![\frac{1}3+\frac{7}{12}*4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D3%2B%5Cfrac%7B7%7D%7B12%7D%2A4)
According to the order of operations, you need to multiply first.
When you multiply into a fraction, the numerator (top number) changes.
In this case, you'd multiply the 7 by 4 to get 28.
![\frac{1}3+\frac{28}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D3%2B%5Cfrac%7B28%7D%7B12%7D)
To add fractions, they have to have the same denominator. (bottom number)
Let's find the lowest common denominator of 3 and 12.
Prime factorization of 3:
3Prime factorization of 12:
2*2*3
Multiply all of these together, ignoring the duplicates.
2*2*3 = 12
How can we change 1/3 to have a denominator of 12?
Well, if you multiply or divide both the numerator and denominator of a fraction by the same number, it will stay equal. For instance, 1/2 = 2/4.
We want the 3 to become 12. That means we'd multiply by 4.
Multiplying 1 by 4 gives us 4.
Thus 1/3 = 4/12.
![\frac{4}{12}+\frac{28}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B12%7D%2B%5Cfrac%7B28%7D%7B12%7D)
Now just add the numerators.
![\frac{32}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B12%7D)
Since the top and bottom are both divisible by 2, we can simplify this by dividing them both by 2.
![\frac{16}6](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D6)
And again.
![\frac{8}3](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D3)
If you wanted that as an improper fraction, that would be
![2\frac{2}3](https://tex.z-dn.net/?f=2%5Cfrac%7B2%7D3)
.