Question

Multiply the following fractions:
${\displaystyle \frac{3}{2}}\times 5{\displaystyle \frac{1}{3}}$

Answer 1

Hint:
At first convert the mixed fraction into improper fraction. Then check if you can cancel out any common factors from the numerator and the denominator.

Complete step-by-step answer:
We have to multiply following the fractions:
${\displaystyle \frac{3}{2}}\times 5{\displaystyle \frac{1}{3}}$
Now, look at the fractions very carefully. The first one, ${\displaystyle \frac{3}{2}}$ is an improper fraction.
Improper fraction: where the numerator is greater than the denominator. Here the numerator is 3 and the denominator is 2. 3 is bigger than 2. So ${\displaystyle \frac{3}{2}}$ is an improper fraction.

The second one $5{\displaystyle \frac{1}{3}}$ is a mixed fraction.

Mixed fraction consists of a whole number and a proper fraction. Here 5 is whole number. The proper fraction is ${\displaystyle \frac{1}{3}}$ .

Proper fraction: where the numerator is less than the denominator. Here the numerator is 1 and the denominator is 3. 1 is smaller than 3. So ${\displaystyle \frac{1}{3}}$ is a proper fraction.
Now, before multiplying we have to convert the mixed fraction into an improper faction.
The formula for converting a mixed fraction into an improper fraction is:
$a{\displaystyle \frac{c}{d}}={\displaystyle \frac{(a\times d)+c}{d}}$

For this problem: $a=5,c=1,d=3$
Now, by substituting the values of a, c and d we will get:
$\begin{array}{rl}& 5{\displaystyle \frac{1}{3}}={\displaystyle \frac{(5\times 3)+1}{3}}={\displaystyle \frac{15+1}{3}}={\displaystyle \frac{16}{3}}\\ & \end{array}$
Now our multiplication looks like:
${\displaystyle \frac{3}{2}}\times {\displaystyle \frac{16}{3}}$

Now in the numerator of the first fraction we have one 3 and in the denominator of the second fraction we also have a 3. So we can cancel them out.
${\displaystyle \frac{3}{2}}\times {\displaystyle \frac{16}{3}}$
$={\displaystyle \frac{1}{2}}\times {\displaystyle \frac{16}{1}}$
$\begin{array}{rl}& ={\displaystyle \frac{16}{2}}\\ & ={\displaystyle \frac{2\times 8}{2}}\end{array}$
Now, cancel out the 2 from the numerator and the denominator.
$\begin{array}{rl}& ={\displaystyle \frac{1\times 8}{1}}\\ & =8\end{array}$
Hence the result of the multiplication is 8.

Note: When we multiply a mixed fraction with a proper fraction or an improper fraction, always convert the mixed fraction into an improper fraction first. Do not multiply the proper fraction part of the mixed fraction with any other fraction before converting the mixed fraction into an improper fraction.
Always cancel out the common factors from the numerator and the denominator.