Question

(\frac{6}{8} \times 9 =)

Explanation:

Step1: Simplify the fraction and integer multiplication

To multiply a fraction by an integer, we can write the integer as a fraction with denominator 1, then multiply the numerators and denominators. But first, we can simplify \(\frac{6}{8}\) and 9. The greatest common divisor of 6 and 8 is 2, so \(\frac{6}{8}=\frac{3}{4}\). Now we multiply \(\frac{3}{4}\) by 9.
\(\frac{6}{8} \times 9=\frac{3}{4} \times 9\)

Step2: Multiply the numerator

Multiply the numerator 3 by 9, and keep the denominator 4.
\(\frac{3\times9}{4}=\frac{27}{4}\)
We can also convert this improper fraction to a mixed number: \(\frac{27}{4} = 6\frac{3}{4}\) or as a decimal \(6.75\). But usually, the fractional form \(\frac{27}{4}\) or the mixed number is acceptable. Let's check the multiplication again without simplifying first: \(\frac{6}{8}\times9=\frac{6\times9}{8}=\frac{54}{8}=\frac{27}{4}\) (dividing numerator and denominator by 2).

Answer:

\(\frac{27}{4}\) (or \(6\frac{3}{4}\) or \(6.75\))