Question

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

Explanation:

Step1: Convert mixed number to improper fraction

To multiply a mixed number \(1\frac{7}{8}\) with a fraction \(\frac{5}{6}\), first convert the mixed number to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). For \(1\frac{7}{8}\), \(a = 1\), \(b=7\), \(c = 8\), so we have \(\frac{1\times8 + 7}{8}=\frac{8 + 7}{8}=\frac{15}{8}\).

Step2: Multiply the two fractions

Now multiply the improper fraction \(\frac{15}{8}\) with \(\frac{5}{6}\). When multiplying fractions, we multiply the numerators together and the denominators together, i.e., \(\frac{15}{8}\times\frac{5}{6}=\frac{15\times5}{8\times6}\).
Calculate the numerator: \(15\times5 = 75\)
Calculate the denominator: \(8\times6=48\)
So we get \(\frac{75}{48}\).

Step3: Simplify the fraction

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 of 75 and 48 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: \(1\frac{9}{16}\) (since \(25\div16 = 1\) with a remainder of 9).

Answer:

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