Simplify: 1/2a + 3/4a.

• A. 5/4a
• B. 3/4a
• C. 1/4a
• D. 2a

Answer: (A)

To simplify the expression ( \frac{1}{2}a + \frac{3}{4}a ), we first need to find a common denominator for the fractions involved. The denominators here are 2 and 4. The least common denominator is 4.

Next, we convert ( \frac{1}{2}a ) into an equivalent fraction with a denominator of 4. To do this, we multiply both the numerator and the denominator by 2:

[

\frac{1}{2}a = \frac{1 \times 2}{2 \times 2}a = \frac{2}{4}a

]

Now we can rewrite the expression:

[

\frac{2}{4}a + \frac{3}{4}a

]

Since both terms now have the same denominator, we can combine the numerators:

[

\frac{2 + 3}{4}a = \frac{5}{4}a

]

Thus, the simplified form of the expression is ( \frac{5}{4}a ).

This shows that the selected answer is correct. The effective method used involves finding a common denominator, rewriting the terms