Please explain the addition property of equality with fractions

Question

tabuordy · Accepted Answer

Step 1
The additive property of equality says what we add to one side of the equality, we must add the same thing to the other side.
Step 2
Suppose we have an equation:
$x - \frac{1}{4} = \frac{3}{4}$
and we need to solve for x
Step 3
In order to solve for x, we need to add $\frac{1}{4}$ to both sides of the equation according to the additive property of equality as shown on the board
$x - \frac{1}{4} + \frac{1}{4} = \frac{3}{4} + \frac{1}{4}$
Step 4
Cancel out $- \frac{1}{4}$ and $+ \frac{1}{4}$ on the left side and we get the equation as shown on the board
$x = \frac{3}{4} + \frac{1}{4}$
Step 5
Since both the fractions have a common denominator, we can simply add up their numerators as shown on the board
$x = \frac{3 + 1}{4}$
Step 6
Simplifying the numerator we get:
$x = \frac{4}{4}$
On further simplification the 4's get cancelled out on the top and bottom and we get:
$x = 1$
Step 7
Final answer
$x = 1$

Please explain the addition property of equality with fractions

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