Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar(s). find the product. if possible, rename the product as a mixed number or a whole number. write your answer in simplest form, using only the blanks needed. \\(\frac{10}{3} \times \frac{1}{3} = \square \frac{\square}{\square}\\)

Explanation:

Step1: Multiply the numerators and denominators

To multiply two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we use the rule \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\). For \(\frac{10}{3}\times\frac{1}{3}\), we multiply the numerators \(10\times1 = 10\) and the denominators \(3\times3=9\). So we get \(\frac{10\times1}{3\times3}=\frac{10}{9}\).

Step2: Convert improper fraction to mixed number

To convert an improper fraction \(\frac{n}{d}\) (where \(n>d\)) to a mixed number, we divide \(n\) by \(d\). Dividing \(10\) by \(9\), we get a quotient of \(1\) and a remainder of \(1\) (since \(9\times1 = 9\) and \(10-9 = 1\)). The mixed number is written as \( \text{quotient}\frac{\text{remainder}}{\text{divisor}}\), so \(\frac{10}{9}=1\frac{1}{9}\).

Answer:

\(1\frac{1}{9}\) (So the first blank is \(1\), the numerator of the fraction part is \(1\), and the denominator of the fraction part is \(9\))