Question

what is $7 \times \frac{2}{5}$?

Explanation:

Step1: Multiply integer and numerator

To multiply a whole number \( 7 \) by a fraction \( \frac{2}{5} \), we use the rule \( a\times\frac{b}{c}=\frac{a\times b}{c} \). Here, \( a = 7 \), \( b=2 \), and \( c = 5 \). So we calculate \( 7\times2=14 \), and the denominator remains \( 5 \). So we get \( \frac{14}{5} \).

Step2: Convert to mixed number

Now we convert the improper fraction \( \frac{14}{5} \) to a mixed number. We divide the numerator \( 14 \) by the denominator \( 5 \). \( 14\div5 = 2 \) with a remainder of \( 4 \) (because \( 5\times2=10 \) and \( 14 - 10=4 \)). The mixed number is written as \( 2\frac{4}{5} \), where the whole number part is the quotient \( 2 \), the numerator of the fractional part is the remainder \( 4 \), and the denominator remains \( 5 \).

Answer:

The mixed number is \( 2\frac{4}{5} \), so the whole number part is \( 2 \), the numerator of the fraction part is \( 4 \), and the denominator is \( 5 \). Filling in the boxes: the whole number box is \( 2 \), the numerator box is \( 4 \), and the denominator box is \( 5 \). So the answer is \( 2\frac{4}{5} \) (with the whole number \( 2 \), numerator \( 4 \), denominator \( 5 \)).