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Decimal Operations

Grade 5 · Decimals · Worksheet 1

  1. 845.63 - 297.48 = ? Answer: ______________
  2. Liam is measuring fabric for a sewing project. He needs 2.75 meters of blue fabric and 1.25 meters of red fabric. How many total meters of fabric does Liam need? Answer: ______________
  3. Sophia is training for a school triathlon. On Saturday, she swam 1.61 kilometers in the pool. On Sunday, she biked 5.36 kilometers and then ran 2.91 kilometers. What is the total distance Sophia traveled over the weekend? Answer: ______________
  4. 15.67 + 9.84 = ? Answer: ______________
  5. Matiu is training for a school triathlon. He swims 0.85 kilometers, then bikes 12.40 kilometers, and finally runs 5.25 kilometers. What is the total distance of Matiu's triathlon training route? Answer: ______________
  6. 7.45 + 3.89 = ? Answer: ______________
  7. Emma is training for a 5K race. On Monday, she ran 1.85 kilometers. On Wednesday, she ran 2.15 kilometers. How many total kilometers did Emma run on these two days? Answer: ______________
  8. Emma is tracking her daily exercise. On Monday, she walked 2.35 kilometers in the morning and 1.75 kilometers in the evening. On Tuesday, she walked 3.10 kilometers. How many total kilometers did Emma walk over these two days? Answer: ______________
  9. Noah draws a rectangular swimming pool on a coordinate grid. The corners are at (1.6, 2.1), (6.6, 2.1), (6.6, 5.1), and (1.6, 5.1). Each unit on the grid represents 1 meter. What is the perimeter of the swimming pool in meters? Answer: ______________
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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 1

  1. 845.63 - 297.48 = ? Answer: 548.15 Solution: 845.63 - 297.48 Subtract the hundredths place: 3 - 8. Since 3 is less than 8, borrow 1 from the tenths place. The 6 in the tenths becomes 5, and the 3 in the hundredths becomes 13.
    Full step-by-step solution

    Step 1: Write the numbers with decimal points aligned: 845.63 - 297.48 Step 2: Subtract the hundredths place: 3 - 8. Since 3 is less than 8, borrow 1 from the tenths place. The 6 in the tenths becomes 5, and the 3 in the hundredths becomes 13. Now 13 - 8 = 5. Write 5 in the hundredths place. Step 3: Subtract the tenths place: 5 - 4 = 1. Write 1 in the tenths place. Step 4: Subtract the ones place: 5 - 7. Since 5 is less than 7, borrow 1 from the tens place. The 4 in the tens becomes 3, and the 5 in the ones becomes 15. Now 15 - 7 = 8. Write 8 in the ones place. Step 5: Subtract the tens place: 3 - 9. Since 3 is less than 9, borrow 1 from the hundreds place. The 8 in the hundreds becomes 7, and the 3 in the tens becomes 13. Now 13 - 9 = 4. Write 4 in the tens place. Step 6: Subtract the hundreds place: 7 - 2 = 5. Write 5 in the hundreds place. Step 7: Place the decimal point in the answer directly below the decimal points in the problem. The final answer is 548.15.

  2. Liam is measuring fabric for a sewing project. He needs 2.75 meters of blue fabric and 1.25 meters of red fabric. How many total meters of fabric does Liam need? Answer: 4.00 Solution: Identify the amounts of fabric needed. Liam needs 2.75 meters of blue fabric and 1.25 meters of red fabric. Write the addition problem.
    Full step-by-step solution

    Step 1: Identify the amounts of fabric needed. Liam needs 2.75 meters of blue fabric and 1.25 meters of red fabric. Step 2: Write the addition problem. Total fabric = 2.75 + 1.25 Step 3: Add the numbers. First, add the hundredths place: 0.05 + 0.05 = 0.10 Write down 0 in the hundredths place, carry over 1 to the tenths place. Step 4: Add the tenths place: 0.7 + 0.2 = 0.9, plus the carried over 1 gives 1.0 Write down 0 in the tenths place, carry over 1 to the units place. Step 5: Add the units place: 2 + 1 = 3, plus the carried over 1 gives 4. Step 6: Combine the results. The total is 4.00 meters. Step 7: Final answer. Liam needs 4.00 meters of fabric in total.

  3. Sophia is training for a school triathlon. On Saturday, she swam 1.61 kilometers in the pool. On Sunday, she biked 5.36 kilometers and then ran 2.91 kilometers. What is the total distance Sophia traveled over the weekend? Answer: 9.88 Solution: Identify all the distances: 1.61 km (swim), 5.36 km (bike), and 2.91 km (run). Write the numbers vertically, aligning the decimal points: 1.61 5.36 + 2.91 Add the hundredths place: 1 + 6 + 1 = 8.
    Full step-by-step solution

    Step 1: Identify all the distances: 1.61 km (swim), 5.36 km (bike), and 2.91 km (run). Step 2: Write the numbers vertically, aligning the decimal points: 1.61 5.36 + 2.91 -------- Step 3: Add the hundredths place: 1 + 6 + 1 = 8. Write 8 in the hundredths place. Step 4: Add the tenths place: 6 + 3 + 9 = 18. Write 8 in the tenths place and carry over 1 to the ones place. Step 5: Add the ones place, including the carry-over: 1 (carried) + 1 + 5 + 2 = 9. Write 9 in the ones place. Step 6: Place the decimal point in the answer directly below the other decimal points. The total distance is 9.88 kilometers.

  4. 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.

  5. Matiu is training for a school triathlon. He swims 0.85 kilometers, then bikes 12.40 kilometers, and finally runs 5.25 kilometers. What is the total distance of Matiu's triathlon training route? Answer: 18.50 Solution: Identify the three distances: 0.85 km (swim), 12.40 km (bike), and 5.25 km (run). Write the numbers vertically, aligning the decimal points: 0.85 12.40 + 5.25 Add the hundredths place: 5 + 0 + 5 = 10.
    Full step-by-step solution

    Step 1: Identify the three distances: 0.85 km (swim), 12.40 km (bike), and 5.25 km (run). Step 2: Write the numbers vertically, aligning the decimal points: 0.85 12.40 + 5.25 ------- Step 3: Add the hundredths place: 5 + 0 + 5 = 10. Write 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) + 8 + 4 + 2 = 15. Write 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) + 0 + 2 + 5 = 8. Write 8 in the ones place. Step 6: Add the tens place: 1 (from 12.40). Write 1 in the tens place. Step 7: The total distance is 18.50 kilometers. The answer is 18.50.

  6. 7.45 + 3.89 = ? Answer: 11.34 Solution: Write the numbers one under the other, aligning the decimal points. 7.45 + 3.89 Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths.
    Full step-by-step solution

    Let's add 7.45 and 3.89 step by step. Step 1: Write the numbers one under the other, aligning the decimal points. 7.45 + 3.89 -------- Step 2: Start adding from the rightmost column (hundredths place). 5 hundredths + 9 hundredths = 14 hundredths. 14 hundredths = 0.14, which means 1 tenth and 4 hundredths. Write down the 4 in the hundredths place and carry over the 1 tenth to the next column. 7.45 + 3.89 -------- .4 (with 1 carried over to the tenths column) Step 3: Add the tenths place, including the carry-over. 4 tenths + 8 tenths + 1 tenth (carried over) = 13 tenths. 13 tenths = 1.3, which means 1 whole and 3 tenths. Write down the 3 in the tenths place and carry over the 1 to the ones column. 7.45 + 3.89 -------- .34 (with 1 carried over to the ones column) Step 4: Add the ones place, including the carry-over. 7 ones + 3 ones + 1 one (carried over) = 11 ones. Write 11 in the ones and tens places. 7.45 + 3.89 -------- 11.34 Step 5: Combine the result: 11 and 0.34 gives 11.34. Final Answer: 11.34

  7. Emma is training for a 5K race. On Monday, she ran 1.85 kilometers. On Wednesday, she ran 2.15 kilometers. How many total kilometers did Emma run on these two days? Answer: 4.00 Solution: Identify the distances run on each day: Monday = 1.85 km, Wednesday = 2.15 km. Add the two distances together to find the total: 1.85 + 2.15. Align the decimal points and add: 1.85 + 2.15 = 4.00.
    Full step-by-step solution

    Step 1: Identify the distances run on each day: Monday = 1.85 km, Wednesday = 2.15 km. Step 2: Add the two distances together to find the total: 1.85 + 2.15. Step 3: Align the decimal points and add: 1.85 + 2.15 = 4.00. The answer is 4.00 kilometers.

  8. Emma is tracking her daily exercise. On Monday, she walked 2.35 kilometers in the morning and 1.75 kilometers in the evening. On Tuesday, she walked 3.10 kilometers. How many total kilometers did Emma walk over these two days? Answer: 7.20 Solution: Calculate Monday's total distance: 2.35 km + 1.75 km = 4.10 km Add Tuesday's distance to Monday's total: 4.10 km + 3.10 km = 7.20 km Emma walked a total of 7.20 kilometers over the two days.
    Full step-by-step solution

    Step 1: Calculate Monday's total distance: 2.35 km + 1.75 km = 4.10 km Step 2: Add Tuesday's distance to Monday's total: 4.10 km + 3.10 km = 7.20 km Step 3: Emma walked a total of 7.20 kilometers over the two days.

  9. Noah draws a rectangular swimming pool on a coordinate grid. The corners are at (1.6, 2.1), (6.6, 2.1), (6.6, 5.1), and (1.6, 5.1). Each unit on the grid represents 1 meter. What is the perimeter of the swimming pool in meters? Answer: 16.0 Solution: Identify the coordinates of the rectangle: A (1.6, 2.1), B (6.6, 2.1), C (6.6, 5.1), D (1.6, 5.1). Find the length of side AB (horizontal).
    Full step-by-step solution

    Step 1: Identify the coordinates of the rectangle: A (1.6, 2.1), B (6.6, 2.1), C (6.6, 5.1), D (1.6, 5.1). Step 2: Find the length of side AB (horizontal). Since A and B have the same y-coordinate (2.1), subtract the x-coordinates: 6.6 - 1.6 = 5.0 meters. Step 3: Find the length of side BC (vertical). Since B and C have the same x-coordinate (6.6), subtract the y-coordinates: 5.1 - 2.1 = 3.0 meters. Step 4: Opposite sides are equal, so CD = 5.0 meters and DA = 3.0 meters. Step 5: Add all four sides to find the perimeter: 5.0 + 3.0 + 5.0 + 3.0 = 16.0 meters. Alternatively, use the formula: Perimeter = 2 x (length + width) = 2 x (5.0 + 3.0) = 2 x 8.0 = 16.0 meters. The answer is 16.0.