Question

How do you multiply \[\dfrac{3}{4} \times \dfrac{2}{3}\]?

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 answer:
Let's assume that there are two fractions below.
These are \[\dfrac{a}{b}\] and \[\dfrac{c}{d}\].
Then we want to multiply these two fractions.
Then,
\[ \Rightarrow \dfrac{a}{b} \times \dfrac{c}{d}\]
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,
\[ \Rightarrow \dfrac{{a \times c}}{{b \times d}}\]
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.
\[ \Rightarrow \dfrac{3}{4} \times \dfrac{2}{3}\]
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 \[2\] and \[4\] is multiplied with\[3\].
Then, the multiplication of two fractions is written as below.
\[ \Rightarrow \dfrac{{3 \times 2}}{{4 \times 3}}\]
By calculating, the result will come as below.
\[ \Rightarrow \dfrac{6}{{12}}\]
Now, we divide both the numerator and denominator with the value of \[6\].
Then, the above expression is written as.
\[ \Rightarrow \dfrac{{6/6}}{{12/6}}\]
Then, by calculating we get,
\[\therefore \dfrac{1}{2}\]

Therefore, the multiplication of \[\dfrac{3}{4} \times \dfrac{2}{3}\] is \[\dfrac{1}{2}\].

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