Question

1. which statement is true?

a the product of $5 \times \frac{2}{5}$ does not equal a whole number.
b $5 \times \frac{2}{5}$ has a fraction as the product because $\frac{2}{5}$ is a fraction.
c $5 \times \frac{2}{5}$ equals a number greater than 2 because 5 is a whole number.
d the product of $5 \times \frac{2}{5}$ is less than the whole number in the problem because $\frac{2}{5}$ is less than one.

Explanation:

Step1: Calculate \( 5\times\frac{2}{5} \)

To multiply a whole number by a fraction, we can write the whole number as a fraction with denominator 1, so \( 5=\frac{5}{1} \). Then we multiply the numerators and the denominators: \( \frac{5}{1}\times\frac{2}{5}=\frac{5\times2}{1\times5}=\frac{10}{5} \). Simplifying \( \frac{10}{5} \), we divide 10 by 5, which gives 2. So \( 5\times\frac{2}{5} = 2 \).

Step2: Analyze each option

• Option A: We just calculated that \( 5\times\frac{2}{5}=2 \), which is a whole number, so this statement is false.
• Option B: The product we found is 2, which is a whole number, not a fraction. The fact that \( \frac{2}{5} \) is a fraction doesn't mean the product will be a fraction (since the 5 and the denominator 5 cancel out). So this statement is false.
• Option C: The product is 2, which is not greater than 2. So this statement is false.
• Option D: The whole number in the problem is 5, and the product is 2. Since \( \frac{2}{5}<1 \), when we multiply 5 by a number less than 1, the result (2) is less than 5. So this statement is true.

Answer:

D. The product of \( 5\times\frac{2}{5} \) is less than the whole number in the problem because \( \frac{2}{5} \) is less than one.