Percent of Quantity

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Answer Key & Explanations

Percent of Quantity · Grade 6 · Worksheet 1

1. Noah is designing a rectangular mural on a coordinate grid. The mural's corners are at (10, 20), (130, 20), (130, 100), and (10, 100). He plans to paint 32% of the total mural area with a sky blue color. What is the area, in square units, that will be painted sky blue? Answer: 3072 Solution: Find the length of the mural. Length = difference in x-coordinates = 130 - 10 = 120 units. Step 2: Find the width of the mural.
   Full step-by-step solution

   Step 1: Find the length of the mural. Length = difference in x-coordinates = 130 - 10 = 120 units. Step 2: Find the width of the mural. Width = difference in y-coordinates = 100 - 20 = 80 units. Step 3: Calculate the total area of the mural. Area = length × width = 120 × 80 = 9600 square units. Step 4: Calculate 32% of the total area. 32% = 0.32, so 0.32 × 9600 = 3072 square units. The area painted sky blue is 3072 square units.

2. 35% of 920 = ? Answer: 322 Solution: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Multiply the decimal by the total quantity: 0.35 × 920 Calculate 0.35 × 920 = 322 The answer is 322.
   Full step-by-step solution

   Step 1: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Step 2: Multiply the decimal by the total quantity: 0.35 × 920 Step 3: Calculate 0.35 × 920 = 322 The answer is 322.

3. 62.5% of 840 = ? Answer: 525 Solution: Convert the percentage to a decimal by dividing by 100: 62.5 ÷ 100 = 0.625 Multiply the decimal by the total quantity: 0.625 × 840 Calculate the multiplication: 0.625 × 840 = 525 The answer is 525.
   Full step-by-step solution

   Step 1: Convert the percentage to a decimal by dividing by 100: 62.5 ÷ 100 = 0.625 Step 2: Multiply the decimal by the total quantity: 0.625 × 840 Step 3: Calculate the multiplication: 0.625 × 840 = 525 The answer is 525.

4. A rectangular mural is being painted on a wall. On a coordinate grid, the mural's corners are at (12, 7), (112, 7), (112, 67), and (12, 67). Isabella plans to paint 42% of the mural's total area with a floral design. What is the area, in square grid units, that will be covered by the floral design? Answer: 2520 Solution: Find the length of the mural. Length = difference in x-coordinates = 112 - 12 = 100 units. Find the width of the mural.
   Full step-by-step solution

   Step 1: Find the length of the mural. Length = difference in x-coordinates = 112 - 12 = 100 units. Step 2: Find the width of the mural. Width = difference in y-coordinates = 67 - 7 = 60 units. Step 3: Calculate the total area of the mural. Area = length × width = 100 × 60 = 6000 square units. Step 4: Calculate 42% of the total area for the floral design. 42% of 6000 = 0.42 × 6000 = 2520 square units. The floral design will cover 2520 square units of the mural.

5. 45% of 680 = ? Answer: 306 Solution: Adding 40% (272) and 5% (34) gives 306.
   Full step-by-step solution

   Step 1: Convert 45% to a decimal by dividing by 100: 45 ÷ 100 = 0.45 Step 2: Multiply the decimal by the original number: 0.45 × 680 Step 3: Calculate 0.45 × 680 = 306 Step 4: Verify: 10% of 680 is 68, so 5% is 34, and 40% is 272. Adding 40% (272) and 5% (34) gives 306. The answer is 306.

6. 35% of 840 = ? Answer: 294 Solution: We want to calculate 35% of 840. Understand that "percent" means "per hundred." So 35% means 35 per hundred, which can be written as 35/100. "Of" in mathematics usually means multiplication.
   Full step-by-step solution

   We want to calculate 35% of 840. Step 1: Understand that "percent" means "per hundred." So 35% means 35 per hundred, which can be written as 35/100. Step 2: "Of" in mathematics usually means multiplication. So 35% of 840 means: (35/100) × 840 Step 3: Simplify the calculation. We can first multiply 35 by 840, then divide by 100. 35 × 840 = ? Break it down: 35 × 800 = 28,000 35 × 40 = 1,400 Add them: 28,000 + 1,400 = 29,400 Step 4: Now divide by 100. 29,400 ÷ 100 = 294 Step 5: Final answer. 35% of 840 = 294 We can check: 10% of 840 is 84, so 30% is 3 × 84 = 252, and 5% is half of 84, which is 42. Then 252 + 42 = 294.

7. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If 40% of the garden area is planted with vegetables, what is the area of the vegetable section? Answer: 9.6 Solution: Find the length and width of the rectangle. The points are (2, 1), (8, 1), (8, 5), and (2, 5). From (2, 1) to (8, 1), the y-coordinate is the same, so the length along x is 8 − 2 = 6.
   Full step-by-step solution

   Step 1: Find the length and width of the rectangle. The points are (2, 1), (8, 1), (8, 5), and (2, 5). From (2, 1) to (8, 1), the y-coordinate is the same, so the length along x is 8 − 2 = 6. From (2, 1) to (2, 5), the x-coordinate is the same, so the width along y is 5 − 1 = 4. Step 2: Calculate the total area of the garden. Area of rectangle = length × width = 6 × 4 = 24. Step 3: Find the area planted with vegetables. 40% of the garden is vegetables, so: Vegetable area = 40% of 24 = (40/100) × 24 = 0.4 × 24. Step 4: Perform the multiplication. 0.4 × 24 = 9.6. Step 5: State the final answer. The area of the vegetable section is 9.6.

8. 25% of 480 = ? Answer: 120 Solution: We are asked to find 25% of 480. Understand that "percent" means "per hundred". So 25% means 25 per hundred, which can be written as 25/100.
   Full step-by-step solution

   We are asked to find 25% of 480. Step 1: Understand that "percent" means "per hundred". So 25% means 25 per hundred, which can be written as 25/100. Step 2: "Of" in mathematics usually means multiplication. So 25% of 480 means (25/100) × 480. Step 3: Simplify 25/100. 25/100 = 1/4. Step 4: Now compute (1/4) × 480. This is the same as 480 ÷ 4. Step 5: 480 ÷ 4 = 120. Step 6: Therefore, 25% of 480 is 120. Final answer: 120

9. A school is planning a field trip for 360 students. The transportation company says they can only provide buses that seat 45 students each. What percentage of the total student capacity would be used if they fill all available buses completely? Answer: 100% Solution: Identify the total number of students: 360 Identify the bus capacity: 45 students per bus Calculate how many buses are needed: 360 ÷ 45 = 8 buses Calculate the total capacity of all buses: 8 buses × 45 students per bus = 360 students Calculate the percentage used: (360 ÷ 360) × 100 = 1 × 100 =…
   Full step-by-step solution

   Step 1: Identify the total number of students: 360 Step 2: Identify the bus capacity: 45 students per bus Step 3: Calculate how many buses are needed: 360 ÷ 45 = 8 buses Step 4: Calculate the total capacity of all buses: 8 buses × 45 students per bus = 360 students Step 5: Calculate the percentage used: (360 ÷ 360) × 100 = 1 × 100 = 100% The answer is 100%.