Question

2\frac{7}{10} \times \frac{5}{6}

Explanation:

Step1: Convert mixed number to improper fraction

To convert \( 2\frac{7}{10} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). Here, \( a = 2 \), \( b = 7 \), and \( c = 10 \). So, \( 2\frac{7}{10}=\frac{2\times10 + 7}{10}=\frac{20 + 7}{10}=\frac{27}{10} \).

Step2: Multiply the two fractions

Now we multiply \( \frac{27}{10} \) by \( \frac{5}{6} \). When multiplying fractions, we multiply the numerators together and the denominators together: \( \frac{27}{10}\times\frac{5}{6}=\frac{27\times5}{10\times6} \).

Step3: Simplify the fraction

First, we can simplify the numerator and denominator by canceling out the common factors. The 5 in the numerator and 10 in the denominator have a common factor of 5. So, \( \frac{27\times5}{10\times6}=\frac{27\times\cancel{5}^1}{\cancel{10}^2\times6}=\frac{27\times1}{2\times6}=\frac{27}{12} \). Then we can simplify \( \frac{27}{12} \) by dividing both the numerator and denominator by their greatest common divisor, which is 3. So, \( \frac{27\div3}{12\div3}=\frac{9}{4} \). We can also convert this improper fraction to a mixed number: \( \frac{9}{4}=2\frac{1}{4} \).

Answer:

\( \frac{9}{4} \) (or \( 2\frac{1}{4} \))