Question

How do you simplify \[\dfrac{3}{8} . \dfrac{3}{8}\]?

Answer 1

Hint: In this question, there are two factions, and each has the numerator and denominator. We want to multiply two fractions. There is a simple rule, which is that when we multiply two fractions then we multiply numerator to numerator and denominator to denominator separately.

Complete step by step solution:
Let's assume that there are two fractions given below.
These are \[\dfrac{a}{b}\] and \[\dfrac{c}{d}\].
Then we want to multiply these two fractions.
Then,
\[\dfrac{a}{b} \times \dfrac{c}{d}\]
In the above, there are two fractions that multiply. According to fraction multiplication, we multiply numerator to numerator and denominator to denominator separately.
Hence, \[a\] is multiplied with \[c\] and \[b\] is multiplied with \[d\].
Then the above expression of multiplication of two fractions is written as below.
Then,
\[\dfrac{{a \times c}}{{b \times d}}\]
This is the multiplication of two fractions.
Now, come to the question, in the question, there are two fractions. And want to multiple these.
In the question, both fractions have a numerator and denominator.
Hence,
From the question, the value is written as below.
\[ \Rightarrow \dfrac{3}{8}.\dfrac{3}{8} = \dfrac{3}{8} \times \dfrac{3}{8}\]
In the above, there are two fractions that multiply. According to fraction multiplication, we multiply numerator to numerator and denominator to denominator separately.
Hence, \[3\] is multiplied with \[3\] and \[8\] is multiplied with \[8\].
Then, the multiplication of two fractions is written as below.
\[ \Rightarrow \dfrac{{3 \times 3}}{{8 \times 8}}\]
By calculating, we will get the result as,
\[\therefore \dfrac{9}{{64}}\]

Therefore, the multiplication of \[\dfrac{3}{8}.\dfrac{3}{8}\] is \[\dfrac{9}{{64}}\].

Note:
If you want to multiply two fractions. Then you would multiply numerator to numerator and denominator to the denominator. You cannot multiply numerator to denominator and denominator to numerator.