimal points. 3.25 4.50 + 2.75 Add the hundredths place: 5 + 0 + 5 = 10.
   Full step-by-step solution

   Step 1: Identify the lengths to add: 3.25 m, 4.50 m, and 2.75 m. Step 2: Write the numbers vertically, aligning the decimal points. 3.25 4.50 + 2.75 ------- Step 3: Add the hundredths place: 5 + 0 + 5 = 10. Write down 0 in the hundredths place and carry over 1 to the tenths place. Step 4: Add the tenths place, including the carry-over: 1 (carried) + 2 + 5 + 7 = 15. Write down 5 in the tenths place and carry over 1 to the ones place. Step 5: Add the ones place, including the carry-over: 1 (carried) + 3 + 4 + 2 = 10. Write down 10. Step 6: The total is 10.50 meters. The answer is 10.50.

5. 15.67 + 9.84 = ? Answer: 25.51 Solution: 15.67 + 9.84 Add the hundredths place: 7 + 4 = 11. Write down 1 and carry over 1 to the tenths place. Add the tenths place: 6 + 8 + 1 (carried over) = 15.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 15.67 + 9.84 Step 2: Add the hundredths place: 7 + 4 = 11. Write down 1 and carry over 1 to the tenths place. Step 3: Add the tenths place: 6 + 8 + 1 (carried over) = 15. Write down 5 and carry over 1 to the ones place. Step 4: Add the ones place: 5 + 9 + 1 (carried over) = 15. Write down 5 and carry over 1 to the tens place. Step 5: Add the tens place: 1 + 1 (carried over) = 2. Step 6: Bring down the decimal point. The final answer is 25.51.

6. Liam is building a wooden bookshelf and needs to cut two pieces of wood. The first piece needs to be 2.75 meters long and the second piece needs to be 1.85 meters long. If he starts with a 5 meter board, how many meters of wood will remain after cutting both pieces? Answer: 0.40 Solution: Identify the total length of wood Liam starts with. He has a board that is 5 meters long. Identify the lengths of the two pieces he needs to cut.
   Full step-by-step solution

   Let's work through this step by step. Step 1: Identify the total length of wood Liam starts with. He has a board that is 5 meters long. Step 2: Identify the lengths of the two pieces he needs to cut. First piece = 2.75 meters Second piece = 1.85 meters Step 3: Add the lengths of the two pieces to find the total wood used. 2.75 + 1.85 = 4.60 meters Step 4: Subtract the total wood used from the original board length to find the remaining wood. 5.00 - 4.60 = 0.40 meters Step 5: Interpret the result. After cutting both pieces, Liam will have 0.40 meters of wood left. Final answer: 0.40

7. 7.85 + 4.29 = ? Answer: 12.14 Solution: Write the numbers one above the other, aligning the decimal points. 7.85 + 4.29 Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths.
   Full step-by-step solution

   Let's add 7.85 and 4.29 step-by-step. Step 1: Write the numbers one above the other, aligning the decimal points. 7.85 + 4.29 -------- Step 2: Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths. 14 hundredths is the same as 1 tenth and 4 hundredths. Write down the 4 in the hundredths place and carry over the 1 to the tenths place. 7.85 + 4.29 -------- .4 (with 1 carried over to the tenths column) Step 3: Add the tenths place, including the carry-over. 8 tenths + 2 tenths = 10 tenths, plus the carried-over 1 tenth = 11 tenths. 11 tenths is the same as 1 whole and 1 tenth. Write down the 1 in the tenths place and carry over the 1 to the ones place. 7.85 + 4.29 -------- 1 .4 (with 1 carried over to the ones column) Step 4: Add the ones place, including the carry-over. 7 ones + 4 ones = 11 ones, plus the carried-over 1 one = 12 ones. Write down 12 in the ones place. 7.85 + 4.29 -------- 12.14 Step 5: Combine the result: 12 and 14 hundredths, which is 12.14. Final Answer: 12.14

8. Maria is tracking her running progress for a school fitness challenge. On Monday, she ran 3.75 kilometers. On Wednesday, she ran 2.15 kilometers. How many total kilometers did Maria run on these two days? Answer: 5.90 Solution: Identify the distances Maria ran: 3.75 km and 2.15 km. To find the total, add the two distances together: 3.75 + 2.15. Line up the decimal points and add the numbers.
   Full step-by-step solution

   Step 1: Identify the distances Maria ran: 3.75 km and 2.15 km. Step 2: To find the total, add the two distances together: 3.75 + 2.15. Step 3: Line up the decimal points and add the numbers. 3.75 + 2.15 ------- Step 4: Add the hundredths place: 5 + 5 = 10. Write down 0 in the hundredths place and carry over 1 to the tenths place. Step 5: Add the tenths place: 7 + 1 + 1 (carried over) = 9. Write down 9 in the tenths place. Step 6: Add the ones place: 3 + 2 = 5. Write down 5 in the ones place. Step 7: The total is 5.90 kilometers. The answer is 5.90.