Decimal Division

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Answer Key & Explanations

Decimal Division · Grade 5 · Worksheet 1

1. 27.6 ÷ 4 = ? Answer: 6.9 Solution: Set up the division problem: 27.6 ÷ 4. Divide the whole number part first. 27 ÷ 4 = 6 with a remainder of 3.
   Full step-by-step solution

   Step 1: Set up the division problem: 27.6 ÷ 4. Step 2: Divide the whole number part first. 27 ÷ 4 = 6 with a remainder of 3. Step 3: Bring down the decimal point and the digit from the tenths place (the 6). Now you are dividing 3.6 by 4. Step 4: Since 4 does not go into 3, write a 0 in the tenths place of the quotient, after the decimal point. Then think of 3.6 as 36 tenths. Step 5: Divide 36 tenths by 4. 36 ÷ 4 = 9. This 9 is 9 tenths, so it goes in the tenths place of the quotient. Step 6: Combine the whole number and the decimal: 6 and 0.9 make 6.9. Step 7: The final answer is 6.9.

2. A construction crew needs to pour 725.6 cubic meters of concrete evenly across 8 identical foundation sections. How many cubic meters of concrete should be poured into each section? Answer: 90.7 Solution: Identify the total concrete: 725.6 cubic meters Identify the number of sections: 8 Set up the division: 725.6 ÷ 8 Divide: 8 goes into 72 nine times (9 × 8 = 72) Bring down the 5: 8 goes into 5 zero times, so write 0 in the quotient Bring down the 6: 8 goes into 56 seven times (7 × 8 = 56) Place…
   Full step-by-step solution

   Step 1: Identify the total concrete: 725.6 cubic meters Step 2: Identify the number of sections: 8 Step 3: Set up the division: 725.6 ÷ 8 Step 4: Divide: 8 goes into 72 nine times (9 × 8 = 72) Step 5: Bring down the 5: 8 goes into 5 zero times, so write 0 in the quotient Step 6: Bring down the 6: 8 goes into 56 seven times (7 × 8 = 56) Step 7: Place the decimal point directly above in the quotient Step 8: The result is 90.7 Each section should receive 90.7 cubic meters of concrete.

3. Charlotte has 50.4 meters of ribbon to decorate 12 identical gift baskets for the school fundraiser. She wants to use an equal amount of ribbon on each basket. How many meters of ribbon will she use for each basket? Answer: 4.2 Solution: Identify the total amount of ribbon: 50.4 meters Identify the number of baskets: 12 To find the amount per basket, divide the total by the number of baskets: 50.4 ÷ 12 Set up the division: 12 into 50.4 12 goes into 50 four times (12 × 4 = 48), with 2 left over.
   Full step-by-step solution

   Step 1: Identify the total amount of ribbon: 50.4 meters Step 2: Identify the number of baskets: 12 Step 3: To find the amount per basket, divide the total by the number of baskets: 50.4 ÷ 12 Step 4: Set up the division: 12 into 50.4 Step 5: 12 goes into 50 four times (12 × 4 = 48), with 2 left over. Bring down the 4 tenths to make 24 tenths. Step 6: 12 goes into 24 exactly 2 times (12 × 2 = 24). Step 7: So 50.4 ÷ 12 = 4.2 Step 8: Check: 12 × 4.2 = 50.4, which is correct. The answer is 4.2 meters.

4. 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

5. 24.75 ÷ 5 = ? Answer: 4.95 Solution: Set up the division problem: 24.75 ÷ 5 Since we are dividing by a whole number, we can divide normally, keeping the decimal point in the same position in the quotient. 5 goes into 24 four times (5 × 4 = 20).
   Full step-by-step solution

   Step 1: Set up the division problem: 24.75 ÷ 5 Step 2: Since we are dividing by a whole number, we can divide normally, keeping the decimal point in the same position in the quotient. Step 3: 5 goes into 24 four times (5 × 4 = 20). Write 4 above the division bar, aligned with the last digit of 24. Step 4: Subtract: 24 - 20 = 4. Bring down the 7 to make 47. Step 5: 5 goes into 47 nine times (5 × 9 = 45). Write 9 above the division bar, to the right of the 4. Step 6: Subtract: 47 - 45 = 2. Bring down the 5 to make 25. Step 7: 5 goes into 25 five times (5 × 5 = 25). Write 5 above the division bar, to the right of the 9. Step 8: Since we brought down digits from after the decimal point in the original number (24.75), we place the decimal point in the quotient directly above its position in the dividend. This gives us 4.95. Step 9: Verify: 4.95 × 5 = 24.75, which matches our original dividend. The answer is 4.95.

6. 18.75 ÷ 5 = ? Answer: 3.75 Solution: Set up the division problem: 18.75 ÷ 5. Divide the whole number part first. 18 ÷ 5 = 3 with a remainder of 3.
   Full step-by-step solution

   Step 1: Set up the division problem: 18.75 ÷ 5. Step 2: Divide the whole number part first. 18 ÷ 5 = 3 with a remainder of 3. Step 3: Bring down the decimal point and the next digit (7) to make 37. Step 4: 37 ÷ 5 = 7 with a remainder of 2. Step 5: Bring down the last digit (5) to make 25. Step 6: 25 ÷ 5 = 5. Step 7: Combine the results: 3, then the decimal point, then 7, then 5, giving 3.75. The answer is 3.75.

7. 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.

8. Emma is baking cookies for a school bake sale. She has 3.75 kilograms of chocolate chips to distribute equally among 15 batches of cookies. How many kilograms of chocolate chips should she use for each batch? Answer: 0.25 Solution: Step 1: Identify the total amount of chocolate chips: 3.75 kilograms Step 2: Identify the number of batches: 15 Step 3: Divide the total chocolate chips by the number of batches: 3.75 ÷ 15 Step 4: Perform the division: 3.75 ÷ 15 = 0.25 Step 5: Verify: 0.25 × 15 = 3.75, which matches our original…
   Full step-by-step solution

   Step 1: Identify the total amount of chocolate chips: 3.75 kilograms Step 2: Identify the number of batches: 15 Step 3: Divide the total chocolate chips by the number of batches: 3.75 ÷ 15 Step 4: Perform the division: 3.75 ÷ 15 = 0.25 Step 5: Verify: 0.25 × 15 = 3.75, which matches our original amount Emma should use 0.25 kilograms of chocolate chips for each batch.

9. A construction company needs to pour a concrete sidewalk that is 725.6 meters long. They want to divide it into 8 equal sections with expansion joints between them. How many meters long will each section be? Answer: 90.7 Solution: Identify the total length of the sidewalk: 725.6 meters Identify the number of equal sections needed: 8 sections Set up the division problem: 725.6 ÷ 8 Divide 725.6 by 8 8 goes into 72 nine times (9 × 8 = 72) Bring down the 5, 8 goes into 5 zero times (0 × 8 = 0) Bring down the 6, 8 goes into 56…
   Full step-by-step solution

   Step 1: Identify the total length of the sidewalk: 725.6 meters Step 2: Identify the number of equal sections needed: 8 sections Step 3: Set up the division problem: 725.6 ÷ 8 Step 4: Divide 725.6 by 8 8 goes into 72 nine times (9 × 8 = 72) Bring down the 5, 8 goes into 5 zero times (0 × 8 = 0) Bring down the 6, 8 goes into 56 seven times (7 × 8 = 56) Bring down the decimal point Bring down the 6 after decimal, 8 goes into 6 zero times (0 × 8 = 0) Add a zero: 8 goes into 60 seven times (7 × 8 = 56) Remainder is 4, add another zero: 8 goes into 40 five times (5 × 8 = 40) Step 5: The result is 90.7 meters Each section will be 90.7 meters long.