Simplify (3/4h-1/2g+(7/8h-3/4g)
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.
To simplify the expression (3/4h - 1/2g + (7/8h - 3/4g)), first distribute the negative sign inside the parentheses:
(3/4h - 1/2g + 7/8h - 3/4g)
Now, let's combine like terms. We have (3/4h + 7/8h) - (1/2g + 3/4g):
(3/4h + 7/8h) - (1/2g + 3/4g)
To combine the terms with h, we need a common denominator. The least common denominator for 4 and 8 is 8, so let's rewrite the fractions with the denominator of 8:
[(3*2)/(4*2)h + 7/8h] - (1/2g + (3*2)/(4*2)g)
Simplifying further:
[6/8h + 7/8h] - (1/2g + 6/8g)
Combining the h terms:
(13/8h) - (1/2g + 6/8g)
To combine the g terms, we need a common denominator. The least common denominator for 2 and 8 is 8, so let's rewrite the fractions with the denominator of 8:
(13/8h) - [(1*4)/(2*4)g + 6/8g]
Simplifying further:
(13/8h) - (4/8g + 6/8g)
Combining the g terms:
(13/8h) - (10/8g)
Now, the expression is simplified to:
(13/8h) - (10/8g)
or
(13h - 10g)/8
To simplify the expression (3/4h - 1/2g + (7/8h - 3/4g)), we can combine like terms.
First, let's simplify within the parentheses:
7/8h - 3/4g can be simplified by finding a common denominator, which in this case is 8. Multiply the fractions by appropriate factors to get the common denominator:
(7/8h - 3/4g) = (7/8 * 2/2)h - (3/4 * 2/2)g
= (14/16h - 6/8g)
Now, the simplified expression becomes:
3/4h - 1/2g + (14/16h - 6/8g)
To combine like terms, we need to make sure the variables and the coefficients are the same. In this case, both h and g are variables, and the coefficients are fractions.
Let's focus on the "h" terms:
3/4h + 14/16h can be simplified by finding a common denominator, which is 16. Multiply the fractions by appropriate factors to get the common denominator:
(3/4 * 4/4)h + 14/16h
= (12/16h + 14/16h)
= (12/16 + 14/16)h
= (26/16)h
Now, let's focus on the "g" terms:
-1/2g - 6/8g can be simplified by finding a common denominator, which is 8. Multiply the fractions by appropriate factors to get the common denominator:
(-1/2 * 4/4)g - (6/8 * 1/1)g
= (-4/8g - 6/8g)
= (-4/8 - 6/8)g
= (-10/8)g
Finally, the simplified expression becomes:
(26/16)h + (-10/8)g
To further simplify, we can reduce the fractions:
(26/16)h can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(26/16)h = (13/8)h
Similarly, (-10/8)g can be reduced by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(-10/8)g = (-5/4)g
So, the fully simplified expression is:
(13/8)h + (-5/4)g