Question

Ms. Bauer was painting a decorative wall panel. She painted yellow and blue stripes on 1/4 of the panel. She painted green and orange stripes on 2/5 of the remaining part of the panel. She painted red and white stripe on the rest of the panel. Which one of equations represents the part of the wall panel painted with green and orange stripes?
a. 2/5 + 3/4 = 23/20
b. 3/4 - 2/5 = 7/20
c. 1-2/5 x 3/4 =7/10
d. 2/5 x 3/4 = 3/10

Answer 1

To find an equation representing the part of the wall panel painted with green and orange stripes, let's analyze the problem step-by-step.

1. **Total part of the panel painted:** The panel can be viewed in fractions. The entire wall panel represents 1 (or 100%).
2. **Part painted with yellow and blue stripes:** Ms. Bauer painted \( \frac{1}{4} \) of the panel with yellow and blue stripes.

Therefore, the remaining part of the panel is:
\[
1 - \frac{1}{4} = \frac{3}{4}
\]

3. **Part painted with green and orange stripes:** Ms. Bauer painted green and orange stripes on \( \frac{2}{5} \) of the remaining part:

So, we calculate \( \frac{2}{5} \) of the remaining \( \frac{3}{4} \):
\[
\text{Part painted with green and orange stripes} = \frac{2}{5} \times \frac{3}{4}
\]

To multiply these fractions:
\[
\frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}
\]

Now we have calculated that the part of the wall panel painted with green and orange stripes is \( \frac{3}{10} \).

Given the answer choices, we look for the equation that reflects this calculation:

- a. \( \frac{2}{5} + \frac{3}{4} = \frac{23}{20} \)
- b. \( \frac{3}{4} - \frac{2}{5} = \frac{7}{20} \)
- c. \( 1 - \frac{2}{5} \times \frac{3}{4} = \frac{7}{10} \)
- d. \( \frac{2}{5} \times \frac{3}{4} = \frac{3}{10} \)

The equation that represents the part of the wall panel painted with green and orange stripes is:

**d. \( \frac{2}{5} \times \frac{3}{4} = \frac{3}{10} \)**.