Simplify (3/4h-1/2g+(7/8h-3/4g)

Answer 1

To simplify the expression (3/4h - 1/2g + (7/8h - 3/4g)), we can start by simplifying the expression inside the parentheses:

(7/8h - 3/4g) can be simplified by finding a common denominator for the fractions, which is 8. Multiplying the fractions by appropriate factors to get the same denominator, we have:

(7/8h - 3/4g) = (7/8 * 1h - 3/4 * 2g) = (7/8h - 6/8g) = (7h/8 - 6g/8).

Now, the simplified expression becomes:

3/4h - 1/2g + (7h/8 - 6g/8).

Next, we can simplify the expression by finding a common denominator for the fractions 3/4h and 6g/8, which is 8. Multiplying the fractions by appropriate factors to get the same denominator, we have:

3/4h = (3/4 * 2h) = 6h/8,

and

6g/8 = 3g/4.

Thus, the simplified expression is:

6h/8 - 1/2g + 7h/8 - 3g/4.

Now, we can combine like terms:

(6h/8 + 7h/8) - (1/2g + 3g/4).

Adding the h terms and multiplying the denominator by 8 to find a common denominator, we have:

(6h + 7h)/8 - (1/2g + 3g)/4 = (13h)/8 - (1/2g + 6/2g)/4 = 13h/8 - 7/2g/4 = 13h/8 - 7/8g.

Therefore, the simplified expression is: 13h/8 - 7/8g.