Question

How do you multiply \[3\dfrac{1}{3}\times \dfrac{3}{8}\]?

Answer 1

Hint: In order to find solution to this problem, we will first write both numbers in normal fraction form and then use the rule for multiplication of fractions, which states that we may multiply numerators and denominators separately to get it in the simplest form and then we can convert back to mixed number form or decimal form if we wanted to.

Complete step by step solution:
As we know we have to multiply rational numbers, therefore, we have to simply multiply the numerators(top) and the denominators(bottom), that is we have to apply this formula:
\[\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}\]
Now, first we will simply write both numbers in normal fraction form.
Therefore, by writing in fraction form, we get:
$\Rightarrow 3\dfrac{1}{3}+\dfrac{3}{8}$
As we have improper fraction, we will convert it into proper fraction format and then proceed:
$\Rightarrow 3\dfrac{1}{3}=\dfrac{\left( 3\times 3 \right)+1}{3}$
On simplifying, we get:
$\Rightarrow \dfrac{10}{3}$
 Now continuing in our solution, we get:
$\Rightarrow \dfrac{10}{3}\times \dfrac{3}{8}$
Now we will use the rule for multiplication of fractions which says we may multiply numerators and denominators separately to get it in simplest form, that is:
\[\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}\]
On evaluating in our formula, we get:
$\Rightarrow \dfrac{10}{3}\times \dfrac{3}{8}=\dfrac{10\times 3}{3\times 8}$
On simplifying, we get:
$\Rightarrow \dfrac{30}{24}$
On further simplification, we get:
$\Rightarrow \dfrac{10}{8}$
Since it can further be simplified, on simplifying, we get:
$\Rightarrow \dfrac{5}{4}$

Therefore, we get our solution as $3\dfrac{1}{3}\times \dfrac{3}{8}=\dfrac{5}{4}$ .

Note: After finding the solution in fraction form, we can then convert back to mixed number form or decimal form if we want to.
On simplifying the solution and finding the decimal form, we get our final solution as:
$\Rightarrow 3\dfrac{1}{3}\times \dfrac{3}{8}=\dfrac{5}{4}=1.25$
That is, the solution is:
$\Rightarrow 3\dfrac{1}{3}\times \dfrac{3}{8}=1.25$