Decimal Division

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Answer Key & Explanations

Decimal Division · Grade 5 · Worksheet 1

1. Sophia is sewing a large quilt for her grandmother. She has a spool of thread that is 22.5 meters long. She needs to cut the thread into 18 equal pieces to use for different sections of the quilt. How many meters long will each piece of thread be? Answer: 1.25 Solution: Identify the total length of thread: 22.5 meters. Identify the number of equal pieces: 18 pieces. To find the length of each piece, divide the total length by the number of pieces: 22.5 ÷ 18.
   Full step-by-step solution

   Step 1: Identify the total length of thread: 22.5 meters. Step 2: Identify the number of equal pieces: 18 pieces. Step 3: To find the length of each piece, divide the total length by the number of pieces: 22.5 ÷ 18. Step 4: Set up the division. Since 18 does not divide evenly into 22, write 22.5 as 225 tenths. Step 5: Divide 225 by 18: 18 × 12 = 216, with 9 remaining. So 225 ÷ 18 = 12.5. Step 6: Since we were working with tenths, 12.5 tenths equals 1.25 meters. Step 7: Check: 18 × 1.25 = 22.5, which matches the original length. The answer is 1.25 meters.

2. 6.48 ÷ 12 = ? Answer: 0.54 Solution: Set up the division: 12 into 6.48 12 goes into 64 (from 6.48) five times (12 × 5 = 60) Subtract: 64 - 60 = 4 Bring down the 8 to make 48 12 goes into 48 four times (12 × 4 = 48) Subtract: 48 - 48 = 0 Place the decimal point directly above where it was in the dividend The answer is 0.54
   Full step-by-step solution

   Step 1: Set up the division: 12 into 6.48 Step 2: 12 goes into 64 (from 6.48) five times (12 × 5 = 60) Step 3: Subtract: 64 - 60 = 4 Step 4: Bring down the 8 to make 48 Step 5: 12 goes into 48 four times (12 × 4 = 48) Step 6: Subtract: 48 - 48 = 0 Step 7: Place the decimal point directly above where it was in the dividend Step 8: The answer is 0.54

3. A rectangular swimming pool is drawn on a coordinate plane with corners at (1, 2), (7, 2), (7, 6), and (1, 6). Each unit on the grid represents 2.5 meters. The pool is divided into 8 equal lanes for swimmers. What is the width of each lane in meters? Answer: 1.875 Solution: Find the width of the pool using the x-coordinates. The left side is at x=1 and the right side is at x=7, so the width in grid units is 7 - 1 = 6 units. Convert grid units to meters.
   Full step-by-step solution

   Step 1: Find the width of the pool using the x-coordinates. The left side is at x=1 and the right side is at x=7, so the width in grid units is 7 - 1 = 6 units. Step 2: Convert grid units to meters. Each unit represents 2.5 meters, so the actual width is 6 × 2.5 = 15 meters. Step 3: Divide the total width by the number of lanes to find the width of each lane: 15 ÷ 8 = 1.875 meters. The width of each lane is 1.875 meters.

4. Emma is organizing a school bake sale and needs to divide 15.75 kilograms of cookie dough equally among 25 baking sheets. How many kilograms of cookie dough should she put on each baking sheet? Answer: 0.63 Solution: Step 1: Identify the total amount of cookie dough: 15.75 kg Step 2: Identify how many baking sheets need to be filled: 25 Step 3: Divide the total dough by the number of sheets: 15.75 ÷ 25 Step 4: Perform the division: 15.75 ÷ 25 = 0.63 Step 5: Verify: 0.63 × 25 = 15.75 The answer is 0.63…
   Full step-by-step solution

   Step 1: Identify the total amount of cookie dough: 15.75 kg Step 2: Identify how many baking sheets need to be filled: 25 Step 3: Divide the total dough by the number of sheets: 15.75 ÷ 25 Step 4: Perform the division: 15.75 ÷ 25 = 0.63 Step 5: Verify: 0.63 × 25 = 15.75 The answer is 0.63 kilograms per baking sheet.

5. 48.75 ÷ 5 = ? Answer: 9.75 Solution: Set up the division problem: 48.75 ÷ 5 Divide the whole number part first. 48 ÷ 5 = 9 with a remainder of 3. Bring down the decimal point and the next digit (7) to make 37.
   Full step-by-step solution

   Step 1: Set up the division problem: 48.75 ÷ 5 Step 2: Divide the whole number part first. 48 ÷ 5 = 9 with a remainder of 3. Step 3: Bring down the decimal point and the next digit (7) to make 37. Step 4: Divide 37 by 5. 37 ÷ 5 = 7 with a remainder of 2. Step 5: Bring down the last digit (5) to make 25. Step 6: Divide 25 by 5. 25 ÷ 5 = 5. Step 7: Combine the results: 9.75 Step 8: Check: 9.75 × 5 = 48.75, which confirms our answer is correct. The final answer is 9.75.

6. Emma is making lemonade for a school fair. She has a large container that holds 12.6 liters of lemonade. If she wants to pour it equally into 15 smaller cups, how many liters of lemonade should she put in each cup? Answer: 0.84 Solution: Identify the total amount of lemonade: 12.6 liters Identify the number of cups: 15 Divide the total amount by the number of cups: 12.6 ÷ 15 Calculate the division: 12.6 ÷ 15 = 0.84 Check the answer: 0.84 liters per cup × 15 cups = 12.6 liters The answer is 0.84 liters.
   Full step-by-step solution

   Step 1: Identify the total amount of lemonade: 12.6 liters Step 2: Identify the number of cups: 15 Step 3: Divide the total amount by the number of cups: 12.6 ÷ 15 Step 4: Calculate the division: 12.6 ÷ 15 = 0.84 Step 5: Check the answer: 0.84 liters per cup × 15 cups = 12.6 liters The answer is 0.84 liters.

7. Liam is building a bookshelf and needs to cut a 7.5-meter long wooden board into equal sections. Each section should be 1.25 meters long. How many sections can Liam cut from the board? Answer: 6 Solution: To find how many sections Liam can cut from the board, we need to divide the total length of the board by the length of each section. Write down the total length of the board and the length of each section. Total board length = 7.5 meters Length of each section = 1.25 meters Set up the division…
   Full step-by-step solution

   To find how many sections Liam can cut from the board, we need to divide the total length of the board by the length of each section. Step 1: Write down the total length of the board and the length of each section. Total board length = 7.5 meters Length of each section = 1.25 meters Step 2: Set up the division to find the number of sections. Number of sections = Total length / Length per section Number of sections = 7.5 / 1.25 Step 3: To make the division easier, we can multiply both numbers by 100 to eliminate the decimals. This is the same as moving the decimal point two places to the right for both numbers. 7.5 * 100 = 750 1.25 * 100 = 125 So, 7.5 / 1.25 becomes 750 / 125. Step 4: Now, perform the division: 750 divided by 125. Think: How many times does 125 go into 750? 125 * 6 = 750 Therefore, 750 / 125 = 6. Step 5: Interpret the result. The result of the division is 6, which means Liam can cut 6 equal sections from the board. Final Answer: 6

8. Mason is preparing bags of trail mix for his hiking club. He has 9.6 kilograms of mixed nuts and wants to divide them equally into 8 bags. How many kilograms of nuts will be in each bag? Answer: 1.2 Solution: Identify the total amount of nuts: 9.6 kilograms. Identify the number of bags: 8 bags. Divide the total by the number of bags: 9.6 ÷ 8.
   Full step-by-step solution

   Step 1: Identify the total amount of nuts: 9.6 kilograms. Step 2: Identify the number of bags: 8 bags. Step 3: Divide the total by the number of bags: 9.6 ÷ 8. Step 4: Set up the division: 9.6 ÷ 8 = ? Step 5: Divide as if 9.6 were 96 tenths: 96 tenths ÷ 8 = 12 tenths. Step 6: 12 tenths equals 1.2. Step 7: Check: 8 × 1.2 = 9.6, which matches the total. The answer is 1.2 kilograms.

9. 72.9 ÷ 9 = ? Answer: 8.1 Solution: Write the division problem: 72.9 ÷ 9 Divide the whole number part first. 72 ÷ 9 = 8 Bring down the decimal point directly above in the quotient Divide the decimal part.
   Full step-by-step solution

   Step 1: Write the division problem: 72.9 ÷ 9 Step 2: Divide the whole number part first. 72 ÷ 9 = 8 Step 3: Bring down the decimal point directly above in the quotient Step 4: Divide the decimal part. 0.9 ÷ 9 = 0.1 Step 5: Combine the results: 8 + 0.1 = 8.1 Step 6: Verify: 8.1 × 9 = 72.9 The answer is 8.1.