Question

How do you multiply \[\dfrac{2}{7} \times 49?\]

Answer 1

Hint: The given question describes the operation of addition/ subtraction/ multiplication/ division. We need to know the multiplication process between the fraction number and whole number. The final answer will be decimal or whole numbers. We try to find the greatest common factor between the numerator and denominator. Also, the given whole term would be multiplied with the numerator and divided by the denominator to solve the given question

Complete step-by-step answer:
The given question is shown below,
 \[\dfrac{2}{7} \times 49 = ? \to \left( 1 \right)\]
We have to multiply the given fraction number with the given whole number term. For this calculation, we need to find the greatest common factor between the numerator and the denominator.
Before that, the whole number term in the given question can also be written as,
 \[49 = \dfrac{{49}}{1} \to \left( 2 \right)\]
Let’s substitute the equation \[\left( 1 \right)\] in the equation \[\left( 2 \right)\] we get,
 \[\dfrac{2}{7} \times 49 = \dfrac{2}{7} \times \dfrac{{49}}{1}\]
Let’s multiply the two numerator values and consider that as a whole numerator part. Also, multiply the two denominator value and consider that as a whole denominator part as follows,
 \[\dfrac{2}{7} \times \dfrac{{49}}{1} = \dfrac{{\left( {2 \times 49} \right)}}{{\left( {7 \times 1} \right)}}\]
So, we get
 \[\dfrac{{\left( {2 \times 49} \right)}}{{\left( {7 \times 1} \right)}} = \dfrac{{98}}{7}\]
Let’s find the greatest common factor between the numerator \[98\] and the denominator \[7\] . So, we know that \[98\] can be divided by \[7\] . So, the greatest common factor is \[7\] . Let’s divide the numerator and denominator by \[7\] . So, we get
 \[\dfrac{{98}}{7} = \dfrac{{14}}{1}\]
We know that the term \[\dfrac{{14}}{1}\] can also be written as \[14\]
So, the final answer is
 \[\dfrac{2}{7} \times 49 = 14\]
So, the correct answer is “14”.

Note: In this type of question we have to assume \[1\] as a denominator for the whole numbers. Also, we can directly divide the term \[98\] by \[7\] instead of finding the greatest common factor. Also, note that we shouldn’t take zero as the greatest common factor. The denominator term would not be equal to zero.