# Why cant you multiply the top only when adding fractions?

I dont understand why you cant multiply the tops of fractions when theyre being added to get rid of the denominator... for example, 1/2 + 2/4 i can make common denominators so they add up to 1 but i can't multiply both tops by 4 and 2, also, why does this only work in equations and not as expressions? For example 1/2 + 2/4 = 1, multiplying everything by 4 and 2 works here, but not earlier. Why is that? Thanks.

Relevance

Multiplying only the numerators by a number other than 1 changes the value of the fractions. For example, 1/4 becomes 1 if we multiply the numerator by 4. Multiplying both numerator and denominator by the same number doesn't change the value. For example, 1/4 multiplied by 4/4 is 4/16. In an equation, multiplying both sides by the same number doesn't change the equality. It does, as I've said before, change the value of each number, but there's a property that says if a = b, then multiplying both sides by some number k keeps the equality true: ka = kb.

• You need common denominators to add/subtract fractions

For instance 1/2 + 1/3

the common denominator is 6

Multiply eact term by (1) so they are not changed.

1/2 *(3/3) + 1/3 * (2/2)

3/6 + 2/6