Question

Which expression is equivalent to the expression quantity negative 7 over 6 times t plus 4 over 9 end quantity minus expression quantity negative 5 over 12 times t plus 2 over 3 end quantity?

negative 12 over 18 times t plus 6 over 12
negative 9 over 12 times t minus 2 over 9
12 over 18 times t plus negative 6 over 12
2 over 12 times t plus 2 over 6

Answer 1

To simplify the expression, combine like terms and find a common denominator for the fractions. The expression is equivalent to 8t/9 + 16/9.

Step-by-step explanation:

To simplify the expression, we need to combine like terms. First, let's multiply:

-7/6 * t = -7t/6

-5/12 * t = -5t/12

Now, let's find a common denominator for the fractions:

6 and 12 have a common denominator of 12. This means we need to rewrite 4/9 as 4/9 * 12/12 = 48/108.

Similarly, we need to rewrite 2/3 as 2/3 * 6/6 = 12/18.

Now, let's combine the terms:

(-7t/6 + 48/108) - (-5t/12 + 12/18)

= -7t/6 + 48/108 + 5t/12 - 12/18

Now, let's simplify the fractions:

= -7t/6 + 48/108 + 5t/12 - 12/18

= (-14t + 288 + 30t - 96)/108

= (16t + 192)/108

= 8t/9 + 16/9

Therefore, the expression is equivalent to 8t/9 + 16/9.