Question

How do you find the product of \[\dfrac{1}{3} \times \dfrac{3}{7}\] ?

Answer 1

Hint: We have a product of two fractions. In this we need to multiply the denominator term of both the fraction and also we need to multiply the numerator term of both the fraction. After that we can cancel the terms and multiplying the remaining terms we get some fractions are numbers. Furthermore we can put the fraction value in the decimal form.

Complete step-by-step answer:
Given, \[\dfrac{1}{3} \times \dfrac{3}{7}\]
Now multiply the numerator terms of both the fraction we have \[1 \times 3 = 3\] .
Now multiply the denominator terms of both the fraction we have \[3 \times 7 = 21\] .
Thus we have,
 \[\dfrac{1}{3} \times \dfrac{3}{7} = \dfrac{3}{{21}}\]
 \[ = \dfrac{3}{{21}}\]
 \[ = \dfrac{1}{7}\] . This is the exact value.
We can put this in decimal form also.
 \[ = 0.1428\] . This is the decimal form.
So, the correct answer is “ \[ = \dfrac{1}{7}\] ”.

Note: A fraction is in the form \[\dfrac{a}{b}\] and \[b \ne 0\] . If ‘b’ is equal to zero then it will be indeterminate from (value which is unknown). Where, ‘a’ and ‘b’ are natural numbers. ‘a’ is called the numerator number and ‘b’ is called the denominator term. We have three types of fraction. Namely proper fraction, improper fraction and mixed fraction. Suppose let’s say that we have division of two fraction then we follow the below formula
 \[\dfrac{{\left( {\dfrac{a}{b}} \right)}}{{\left( {\dfrac{c}{d}} \right)}} = \dfrac{a}{b} \times \dfrac{d}{c}\] .
That is we turn the second fraction (the one we want to divide by) upside down (this is now a reciprocal) then we multiply the first fraction by the reciprocal. Then we simplify the fraction if needed. We do the same for the rational number. Rational number is of the form \[\dfrac{a}{b}\] and \[b \ne 0\] . But here ‘a’ and ‘b’ are integers.