Decimal Division

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Answer Key & Explanations

Decimal Division · Grade 5 · Worksheet 3

1. Noah is preparing gift bags for his soccer team's end-of-season party. He has a 22.4-meter roll of ribbon to decorate the bags. If he wants to cut the ribbon into 8 equal pieces, how many meters of ribbon will each piece be? Answer: 2.8 Solution: Identify the total amount of ribbon: 22.4 meters. Identify the number of equal pieces: 8. Divide the total ribbon by the number of pieces: 22.4 ÷ 8.
   Full step-by-step solution

   Step 1: Identify the total amount of ribbon: 22.4 meters. Step 2: Identify the number of equal pieces: 8. Step 3: Divide the total ribbon by the number of pieces: 22.4 ÷ 8. Step 4: Set up the division: 22.4 ÷ 8. Step 5: Divide as you would with whole numbers: 22 ÷ 8 = 2 remainder 6. Step 6: Bring down the 4 tenths to make 64 tenths: 64 ÷ 8 = 8. Step 7: Combine: 2 whole meters and 8 tenths = 2.8 meters. Step 8: Check: 8 × 2.8 = 22.4, so the answer is correct. Each piece of ribbon will be 2.8 meters long.

2. Olivia is drawing a rectangular flower bed on a coordinate grid. The corners of the flower bed are at (1, 1), (15, 1), (15, 7), and (1, 7). Each unit on the grid represents 1.5 feet. Olivia wants to divide the flower bed into 9 equal horizontal rows by drawing equally spaced lines parallel to the bottom edge. What is the height of each row in feet? Answer: 1.0 Solution: Find the height in grid units. The bottom edge is at y = 1 and the top edge is at y = 7. Convert the height to feet.
   Full step-by-step solution

   Step 1: Find the height in grid units. The bottom edge is at y = 1 and the top edge is at y = 7. So the height is 7 - 1 = 6 units. Step 2: Convert the height to feet. Each unit represents 1.5 feet. So total height = 6 x 1.5 = 9.0 feet. Step 3: Divide the total height by the number of rows. 9.0 feet / 9 rows = 1.0 foot. The height of each row is 1.0 foot.

3. 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.

4. 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.

5. 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.

6. A rectangular mural is painted on a wall with corners at coordinates (3, 4), (15, 4), (15, 10), and (3, 10) on a grid. Each unit on the grid represents 1.5 feet. The mural is divided into 9 equal vertical sections, each painted a different color. What is the width of each vertical section in feet? Answer: 2.0 Solution: Find the width of the mural in grid units. The left side is at x = 3 and the right side is at x = 15. Width = 15 - 3 = 12 units.
   Full step-by-step solution

   Step 1: Find the width of the mural in grid units. The left side is at x = 3 and the right side is at x = 15. Width = 15 - 3 = 12 units. Step 2: Convert grid units to feet. Each unit represents 1.5 feet, so total width = 12 × 1.5 = 18 feet. Step 3: Divide the total width by the number of vertical sections to find the width of each section. Width per section = 18 ÷ 9 = 2.0 feet. The answer is 2.0.

7. 7.56 ÷ 4 = ? Answer: 1.89 Solution: Set up the division: 7.56 ÷ 4 Divide the whole number part: 7 ÷ 4 = 1 with remainder 3 Bring down the decimal point and the next digit (5): 35 ÷ 4 = 8 with remainder 3 Bring down the last digit (6): 36 ÷ 4 = 9 Combine the results: 1.89 Check: 1.89 × 4 = 7.56 The answer is 1.89.
   Full step-by-step solution

   Step 1: Set up the division: 7.56 ÷ 4 Step 2: Divide the whole number part: 7 ÷ 4 = 1 with remainder 3 Step 3: Bring down the decimal point and the next digit (5): 35 ÷ 4 = 8 with remainder 3 Step 4: Bring down the last digit (6): 36 ÷ 4 = 9 Step 5: Combine the results: 1.89 Step 6: Check: 1.89 × 4 = 7.56 The answer is 1.89.

8. Aroha is helping to organize supplies for a large community art project. She has a 52.8-meter roll of decorative ribbon that needs to be cut into 16 equal pieces for different craft stations. How many meters of ribbon will each station receive? Answer: 3.3 Solution: Identify the total amount of ribbon: 52.8 meters. Identify the number of stations: 16. We need to divide: 52.8 ÷ 16.
   Full step-by-step solution

   Step 1: Identify the total amount of ribbon: 52.8 meters. Step 2: Identify the number of stations: 16. Step 3: We need to divide: 52.8 ÷ 16. Step 4: Set up the division: 16 goes into 52 three times (16 × 3 = 48). Subtract: 52 - 48 = 4. Bring down the 8 from the tenths place to make 48 tenths. Step 5: 16 goes into 48 exactly 3 times (16 × 3 = 48). So we have 3 tenths, or 0.3. Step 6: Combine the whole number part (3) and the decimal part (0.3) to get 3.3. Step 7: Check: 16 × 3.3 = 16 × 3 + 16 × 0.3 = 48 + 4.8 = 52.8. This matches the total. The answer is 3.3 meters.