Question

Complete the area model to find the product. The area model represents 1 for / x 2/5 = /

Answer 1

The simplified product is
`\( (2)/(5) \).`

To solve for the product of
`\( (1)/(4) * (2)/(5) \)`, we can use the area model for multiplying fractions. Here are the steps:
1. The rectangle will be our "area model."
2. Since the first fraction is
`\( (1)/(4) \)`, divide the rectangle into 4 equal parts vertically.
3. Shade one part out of these four to represent
`\( (1)/(4) \).`
4. Next, we need to multiply this fraction by
`\( (2)/(5) \)`. Divide each of the 4 parts of the rectangle into 5 equal parts horizontally. Now your rectangle will have
`\( 4 * 5 = 20 \)` smaller rectangles (or squares).
5. Shade 2 horizontal parts within each vertical part, representing
`\( (2)/(5) \)` . In total, you should have
`\( 2 * 4 = 8 \)` small rectangles shaded for the second fraction out of the 20 smaller rectangles.
6. The product of the two fractions is the ratio of the number of shaded small rectangles to the total number of small rectangles. Since we shaded 8 out of the 20 small rectangles, the product of
`\( (1)/(4) \)` and
`\( (2)/(5) \) is \( (8)/(20) \).`
7. To simplify the fraction, we find the greatest common divisor (GCD) of 8 and 20, which is 4.
8. We divide the numerator and the denominator by their GCD to get the simplified product.
9.
`\( (8)/(20) / (4)/(4) = (8 / 4)/(20 / 4) \)`
10. So the simplified product is
`\( (2)/(5) \).`
Therefore,
`\( (1)/(4) * (2)/(5) = (2)/(5) \)` when calculated using the area model.