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Decimal Operations

Grade 5 · Decimals · Worksheet 2

  1. Liam is measuring fabric for a school 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: ______________
  2. Emma is drawing a rectangular playground on a coordinate grid. The four corners of the playground are at (1.5, 2.0), (6.5, 2.0), (6.5, 5.5), and (1.5, 5.5). What is the perimeter of this playground in meters? Answer: ______________
  3. 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: ______________
  4. 834.56 + 127.89 - 362.45 = ? Answer: ______________
  5. Maria is tracking her daily jogging distances. On Monday, she jogged 3.45 kilometers. On Tuesday, she jogged 2.78 kilometers. On Wednesday, she increased her distance and jogged 4.15 kilometers. What is the total distance Maria jogged over these three days? Answer: ______________
  6. 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: ______________
  7. 15.78 + 9.45 = ? Answer: ______________
  8. Sophia is designing a rectangular flower garden on a coordinate grid for a school project. The four corners of the garden are at (8.50, 12.75), (16.25, 12.75), (16.25, 18.50), and (8.50, 18.50). Each unit on the grid represents 1 meter. Sophia wants to place a decorative border along the entire perimeter of the garden. What is the total length of the border needed in meters? Answer: ______________
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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 2

  1. Liam is measuring fabric for a school 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: Write down the amounts of fabric needed. Blue fabric: 2.75 meters Red fabric: 1.25 meters Add the two numbers together.
    Full step-by-step solution

    Let's add the two lengths of fabric step by step. Step 1: Write down the amounts of fabric needed. Blue fabric: 2.75 meters Red fabric: 1.25 meters Step 2: Add the two numbers together. First, add the whole numbers: 2 + 1 = 3 Step 3: Add the decimal parts: 0.75 + 0.25 = 1.00 Step 4: Combine the results from Step 2 and Step 3: 3 + 1.00 = 4.00 So, the total meters of fabric Liam needs is 4.00 meters.

  2. Emma is drawing a rectangular playground on a coordinate grid. The four corners of the playground are at (1.5, 2.0), (6.5, 2.0), (6.5, 5.5), and (1.5, 5.5). What is the perimeter of this playground in meters? Answer: 17.0 Solution: Identify the coordinates. A = (1.5, 2.0) B = (6.5, 2.0) C = (6.5, 5.5) D = (1.5, 5.5) Find the length (horizontal side). Points A and B have the same y-coordinate (2.0).
    Full step-by-step solution

    Step 1: Identify the coordinates. The corners are: A = (1.5, 2.0) B = (6.5, 2.0) C = (6.5, 5.5) D = (1.5, 5.5) Step 2: Find the length (horizontal side). Points A and B have the same y-coordinate (2.0). The length is the difference in x-coordinates: 6.5 - 1.5 = 5.0 meters. Step 3: Find the width (vertical side). Points B and C have the same x-coordinate (6.5). The width is the difference in y-coordinates: 5.5 - 2.0 = 3.5 meters. Step 4: Calculate the perimeter. Perimeter of a rectangle = 2 × (length + width) = 2 × (5.0 + 3.5) = 2 × 8.5 = 17.0 meters. The answer is 17.0.

  3. 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.

  4. 834.56 + 127.89 - 362.45 = ? Answer: 600.00 Solution: Write the numbers with aligned decimal points: 834.56 + 127.89 - 362.45 First, add 834.56 and 127.89. Add the hundredths: 6 + 9 = 15. Write 5, carry 1 to tenths.
    Full step-by-step solution

    Step 1: Write the numbers with aligned decimal points: 834.56 + 127.89 - 362.45 Step 2: First, add 834.56 and 127.89. Add the hundredths: 6 + 9 = 15. Write 5, carry 1 to tenths. Add the tenths: 5 + 8 + 1 (carried) = 14. Write 4, carry 1 to ones. Add the ones: 4 + 7 + 1 (carried) = 12. Write 2, carry 1 to tens. Add the tens: 3 + 2 + 1 (carried) = 6. Write 6. Add the hundreds: 8 + 1 = 9. Write 9. The sum is 962.45. Step 3: Now subtract 362.45 from 962.45. Subtract the hundredths: 5 - 5 = 0. Subtract the tenths: 4 - 4 = 0. Subtract the ones: 2 - 2 = 0. Subtract the tens: 6 - 6 = 0. Subtract the hundreds: 9 - 3 = 6. The difference is 600.00. Step 4: The final answer is 600.00.

  5. Maria is tracking her daily jogging distances. On Monday, she jogged 3.45 kilometers. On Tuesday, she jogged 2.78 kilometers. On Wednesday, she increased her distance and jogged 4.15 kilometers. What is the total distance Maria jogged over these three days? Answer: 10.38 Solution: Identify the distances to add: 3.45 km, 2.78 km, and 4.15 km. Add the first two distances: 3.45 + 2.78. Align the decimals: 3.45 + 2.78 = 6.23 Add the third distance to the result from Step 2: 6.23 + 4.15.
    Full step-by-step solution

    Step 1: Identify the distances to add: 3.45 km, 2.78 km, and 4.15 km. Step 2: Add the first two distances: 3.45 + 2.78. Align the decimals: 3.45 + 2.78 = 6.23 Step 3: Add the third distance to the result from Step 2: 6.23 + 4.15. Align the decimals: 6.23 + 4.15 = 10.38 Step 4: The total distance jogged is 10.38 kilometers.

  6. 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.

  7. 15.78 + 9.45 = ? Answer: 25.23 Solution: Write the numbers vertically, aligning the decimal points: 15.78 + 9.45 Add the hundredths place: 8 + 5 = 13. Write 3 in the hundredths place and carry over 1 to the tenths place.
    Full step-by-step solution

    Step 1: Write the numbers vertically, aligning the decimal points: 15.78 + 9.45 Step 2: Add the hundredths place: 8 + 5 = 13. Write 3 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place: 7 + 4 + 1 (carried over) = 12. Write 2 in the tenths place and carry over 1 to the ones place. Step 4: Add the ones place: 5 + 9 + 1 (carried over) = 15. Write 5 in the ones place and carry over 1 to the tens place. Step 5: Add the tens place: 1 + 1 (carried over) = 2. Write 2 in the tens place. Step 6: Bring down the decimal point. The final answer is 25.23.

  8. Sophia is designing a rectangular flower garden on a coordinate grid for a school project. The four corners of the garden are at (8.50, 12.75), (16.25, 12.75), (16.25, 18.50), and (8.50, 18.50). Each unit on the grid represents 1 meter. Sophia wants to place a decorative border along the entire perimeter of the garden. What is the total length of the border needed in meters? Answer: 27.00 Solution: Identify the four corners: A = (8.50, 12.75), B = (16.25, 12.75), C = (16.25, 18.50), D = (8.50, 18.50). This forms a rectangle. Find the horizontal side length (top or bottom).
    Full step-by-step solution

    Step 1: Identify the four corners: A = (8.50, 12.75), B = (16.25, 12.75), C = (16.25, 18.50), D = (8.50, 18.50). This forms a rectangle. Step 2: Find the horizontal side length (top or bottom). Look at points A and B, which share the same y-coordinate (12.75). Length AB = 16.25 - 8.50 = 7.75 meters. Step 3: Find the vertical side length (left or right). Look at points B and C, which share the same x-coordinate (16.25). Length BC = 18.50 - 12.75 = 5.75 meters. Step 4: In a rectangle, opposite sides are equal. So side CD = AB = 7.75 meters, and side DA = BC = 5.75 meters. Step 5: Add all four side lengths to find the perimeter: 7.75 + 7.75 + 5.75 + 5.75 = 15.50 + 11.50 = 27.00 meters. The answer is 27.00.