Question

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

Answer 1

Hint:In this question, first we will convert the numbers in the fraction form and there is a simple rule, which is that when we multiply two fractions then we multiply numerator to numerator and denominator to denominator separately. If the number has no denominator then we assume that the denominator is\[1\].

Complete step by step answer:
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 fractions. And want to multiple these.
In the question, one has a numerator and there is no denominator in the first fraction. Then we assume that \[1\] is the denominator of that part to make a perfect fraction.
Hence,
From the question, the value is written as below:
=\[3 \times \dfrac{3}{4}\]
We can write the above expression as below.
=\[\dfrac{3}{1} \times \dfrac{3}{4}\]

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 \[4\]is multiplied with\[1\].
Then, the multiplication of two fractions is written as below,
=\[\dfrac{{3 \times 3}}{{1 \times 4}}\]
After calculation we will get,
=\[\dfrac{{3 \times 3}}{{1 \times 4}} = \dfrac{9}{4}\].

Therefore, the multiplication of \[3 \times \dfrac{3}{4}\] is\[\dfrac{9}{4}\].

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