[tex]\frac{1}3+\frac{7}{12}*4[/tex]
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.
[tex]\frac{1}3+\frac{28}{12}[/tex]
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: 3
Prime 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.
[tex]\frac{4}{12}+\frac{28}{12}[/tex]
Now just add the numerators.
[tex]\frac{32}{12}[/tex]
Since the top and bottom are both divisible by 2, we can simplify this by dividing them both by 2.
[tex]\frac{16}6[/tex]
And again.
[tex]\frac{8}3[/tex]
If you wanted that as an improper fraction, that would be [tex]2\frac{2}3[/tex].
