Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 3

1. Liam is saving money for a new video game that costs $45.75. He already has $28.50 saved from doing chores. For his birthday, his grandmother gives him $15.25. How much more money does Liam need to buy the video game? Answer: 2.00 Solution: Identify the total cost of the video game. The video game costs $45.75. Add up the money Liam already has.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Identify the total cost of the video game.** The video game costs $45.75. --- **Step 2: Add up the money Liam already has.** From chores: $28.50 From his grandmother: $15.25 Total money Liam has now: 28.50 + 15.25 = 43.75 --- **Step 3: Find how much more money he needs.** We subtract the money he has from the cost of the game: 45.75 - 43.75 = ? --- **Step 4: Perform the subtraction.** 45.75 - 43.75 ______ 2.00 --- **Step 5: Conclusion** Liam still needs $2.00 to buy the video game. **Final answer:** 2.00

2. Hana is helping her family prepare for a community fundraiser. She measures out 12.85 meters of red ribbon for decorating the tables and 15.70 meters of blue ribbon for the banners. Later, she uses 8.90 meters of ribbon to make bows. How much ribbon does Hana have left? Answer: 19.65 Solution: Find the total length of ribbon Hana started with by adding the red and blue ribbon: 12.85 + 15.70.
   Full step-by-step solution

   Step 1: Find the total length of ribbon Hana started with by adding the red and blue ribbon: 12.85 + 15.70. Step 2: Line up the decimal points and add: 12.85 + 15.70 -------- Hundredths: 5 + 0 = 5 Tenths: 8 + 7 = 15, write 5, carry 1 to ones Ones: 2 + 5 + 1 (carried) = 8 Tens: 1 + 1 = 2 Total = 28.55 meters. Step 3: Subtract the ribbon used for bows from the total: 28.55 - 8.90. Step 4: Line up the decimal points and subtract: 28.55 - 8.90 -------- Hundredths: 5 - 0 = 5 Tenths: 5 - 9: since 5 is less than 9, regroup 1 one as 10 tenths. The 8 in the ones place becomes 7, and the tenths become 15. Then 15 - 9 = 6. Ones: 7 - 8: since 7 is less than 8, regroup 1 ten as 10 ones. The 2 in the tens place becomes 1, and the ones become 17. Then 17 - 8 = 9. Tens: 1 - 0 = 1. Result = 19.65 meters. The answer is 19.65.

3. 823.57 - 496.89 = ? Answer: 326.68 Solution: 823.57 - 496.89 Subtract the hundredths place: 7 - 9. Since 7 is less than 9, borrow 1 from the tenths place. The 5 in the tenths becomes 4, and the 7 in the hundredths becomes 17.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 823.57 - 496.89 Step 2: Subtract the hundredths place: 7 - 9. Since 7 is less than 9, borrow 1 from the tenths place. The 5 in the tenths becomes 4, and the 7 in the hundredths becomes 17. Now 17 - 9 = 8. Write 8 in the hundredths place. Step 3: Subtract the tenths place: 4 - 8. Since 4 is less than 8, borrow 1 from the ones place. The 3 in the ones becomes 2, and the 4 in the tenths becomes 14. Now 14 - 8 = 6. Write 6 in the tenths place. Step 4: Subtract the ones place: 2 - 6. Since 2 is less than 6, borrow 1 from the tens place. The 2 in the tens becomes 1, and the 2 in the ones becomes 12. Now 12 - 6 = 6. Write 6 in the ones place. Step 5: Subtract the tens place: 1 - 9. Since 1 is less than 9, borrow 1 from the hundreds place. The 8 in the hundreds becomes 7, and the 1 in the tens becomes 11. Now 11 - 9 = 2. Write 2 in the tens place. Step 6: Subtract the hundreds place: 7 - 4 = 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 326.68.

4. Emma is tracking her weekly jogging distances. On Monday, she jogged 3.45 kilometers. On Wednesday, she jogged 2.75 kilometers. On Friday, she jogged 4.10 kilometers. What was the total distance Emma jogged over these three days? Answer: 10.30 Solution: Identify the distances to add: 3.45 km, 2.75 km, and 4.10 km. Write the numbers vertically, aligning the decimal points. 3.45 2.75 + 4.10 Add the numbers in the hundredths place: 5 + 5 + 0 = 10.
   Full step-by-step solution

   Step 1: Identify the distances to add: 3.45 km, 2.75 km, and 4.10 km. Step 2: Write the numbers vertically, aligning the decimal points. 3.45 2.75 + 4.10 ------- Step 3: Add the numbers in the hundredths place: 5 + 5 + 0 = 10. Write down the 0 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: 1 (carried) + 4 + 7 + 1 = 13. Write down the 3 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 (carried) + 3 + 2 + 4 = 10. Write down the 10. Step 6: The final sum is 10.30 kilometers.

5. 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

6. Aroha is helping her family prepare for a cultural festival. She needs to cut three ribbons for decorating a woven basket. The first ribbon must be 3.75 meters long, the second ribbon must be 2.25 meters long, and the third ribbon must be 1.89 meters long. What is the total length of ribbon Aroha needs to cut? Answer: 7.89 Solution: Write the three lengths one above the other, lining up the decimal points: 3.75 2.25 + 1.89 Add the hundredths place: 5 + 5 + 9 = 19. Write down 9 in the hundredths place and carry over 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the three lengths one above the other, lining up the decimal points: 3.75 2.25 + 1.89 --------- Step 2: Add the hundredths place: 5 + 5 + 9 = 19. Write down 9 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place, including the carry-over: 1 (carried) + 7 + 2 + 8 = 18. Write down 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) + 3 + 2 + 1 = 7. Write down 7 in the ones place. Step 5: The total is 7.89 meters. The answer is 7.89.

7. Mason is drawing a rectangular sandbox on a coordinate grid for a school project. The corners of the sandbox are at (2.7, 3.2), (7.2, 3.2), (7.2, 5.7), and (2.7, 5.7). What is the perimeter of the sandbox in meters? Answer: 14.0 Solution: Identify the coordinates: A = (2.7, 3.2), B = (7.2, 3.2), C = (7.2, 5.7), D = (2.7, 5.7). Find the horizontal side length (AB or CD). Same y-coordinate (3.2), so subtract x-coordinates: 7.2 - 2.7 = 4.5 meters.
   Full step-by-step solution

   Step 1: Identify the coordinates: A = (2.7, 3.2), B = (7.2, 3.2), C = (7.2, 5.7), D = (2.7, 5.7). Step 2: Find the horizontal side length (AB or CD). Same y-coordinate (3.2), so subtract x-coordinates: 7.2 - 2.7 = 4.5 meters. Step 3: Find the vertical side length (BC or DA). Same x-coordinate (7.2), so subtract y-coordinates: 5.7 - 3.2 = 2.5 meters. Step 4: Perimeter of a rectangle = 2 × (length + width) = 2 × (4.5 + 2.5) = 2 × 7.0 = 14.0 meters. The answer is 14.0.

8. 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

9. 956.73 - 428.59 = ? Answer: 528.14 Solution: 956.73 - 428.59 Subtract the hundredths place: 3 - 9. Since 3 is less than 9, borrow 1 from the tenths place. The 7 in the tenths becomes 6, and the 3 in the hundredths becomes 13.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 956.73 - 428.59 Step 2: Subtract the hundredths place: 3 - 9. Since 3 is less than 9, borrow 1 from the tenths place. The 7 in the tenths becomes 6, and the 3 in the hundredths becomes 13. Now 13 - 9 = 4. Write 4 in the hundredths place. Step 3: Subtract the tenths place: 6 - 5 = 1. Write 1 in the tenths place. Step 4: Subtract the ones place: 6 - 8. Since 6 is less than 8, borrow 1 from the tens place. The 5 in the tens becomes 4, and the 6 in the ones becomes 16. Now 16 - 8 = 8. Write 8 in the ones place. Step 5: Subtract the tens place: 4 - 2 = 2. Write 2 in the tens place. Step 6: Subtract the hundreds place: 9 - 4 = 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 528.14.