At the fair there are two bean bag toss games. You gain 3/4 of a point for each bean bag that you get on the target and you lose 1/2 point for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 3/4h - 1/2g. In a different bean bag toss game you gain 7/8 points for each bean bag that get on the target and you lose 3/4 points for each bean bag that does not land on the target. Your total amount of points for this game can be represented by 7/8h - 3/4g. You can figure out the total number of points earned by simplifying this expression: (3/4h - 1/2g) + (7/8h - 3/4g). What would this expression be simplified? (Hint: Combine like terms!)
To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), we can combine like terms.
Starting with the h terms, we have:
(3/4h + 7/8h)
To add these fractions, we need to find a common denominator. In this case, the lowest common multiple of 4 and 8 is 8. So, we need to express 3/4h with a denominator of 8:
(3/4h) = (3/4h * 2/2) = (6/8h)
Now we can combine the h terms:
(6/8h + 7/8h) = (13/8h)
Moving on to the g terms, we have:
(-1/2g - 3/4g)
To add these fractions, we need to find a common denominator. In this case, the lowest common multiple of 2 and 4 is 4. So, we need to express -1/2g with a denominator of 4:
(-1/2g) = (-1/2g * 2/2) = (-2/4g)
Now we can combine the g terms:
(-2/4g - 3/4g) = (-5/4g)
Putting it all together, the simplified expression is:
(13/8h - 5/4g)