Decimal Division

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Answer Key & Explanations

Decimal Division · Grade 5 · Worksheet 2

1. Emma is organizing a school science fair and needs to distribute 12.6 liters of liquid for experiments equally among 15 student groups. How many liters of liquid should each group receive? Answer: 0.84 Solution: Identify the total amount of liquid: 12.6 liters Identify the number of groups: 15 groups Divide the total liquid by the number of groups: 12.6 ÷ 15 Set up the division: 12.6 ÷ 15 = ?
   Full step-by-step solution

   Step 1: Identify the total amount of liquid: 12.6 liters Step 2: Identify the number of groups: 15 groups Step 3: Divide the total liquid by the number of groups: 12.6 ÷ 15 Step 4: Set up the division: 12.6 ÷ 15 = ? Step 5: Since 15 doesn't go into 12, we consider 126 tenths ÷ 15 Step 6: 126 ÷ 15 = 8.4 Step 7: Since we were working with tenths, 8.4 tenths = 0.84 liters Step 8: Each group receives 0.84 liters of liquid

2. Noah has a rectangular garden that is 18.9 meters long. He wants to divide it into 6 equal sections to plant different types of flowers. How many meters long will each section be? Answer: 3.15 Solution: Identify the total length of the garden: 18.9 meters. Identify the number of equal sections: 6. To find the length of each section, divide the total length by the number of sections: 18.9 ÷ 6.
   Full step-by-step solution

   Step 1: Identify the total length of the garden: 18.9 meters. Step 2: Identify the number of equal sections: 6. Step 3: To find the length of each section, divide the total length by the number of sections: 18.9 ÷ 6. Step 4: Set up the division: 18.9 ÷ 6. Step 5: Divide as you would with whole numbers: 18 ÷ 6 = 3, and 9 ÷ 6 = 1.5. But since we have a decimal, we can do: 18.9 ÷ 6 = (189 tenths) ÷ 6 = 31.5 tenths = 3.15. Step 6: Check: 6 × 3.15 = 18.9, which matches the original length. The answer is 3.15 meters.

3. Mere is designing a rectangular garden on a coordinate grid. The garden has corners at (3, 2), (12, 2), (12, 7), and (3, 7). Each unit on the grid represents 0.8 meters. Mere wants to divide the garden into 5 equal rectangular sections by drawing 4 equally spaced vertical lines. What is the width of each section in meters? Answer: 1.44 Solution: Find the width of the garden in grid units. The x-coordinates go from 3 to 12, so the width is 12 - 3 = 9 units. Convert grid units to meters.
   Full step-by-step solution

   Step 1: Find the width of the garden in grid units. The x-coordinates go from 3 to 12, so the width is 12 - 3 = 9 units. Step 2: Convert grid units to meters. Each unit represents 0.8 meters, so the total width in meters is 9 × 0.8 = 7.2 meters. Step 3: Determine the number of sections. Four equally spaced vertical lines divide the garden into 5 equal rectangular sections. Step 4: Divide the total width by the number of sections to find the width of each section: 7.2 ÷ 5 = 1.44 meters. The width of each section is 1.44 meters.

4. A rectangular community garden is drawn on a coordinate grid. The corners are at (2, 1), (20, 1), (20, 10), and (2, 10). Each unit on the grid represents 2.4 meters. Noah wants to divide the garden into 8 equal rectangular plots by drawing 7 equally spaced horizontal lines from left to right across the garden. What is the height of each plot in meters? Answer: 2.7 Solution: Find the height of the garden in grid units. The bottom y-coordinate is 1 and the top y-coordinate is 10. Convert the height to meters.
   Full step-by-step solution

   Step 1: Find the height of the garden in grid units. The bottom y-coordinate is 1 and the top y-coordinate is 10. So the height is 10 - 1 = 9 units. Step 2: Convert the height to meters. Each unit represents 2.4 meters, so total height = 9 x 2.4 = 21.6 meters. Step 3: The garden is divided into 8 equal horizontal plots. To find the height of each plot, divide the total height by 8: 21.6 divided by 8 = 2.7 meters. The height of each plot is 2.7 meters.

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. 37.5 ÷ 5 = ? Answer: 7.5 Solution: Write the division problem: 37.5 ÷ 5 Since 37.5 means 37 and 5 tenths, we can divide the whole number part and the decimal part separately.
   Full step-by-step solution

   Step 1: Write the division problem: 37.5 ÷ 5 Step 2: Since 37.5 means 37 and 5 tenths, we can divide the whole number part and the decimal part separately. Step 3: Divide 37 by 5: 37 ÷ 5 = 7 with remainder 2 Step 4: Bring down the .5 to make 2.5 Step 5: Divide 2.5 by 5: 2.5 ÷ 5 = 0.5 Step 6: Add the results: 7 + 0.5 = 7.5 Step 7: Therefore, 37.5 ÷ 5 = 7.5

7. Matiu is helping his family pack honey jars for the local market. They have 52.8 kilograms of honey to divide equally into 16 jars. How many kilograms of honey will each jar contain? Answer: 3.3 Solution: Identify the total amount of honey: 52.8 kilograms Identify the number of jars: 16 Set up the division: 52.8 ÷ 16 Divide as if it were a whole number: 528 ÷ 16 16 × 33 = 528, so 528 ÷ 16 = 33 Since we used 528 (which is 52.8 × 10), the answer must be divided by 10: 33 ÷ 10 = 3.3 Check: 16 × 3.3…
   Full step-by-step solution

   Step 1: Identify the total amount of honey: 52.8 kilograms Step 2: Identify the number of jars: 16 Step 3: Set up the division: 52.8 ÷ 16 Step 4: Divide as if it were a whole number: 528 ÷ 16 Step 5: 16 × 33 = 528, so 528 ÷ 16 = 33 Step 6: Since we used 528 (which is 52.8 × 10), the answer must be divided by 10: 33 ÷ 10 = 3.3 Step 7: Check: 16 × 3.3 = 52.8, which matches the total. Each jar will contain 3.3 kilograms of honey.

8. Hana is designing a rectangular garden bed on a grid. The corners of the garden bed are at (2, 3), (10, 3), (10, 7), and (2, 7). Each unit on the grid represents 1.6 meters. She wants to divide the garden bed into 8 equal rectangular plots by drawing vertical lines. What will be the width of each plot in meters? Answer: 1.6 Solution: Find the width of the garden bed in grid units. The left side is at x = 2 and the right side is at x = 10. Width = 10 - 2 = 8 units.
   Full step-by-step solution

   Step 1: Find the width of the garden bed in grid units. The left side is at x = 2 and the right side is at x = 10. Width = 10 - 2 = 8 units. Step 2: Convert the width to meters. Each unit is 1.6 meters. Total width = 8 × 1.6 = 12.8 meters. Step 3: Divide the total width by the number of plots. There are 8 equal plots. Width of each plot = 12.8 ÷ 8 = 1.6 meters. The answer is 1.6.