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Decimal Operations

Grade 5 · Decimals · Worksheet 2

  1. Noah is comparing the weights of three pumpkins he grew in his garden. The first pumpkin weighs 7.85 pounds, the second pumpkin weighs 9.40 pounds, and the third pumpkin weighs 8.60 pounds. What is the total weight of all three pumpkins combined? Answer: ______________
  2. Noa plots a rectangle on a coordinate grid. The corners are at (1.6, 2.1), (7.6, 2.1), (7.6, 5.1), and (1.6, 5.1). What is the perimeter of this rectangle in units? Answer: ______________
  3. Emma is tracking her family's road trip. On the first day, they drove 287.65 kilometers. On the second day, they drove 154.30 kilometers. How many total kilometers did Emma's family drive over the two days? Answer: ______________
  4. Noa is drawing a rectangular playground on a coordinate grid for a school project. The corners of the playground are at (3.1, 1.6), (9.6, 1.6), (9.6, 6.1), and (3.1, 6.1). Each unit on the grid represents 1 meter. What is the perimeter of the playground in meters? Answer: ______________
  5. 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: ______________
  6. 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: ______________
  7. 7.45 + 3.89 = ? Answer: ______________
  8. 713.45 + 289.67 - 156.89 = ? Answer: ______________
  9. 7.45 + 3.28 = ? Answer: ______________
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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 2

  1. Noah is comparing the weights of three pumpkins he grew in his garden. The first pumpkin weighs 7.85 pounds, the second pumpkin weighs 9.40 pounds, and the third pumpkin weighs 8.60 pounds. What is the total weight of all three pumpkins combined? Answer: 25.85 Solution: Write the three weights with decimal points lined up: 7.85, 9.40, and 8.60. Add the hundredths place: 5 + 0 + 0 = 5. Write 5 in the hundredths place.
    Full step-by-step solution

    Step 1: Write the three weights with decimal points lined up: 7.85, 9.40, and 8.60. Step 2: Add the hundredths place: 5 + 0 + 0 = 5. Write 5 in the hundredths place. Step 3: Add the tenths place: 8 + 4 + 6 = 18. Write 8 in the tenths place and carry over 1 to the ones place. Step 4: Add the ones place, including the carry-over: 1 (carried) + 7 + 9 + 8 = 25. Write 25. Step 5: The total is 25.85 pounds. The answer is 25.85.

  2. Noa plots a rectangle on a coordinate grid. The corners are at (1.6, 2.1), (7.6, 2.1), (7.6, 5.1), and (1.6, 5.1). What is the perimeter of this rectangle in units? Answer: 18.0 Solution: Identify the side lengths from the coordinates. The bottom side from (1.6, 2.1) to (7.6, 2.1) is horizontal: 7.6 - 1.6 = 6.0 units. The right side from (7.6, 2.1) to (7.6, 5.1) is vertical: 5.1 - 2.1 = 3.0 units.
    Full step-by-step solution

    Step 1: Identify the side lengths from the coordinates. The bottom side from (1.6, 2.1) to (7.6, 2.1) is horizontal: 7.6 - 1.6 = 6.0 units. The right side from (7.6, 2.1) to (7.6, 5.1) is vertical: 5.1 - 2.1 = 3.0 units. Step 2: Since it is a rectangle, opposite sides are equal. So the top side is also 6.0 units and the left side is also 3.0 units. Step 3: Add all four sides: 6.0 + 3.0 + 6.0 + 3.0 = 18.0 units. Step 4: The perimeter is 18.0 units.

  3. Emma is tracking her family's road trip. On the first day, they drove 287.65 kilometers. On the second day, they drove 154.30 kilometers. How many total kilometers did Emma's family drive over the two days? Answer: 441.95 Solution: Write down the two distances: 287.65 and 154.30. Align the numbers by their decimal points. Add the hundredths place: 5 + 0 = 5.
    Full step-by-step solution

    Step 1: Write down the two distances: 287.65 and 154.30. Step 2: Align the numbers by their decimal points. Step 3: Add the hundredths place: 5 + 0 = 5. Write down 5 in the hundredths place. Step 4: Add the tenths place: 6 + 3 = 9. Write down 9 in the tenths place. Step 5: Add the ones place: 7 + 4 = 11. Write down 1 in the ones place and carry over the 1 to the tens place. Step 6: Add the tens place: 8 + 5 = 13, plus the carried over 1 makes 14. Write down 4 in the tens place and carry over the 1 to the hundreds place. Step 7: Add the hundreds place: 2 + 1 = 3, plus the carried over 1 makes 4. Write down 4 in the hundreds place. Step 8: The final answer is 441.95 kilometers.

  4. Noa is drawing a rectangular playground on a coordinate grid for a school project. The corners of the playground are at (3.1, 1.6), (9.6, 1.6), (9.6, 6.1), and (3.1, 6.1). Each unit on the grid represents 1 meter. What is the perimeter of the playground in meters? Answer: 22.0 Solution: Identify the coordinates of the corners: A (3.1, 1.6), B (9.6, 1.6), C (9.6, 6.1), D (3.1, 6.1). Find the length of the horizontal side AB.
    Full step-by-step solution

    Step 1: Identify the coordinates of the corners: A (3.1, 1.6), B (9.6, 1.6), C (9.6, 6.1), D (3.1, 6.1). Step 2: Find the length of the horizontal side AB. Since A and B have the same y-coordinate (1.6), subtract the x-coordinates: 9.6 - 3.1 = 6.5 meters. Step 3: Find the length of the vertical side BC. Since B and C have the same x-coordinate (9.6), subtract the y-coordinates: 6.1 - 1.6 = 4.5 meters. Step 4: In a rectangle, opposite sides are equal. So the other horizontal side CD is also 6.5 meters, and the other vertical side DA is also 4.5 meters. Step 5: Calculate the perimeter: 6.5 + 4.5 + 6.5 + 4.5 = 22.0 meters. Final answer: 22.0.

  5. 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.

  6. 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.

  7. 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

  8. 713.45 + 289.67 - 156.89 = ? Answer: 846.23 Solution: Add 713.45 and 289.67.
    Full step-by-step solution

    Step 1: Add 713.45 and 289.67. 713.45 + 289.67 -------- 1003.12 (Hundredths: 5+7=12, write 2 carry 1; Tenths: 4+6+1=11, write 1 carry 1; Ones: 3+9+1=13, write 3 carry 1; Tens: 1+8+1=10, write 0 carry 1; Hundreds: 7+2+1=10, write 0 carry 1; Thousands: 1) Step 2: Subtract 156.89 from 1003.12. 1003.12 - 156.89 -------- 846.23 (Hundredths: 2-9, borrow 1 from tenths: 12-9=3; Tenths: 0-8, borrow from ones: 10-8=2; Ones: 2-6, borrow from tens: 12-6=6; Tens: 9-5=4; Hundreds: 9-1=8; Thousands: 0) The final answer is 846.23.

  9. 7.45 + 3.28 = ? Answer: 10.73 Solution: Write the numbers one under the other, aligning the decimal points. 7.45 + 3.28 Start adding from the rightmost column (hundredths place). 5 hundredths + 8 hundredths = 13 hundredths.
    Full step-by-step solution

    Let's add 7.45 and 3.28 step by step. Step 1: Write the numbers one under the other, aligning the decimal points. 7.45 + 3.28 -------- Step 2: Start adding from the rightmost column (hundredths place). 5 hundredths + 8 hundredths = 13 hundredths. 13 hundredths is the same as 1 tenth and 3 hundredths. Write down the 3 in the hundredths place and carry over the 1 to the tenths place. Hundredths column result: 3 Carry over: 1 Step 3: Move to the tenths place. 4 tenths + 2 tenths = 6 tenths. Now add the carried-over 1 tenth: 6 tenths + 1 tenth = 7 tenths. Write down the 7 in the tenths place. Tenths column result: 7 Carry over: 0 Step 4: Move to the ones place. 7 ones + 3 ones = 10 ones. Write down the 0 in the ones place and carry over the 1 to the tens place. Ones column result: 0 Carry over: 1 Step 5: Move to the tens place. There is only the carried-over 1 ten. Write down the 1 in the tens place. Tens column result: 1 Step 6: Combine all digits, placing the decimal point in line with the original numbers. The result is 10.73. ANSWER: 10.73