A wall in Marcus’s bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 of the wall blue, how many square feet will be blue?
The correct answer and explanation is:
To find how many square feet of Marcus’s wall will be painted blue, we follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
- Height of the wall:
825=8×5+25=4258 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} - Length of the wall:
1623=16×3+23=50316 \frac{2}{3} = \frac{16 \times 3 + 2}{3} = \frac{50}{3}
Step 2: Calculate the total area of the wall.
Area = Height × Length Area=425×503=42×505×3=210015=140 square feet\text{Area} = \frac{42}{5} \times \frac{50}{3} = \frac{42 \times 50}{5 \times 3} = \frac{2100}{15} = 140 \text{ square feet}
Step 3: Calculate 1/2 of the area.
12×140=70 square feet\frac{1}{2} \times 140 = 70 \text{ square feet}
✅ Final Answer:
70 square feet of the wall will be painted blue.
📘 Explanation (300 words):
This problem involves calculating the area of a rectangular wall and then finding a fraction of that area. First, we convert the height and length of the wall from mixed numbers to improper fractions to make multiplication easier. The height is 8 2/5, which becomes 42/5, and the length is 16 2/3, which becomes 50/3.
Area is found by multiplying height by length. Multiplying fractions involves multiplying the numerators and then the denominators:
425×503=210015=140\frac{42}{5} \times \frac{50}{3} = \frac{2100}{15} = 140.
This result gives us the total area of the wall in square feet. Since Marcus is painting only half of the wall, we multiply the area by 1/2:
12×140=70\frac{1}{2} \times 140 = 70 square feet.
This means 70 square feet of the wall will be blue.
This kind of problem tests skills in fraction operations, area calculation, and applying proportions. It’s a good example of how math is used in real-life situations like home improvement and interior design.