Question

How do you multiply $\dfrac{3}{7} \times \dfrac{4}{5}$?

Answer 1

Hint: Let us first know what a fraction is. It is defined as equal parts of a whole. When we divide a collection or whole into equal parts, each part is a fraction of the whole. It simply shows how much or into how many parts is a whole thing divided. The fraction is expressed in the form $\dfrac{x}{y}$ where $x$ is known as the numerator of the fraction and $y$ is known as the denominator of the fraction. The numerator can be explained as the number of equal parts considered whereas the denominator can be defined as the total number of equal parts of the whole.

Complete Step by Step Solution:
The given question is on the multiplication of fractions. When we multiply two or more fractions together, we multiply all the numerators of the given fractions to get the numerator of the product. Similarly, we multiply all the denominators of the given fractions to get the denominator of the product.
The fractions given are $\dfrac{3}{7}$ and $\dfrac{4}{5}$. Now on using the above-given information and multiplying, we will get
$ \Rightarrow \dfrac{3}{7} \times \dfrac{4}{5} = \dfrac{{12}}{{35}}$ (Since $3 \times 4 = 12$ and $7 \times 5 = 35$)

Hence, when we multiply $\dfrac{3}{7}$ and $\dfrac{4}{5}$, we get $\dfrac{{12}}{{35}}$ as the answer.

Note:
The answer which we got after multiplying the fractions can be further simplified into a decimal. Since the answer $\dfrac{{12}}{{35}}$ is already in its simplest form as there are no common factors of $12$ and $35$, we can further simplify it by dividing $12$ by $35$ with the help of the long division method. The simplified form of $\dfrac{{12}}{{35}}$ in decimal is $0.342857143$.