Question

find the product of the fractions. simplify your answer when possible.
46.)
$\frac{4}{11} \times \frac{2}{12}$
=
47.)
$\frac{4}{6} \times \frac{2}{4}$
=
48.)
$\frac{5}{7} \times \frac{7}{10}$
=
49.)
$\frac{3}{6} \times \frac{5}{10}$

Explanation:

46.

Step1: Multiply numerators and denominators

To find the product of two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we use the formula \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\). For \(\frac{4}{11} \times \frac{2}{12}\), we multiply the numerators \(4\times2 = 8\) and the denominators \(11\times12=132\), so we get \(\frac{8}{132}\).

Step2: Simplify the fraction

We can simplify \(\frac{8}{132}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So \(\frac{8\div4}{132\div4}=\frac{2}{33}\).

Step1: Multiply numerators and denominators

Using the fraction multiplication formula \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\), for \(\frac{4}{6} \times \frac{2}{4}\), we have \(4\times2 = 8\) (numerators) and \(6\times4 = 24\) (denominators), so \(\frac{8}{24}\).

Step2: Simplify the fraction

The greatest common divisor of 8 and 24 is 8. Dividing both by 8, we get \(\frac{8\div8}{24\div8}=\frac{1}{3}\).

Step1: Multiply numerators and denominators

For \(\frac{5}{7} \times \frac{7}{10}\), using \(\frac{a}{b} \times \frac{c}{d}=\frac{a\times c}{b\times d}\), we get \(5\times7 = 35\) (numerators) and \(7\times10=70\) (denominators), so \(\frac{35}{70}\).

Step2: Simplify the fraction

The greatest common divisor of 35 and 70 is 35. Dividing both by 35, we have \(\frac{35\div35}{70\div35}=\frac{1}{2}\).

Answer:

\(\frac{2}{33}\)

47.