Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 3

1. 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.

2. Isabella is tracking the rainfall in her town for a science project. On Monday, it rained 1.25 inches. On Tuesday, it rained 0.75 inches. On Wednesday, it rained 2.50 inches. What was the total rainfall for these three days? Answer: 4.50 Solution: Identify the amounts to add: 1.25 inches, 0.75 inches, and 2.50 inches. Write the numbers vertically, aligning the decimal points. 1.25 0.75 + 2.50 Add the hundredths place: 5 + 5 + 0 = 10.
   Full step-by-step solution

   Step 1: Identify the amounts to add: 1.25 inches, 0.75 inches, and 2.50 inches. Step 2: Write the numbers vertically, aligning the decimal points. 1.25 0.75 + 2.50 ------- Step 3: Add the hundredths place: 5 + 5 + 0 = 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) + 2 + 7 + 5 = 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) + 1 + 0 + 2 = 4. Write 4 in the ones place. Step 6: The total is 4.50 inches. The answer is 4.50.

3. 15.78 - 9.35 = ? Answer: 6.43 Solution: Write the numbers vertically, aligning the decimal points: 15.78 - 9.35 Subtract the hundredths place: 8 - 5 = 3 Subtract the tenths place: 7 - 3 = 4 Subtract the whole numbers: 15 - 9 = 6 The result is 6.43 The answer is 6.43.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning the decimal points: 15.78 - 9.35 Step 2: Subtract the hundredths place: 8 - 5 = 3 Step 3: Subtract the tenths place: 7 - 3 = 4 Step 4: Subtract the whole numbers: 15 - 9 = 6 Step 5: Bring down the decimal point Step 6: The result is 6.43 The answer is 6.43.

4. Liam is building a wooden bookshelf and needs to cut two pieces of wood. The first piece needs to be 1.75 meters long and the second piece needs to be 0.89 meters long. What is the total length of wood Liam needs to cut for his project? Answer: 2.64 Solution: To find the total length of wood Liam needs, we add the lengths of the two pieces together. Write down the lengths that need to be added. First piece: 1.75 meters Second piece: 0.89 meters Set up the addition problem, aligning the decimal points.
   Full step-by-step solution

   To find the total length of wood Liam needs, we add the lengths of the two pieces together. Step 1: Write down the lengths that need to be added. First piece: 1.75 meters Second piece: 0.89 meters Step 2: Set up the addition problem, aligning the decimal points. 1.75 + 0.89 _______ Step 3: Add the numbers in the hundredths place (the farthest right column). 5 hundredths + 9 hundredths = 14 hundredths. Since 14 hundredths is the same as 1 tenth and 4 hundredths, we write down the 4 in the hundredths place and carry over the 1 to the tenths place. Step 4: Add the numbers in the tenths place, including the carry-over. 7 tenths + 8 tenths + 1 tenth (carried over) = 16 tenths. Since 16 tenths is the same as 1 one and 6 tenths, we write down the 6 in the tenths place and carry over the 1 to the ones place. Step 5: Add the numbers in the ones place, including the carry-over. 1 one + 0 ones + 1 one (carried over) = 2 ones. We write down the 2 in the ones place. Step 6: Combine the results from each column. The final number is 2 ones, 6 tenths, and 4 hundredths, which is written as 2.64. Therefore, the total length of wood Liam needs to cut is 2.64 meters.

5. Liam is building a bookshelf and needs to cut two pieces of wood. The first piece needs to be 1.75 meters long and the second piece needs to be 0.89 meters long. What is the total length of wood Liam needs to cut? Answer: 2.64 Solution: To find the total length of wood Liam needs, we add the length of the first piece and the length of the second piece. Write down the two lengths that need to be added. First piece: 1.75 meters Second piece: 0.89 meters Set up the addition problem.
   Full step-by-step solution

   To find the total length of wood Liam needs, we add the length of the first piece and the length of the second piece. Step 1: Write down the two lengths that need to be added. First piece: 1.75 meters Second piece: 0.89 meters Step 2: Set up the addition problem. We need to calculate: 1.75 + 0.89 Step 3: Align the numbers by their decimal points and add, starting from the rightmost column (the hundredths place). 1.75 + 0.89 Step 4: Add the digits in the hundredths place (the second digit after the decimal). 5 hundredths + 9 hundredths = 14 hundredths. Since 14 hundredths is the same as 1 tenth and 4 hundredths, we write down the 4 in the hundredths place and carry over the 1 to the tenths place. Step 5: Add the digits in the tenths place, including the carry-over. 7 tenths + 8 tenths = 15 tenths. Add the 1 tenth we carried over: 15 tenths + 1 tenth = 16 tenths. Since 16 tenths is the same as 1 whole and 6 tenths, we write down the 6 in the tenths place and carry over the 1 to the ones place. Step 6: Add the digits in the ones place, including the carry-over. 1 one + 0 ones = 1 one. Add the 1 one we carried over: 1 one + 1 one = 2 ones. We write down the 2 in the ones place. Step 7: Combine the results from each column. Ones place: 2 Tenths place: 6 Hundredths place: 4 This gives us the number 2.64 Therefore, the total length of wood Liam needs to cut is 2.64 meters.

6. 501.37 - 289.45 = ? Answer: 211.92 Solution: 501.37 - 289.45 Subtract the hundredths place: 7 - 5 = 2. Write 2 in the hundredths place. Subtract the tenths place: 3 - 4.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 501.37 - 289.45 Step 2: Subtract the hundredths place: 7 - 5 = 2. Write 2 in the hundredths place. Step 3: Subtract the tenths place: 3 - 4. Since 3 is less than 4, borrow 1 from the ones place. The 1 in the ones place becomes 0, and the 3 in the tenths becomes 13. Now 13 - 4 = 9. Write 9 in the tenths place. Step 4: Subtract the ones place: 0 - 9. Since 0 is less than 9, borrow 1 from the tens place. The 0 in the tens place becomes 9 (since we borrowed from 10), and the 0 in the ones becomes 10. Now 10 - 9 = 1. Write 1 in the ones place. Step 5: Subtract the tens place: 9 - 8 = 1. Write 1 in the tens place. Step 6: Subtract the hundreds place: 5 - 2 = 3. Write 3 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 211.92.

7. 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.

8. Mere is drawing a rectangular flower bed on a coordinate grid. The corners are at (15.25, 22.50), (27.75, 22.50), (27.75, 30.25), and (15.25, 30.25). What is the perimeter of the flower bed in meters? Answer: 40.50 Solution: Identify the coordinates. A = (15.25, 22.50), B = (27.75, 22.50), C = (27.75, 30.25), D = (15.25, 30.25). Going from A to B to C to D and back to A forms a rectangle.
   Full step-by-step solution

   Step 1: Identify the coordinates. A = (15.25, 22.50), B = (27.75, 22.50), C = (27.75, 30.25), D = (15.25, 30.25). Going from A to B to C to D and back to A forms a rectangle. Step 2: Find the horizontal side length. Points A and B share the same y-coordinate (22.50). The length AB = 27.75 - 15.25 = 12.50 meters. The opposite side CD is also 12.50 meters. Step 3: Find the vertical side length. Points B and C share the same x-coordinate (27.75). The length BC = 30.25 - 22.50 = 7.75 meters. The opposite side DA is also 7.75 meters. Step 4: Calculate the perimeter. Perimeter = 12.50 + 7.75 + 12.50 + 7.75 = 40.50 meters. Alternatively, 2 × (12.50 + 7.75) = 2 × 20.25 = 40.50 meters. The answer is 40.50.

9. Hana draws a rectangle on a coordinate grid. The corners are at (2.50, 3.00), (8.50, 3.00), (8.50, 6.00), and (2.50, 6.00). What is the perimeter of the rectangle in units? Answer: 18.00 Solution: Find the length. The bottom side goes from (2.50, 3.00) to (8.50, 3.00). Length = 8.50 - 2.50 = 6.00 units.
   Full step-by-step solution

   Step 1: Find the length. The bottom side goes from (2.50, 3.00) to (8.50, 3.00). Length = 8.50 - 2.50 = 6.00 units. Step 2: Find the width. The right side goes from (8.50, 3.00) to (8.50, 6.00). Width = 6.00 - 3.00 = 3.00 units. Step 3: A rectangle has two lengths and two widths. Perimeter = 2 × (length + width) = 2 × (6.00 + 3.00) = 2 × 9.00 = 18.00 units. The answer is 18.00.