Question

1\frac{7}{8}\times\frac{5}{6}

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(1\frac{7}{8}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(1\frac{7}{8}\), we have \(a = 1\), \(b=7\), \(c = 8\). Then \(\frac{1\times8 + 7}{8}=\frac{8 + 7}{8}=\frac{15}{8}\).

Step2: Multiply the two fractions

Now we multiply \(\frac{15}{8}\) by \(\frac{5}{6}\). When multiplying fractions, we multiply the numerators together and the denominators together. So \(\frac{15}{8}\times\frac{5}{6}=\frac{15\times5}{8\times6}=\frac{75}{48}\).

Step3: Simplify the fraction

We can simplify \(\frac{75}{48}\) by finding the greatest common divisor (GCD) of 75 and 48. The factors of 75 are 1, 3, 5, 15, 25, 75. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The GCD is 3. Divide both the numerator and the denominator by 3: \(\frac{75\div3}{48\div3}=\frac{25}{16}\). We can also write this as a mixed number: \(1\frac{9}{16}\).

Answer:

\(\frac{25}{16}\) (or \(1\frac{9}{16}\))