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!) (2 points)

Question

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!) (2 points)

Responses

10/14h - 4/6g
10/14h - 4/6g

15/8h + 5/4g
15/8h + 5/4g

1 5/8h - 1 1/4g
1 5/8h - 1 1/4g

1 1/2h - 1 3/4g

Answer 1

To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), you need to combine like terms.

The terms with "h" are (3/4h + 7/8h), which can be added together to get (15/8h).
The terms with "g" are (-1/2g - 3/4g), which can be added together to get (-5/4g).

Therefore, the simplified expression is 15/8h - 5/4g.

Answer 2

To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), you need to combine like terms.

First, let's simplify the terms with 'h':

The terms 3/4h and 7/8h have the same variable 'h'. To add them, we need to find a common denominator. The least common multiple of 4 and 8 is 8. So, we multiply the first term by 2/2 and the second term by 1/1 to get a common denominator of 8:

(3/4h) + (7/8h) = (6/8h) + (7/8h) = (13/8h)

Now let's simplify the terms with 'g':

The terms -1/2g and -3/4g also have the same variable 'g'. To add them, we need to find a common denominator. The least common multiple of 2 and 4 is 4. So, we multiply the first term by 2/2 and the second term by 1/1 to get a common denominator of 4:

(-1/2g) + (-3/4g) = (-2/4g) + (-3/4g) = (-5/4g)

Now let's put it all together:

(13/8h) + (-5/4g)

To simplify this further, we can change the improper fraction 13/8 to a mixed number:

13/8 = 1 5/8

So the simplified expression is:

1 5/8h - 5/4g

Answer 3

To simplify the expression (3/4h - 1/2g) + (7/8h - 3/4g), we can combine like terms.

First, let's add the coefficients of h together: (3/4h + 7/8h). To add these fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 8. Therefore, we can rewrite the expression as (6/8h + 7/8h).

Now, we can add the coefficients: 6/8h + 7/8h = (6h + 7h)/8 = 13h/8.

Next, let's add the coefficients of g together: (-1/2g - 3/4g). Again, we need a common denominator, which is 4. So the expression becomes (-2/4g - 3/4g).

Now, let's add the coefficients: -2/4g - 3/4g = (-2g - 3g)/4 = -5g/4.

Now, we have (13h/8 - 5g/4) as the simplified expression for (3/4h - 1/2g) + (7/8h - 3/4g).