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Decimal Division

Grade 5 · Decimals · Worksheet 3

  1. Liam is building a bookshelf and needs to cut a 7.5-meter long wooden board into equal sections. If he wants 6 identical shelves, how many meters long will each shelf be? Answer: ______________
  2. Hana is helping to organize the school's sports equipment. She has 14.4 meters of rope that she needs to cut into 12 equal pieces for a tug-of-war game. How many meters long will each piece of rope be? Answer: ______________
  3. 72.9 ÷ 9 = ? Answer: ______________
  4. Emma is organizing a school science fair and needs to divide 15.75 liters of liquid nitrogen equally among 9 experiment stations. How many liters of liquid nitrogen should she allocate to each station? Answer: ______________
  5. Emma is making fruit punch for a class party. She has 6.75 liters of pineapple juice and wants to pour it equally into 9 smaller containers. How many liters of pineapple juice should she pour into each container? Answer: ______________
  6. 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 4 equal lanes by drawing three equally spaced vertical lines. What is the width of each lane in meters? Answer: ______________
  7. Isabella is sewing costumes for a school play. She has a spool of ribbon that is 8.2 meters long. She needs to cut the ribbon into 4 equal pieces for the costumes. How many meters long will each piece of ribbon be? Answer: ______________
  8. A rectangular park is drawn on a coordinate grid. Its corners are at (1, 2), (13, 2), (13, 9), and (1, 9). Each unit on the grid represents 4.5 meters. The park is divided into 6 equal rectangular sections by drawing equally spaced vertical lines. What is the width of each section in meters? Answer: ______________
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Answer Key & Explanations

Decimal Division · Grade 5 · Worksheet 3

  1. Liam is building a bookshelf and needs to cut a 7.5-meter long wooden board into equal sections. If he wants 6 identical shelves, how many meters long will each shelf be? Answer: 1.25 Solution: We are told that Liam has a 7.5-meter board and wants to cut it into 6 equal sections. If we split a total length into equal parts, we divide the total length by the number of parts.
    Full step-by-step solution

    We are told that Liam has a 7.5-meter board and wants to cut it into 6 equal sections. Step 1: Understand the operation needed. If we split a total length into equal parts, we divide the total length by the number of parts. So: Total length = 7.5 meters Number of shelves = 6 Length of each shelf = 7.5 ÷ 6 Step 2: Perform the division. 7.5 ÷ 6 can be calculated by first writing 7.5 as 15/2. 7.5 ÷ 6 = (15/2) ÷ 6 Step 3: Dividing by 6 is the same as multiplying by 1/6. (15/2) × (1/6) = 15 / (2 × 6) = 15 / 12 Step 4: Simplify 15/12. Divide numerator and denominator by 3: 15 ÷ 3 = 5 12 ÷ 3 = 4 So 15/12 = 5/4 Step 5: Convert 5/4 to decimal. 5 ÷ 4 = 1.25 Step 6: Conclusion. Each shelf will be 1.25 meters long. Final answer: 1.25

  2. Hana is helping to organize the school's sports equipment. She has 14.4 meters of rope that she needs to cut into 12 equal pieces for a tug-of-war game. How many meters long will each piece of rope be? Answer: 1.2 Solution: Identify the total length of rope: 14.4 meters. Identify the number of equal pieces: 12 pieces. To find the length of each piece, divide the total length by the number of pieces: 14.4 ÷ 12.
    Full step-by-step solution

    Step 1: Identify the total length of rope: 14.4 meters. Step 2: Identify the number of equal pieces: 12 pieces. Step 3: To find the length of each piece, divide the total length by the number of pieces: 14.4 ÷ 12. Step 4: Perform the division: 14.4 ÷ 12 = 1.2. Step 5: Check the answer by multiplying: 12 × 1.2 = 14.4, which matches the total length. The answer is 1.2 meters.

  3. 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.

  4. Emma is organizing a school science fair and needs to divide 15.75 liters of liquid nitrogen equally among 9 experiment stations. How many liters of liquid nitrogen should she allocate to each station? Answer: 1.75 Solution: Step 1: Identify the total amount of liquid nitrogen: 15.75 liters Step 2: Identify the number of stations: 9 Step 3: Divide the total amount by the number of stations: 15.75 ÷ 9 Step 4: Perform the division: 15.75 ÷ 9 = 1.75 Step 5: Verify: 1.75 × 9 = 15.75 The answer is 1.75 liters.
    Full step-by-step solution

    Step 1: Identify the total amount of liquid nitrogen: 15.75 liters Step 2: Identify the number of stations: 9 Step 3: Divide the total amount by the number of stations: 15.75 ÷ 9 Step 4: Perform the division: 15.75 ÷ 9 = 1.75 Step 5: Verify: 1.75 × 9 = 15.75 The answer is 1.75 liters.

  5. Emma is making fruit punch for a class party. She has 6.75 liters of pineapple juice and wants to pour it equally into 9 smaller containers. How many liters of pineapple juice should she pour into each container? Answer: 0.75 Solution: Identify the total amount of juice: 6.75 liters Identify the number of containers: 9 Set up the division: 6.75 ÷ 9 Divide 6 by 9: 6 ÷ 9 = 0 with remainder 6 Bring down the decimal point and the 7: Now we have 67 ÷ 9 67 ÷ 9 = 7 (since 9 × 7 = 63) with remainder 4 Bring down the 5: Now we have 45…
    Full step-by-step solution

    Step 1: Identify the total amount of juice: 6.75 liters Step 2: Identify the number of containers: 9 Step 3: Set up the division: 6.75 ÷ 9 Step 4: Divide 6 by 9: 6 ÷ 9 = 0 with remainder 6 Step 5: Bring down the decimal point and the 7: Now we have 67 ÷ 9 Step 6: 67 ÷ 9 = 7 (since 9 × 7 = 63) with remainder 4 Step 7: Bring down the 5: Now we have 45 ÷ 9 Step 8: 45 ÷ 9 = 5 (since 9 × 5 = 45) with no remainder Step 9: Combine the results: 0.75 Step 10: The answer is 0.75 liters per container.

  6. 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 4 equal lanes by drawing three equally spaced vertical lines. What is the width of each lane in meters? Answer: 3.75 Solution: Find the width of the pool in coordinate units. The x-coordinates go from 1 to 7, so width = 7 - 1 = 6 units. Convert the width to meters.
    Full step-by-step solution

    Step 1: Find the width of the pool in coordinate units. The x-coordinates go from 1 to 7, so width = 7 - 1 = 6 units. Step 2: Convert the width to meters. Each unit represents 2.5 meters, so total width = 6 × 2.5 = 15 meters. Step 3: Determine how the lanes are divided. Three vertical lines divide the pool into 4 equal lanes. Step 4: Calculate the width of each lane. Width per lane = total width ÷ number of lanes = 15 ÷ 4 = 3.75 meters. The answer is 3.75.

  7. Isabella is sewing costumes for a school play. She has a spool of ribbon that is 8.2 meters long. She needs to cut the ribbon into 4 equal pieces for the costumes. How many meters long will each piece of ribbon be? Answer: 2.05 Solution: Identify the total length of ribbon: 8.2 meters. Identify the number of pieces: 4. Divide the total length by the number of pieces: 8.2 ÷ 4.
    Full step-by-step solution

    Step 1: Identify the total length of ribbon: 8.2 meters. Step 2: Identify the number of pieces: 4. Step 3: Divide the total length by the number of pieces: 8.2 ÷ 4. Step 4: Write 8.2 as 82 tenths (since 8.2 = 82/10). Step 5: Divide 82 by 4: 82 ÷ 4 = 20.5. Step 6: Since we had tenths, 20.5 tenths equals 2.05. Step 7: Check: 4 × 2.05 = 8.2, which matches the total. The answer is 2.05 meters.

  8. A rectangular park is drawn on a coordinate grid. Its corners are at (1, 2), (13, 2), (13, 9), and (1, 9). Each unit on the grid represents 4.5 meters. The park is divided into 6 equal rectangular sections by drawing equally spaced vertical lines. What is the width of each section in meters? Answer: 9 Solution: Find the width of the park in grid units. The x-coordinates go from 1 to 13, so the width is 13 - 1 = 12 units. Convert the width to meters.
    Full step-by-step solution

    Step 1: Find the width of the park in grid units. The x-coordinates go from 1 to 13, so the width is 13 - 1 = 12 units. Step 2: Convert the width to meters. Each unit is 4.5 meters, so the total width is 12 x 4.5 = 54 meters. Step 3: The park is divided into 6 equal sections by vertical lines. Divide the total width by 6: 54 / 6 = 9 meters. The width of each section is 9 meters.