MHB Fraction multiplication problem

[mathlearn]

This problem is a little elementary,

If we were to multiply the fraction $\frac{3}{7}$ by two which way should I be using,

$2\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 1

or

$\frac{2}{2}\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 2

I usually multiply fractions using the method in 1 But looks like It is wrong,

$\frac{2}{1}\left(\frac{3}{7}\right)=\frac{6}{14}$ which is incorrect

I have been used to multiply fractions using the method in 1, So which one of them are correct to multiply $\frac{3}{7}$ by two

 

[SuperSonic4]

This problem is a little elementary,

If we were to multiply the fraction $\frac{3}{7}$ by two which way should I be using,

$2\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 1

or

$\frac{2}{2}\left(\frac{3}{7}\right)=\frac{6}{14}$ --------------- 2

I usually multiply fractions using the method in 1 But looks like It is wrong,

$\frac{2}{1}\left(\frac{3}{7}\right)=\frac{6}{14}$ which is incorrect

I have been used to multiply fractions using the method in 1, So which one of them are correct to multiply $\frac{3}{7}$ by two

Number 2 is wrong because since you have $\dfrac{2}{2}$ you are multiplying by 1 instead of by 2.

Number 1 is also incorrect, what you're doing below when trying it out is to multiply top and bottom by 2 which is the same method as the incorrect "equation" 2 - you're going from 7 to 14 in the denominator for no reason

$\frac{2}{1}\left(\frac{3}{7}\right)=\frac{6}{14}$ which is incorrect

---

What you should be doing is:

$2 \left(\dfrac{3}{7}\right) = \dfrac{2}{1} \cdot \dfrac{3}{7} = \dfrac{2 \cdot 3}{1 \cdot 7} = \dfrac{6}{7}$

edit: if you have an integer (or something not written in fractional form - for example $e$ or $\pi$) you multiply only by the numerator