Add the expressions 4 minus two-thirds b + one-fourth a and One-half a + one-sixth b minus 7. What is the simplified sum?
Negative one-sixth a + StartFraction 5 over 12 EndFraction b minus 3
Three-fourths a minus one-half b minus 3
Three-fourths a + StartFraction 5 over 6 EndFraction b minus 3
StartFraction 5 over 12 EndFraction a minus StartFraction 1 over 6 EndFraction b minus 3
To simplify the sum of the two expressions, we first add the like terms:
4 - 2/3b + 1/4a + 1/2a + 1/6b - 7
= (1/4a + 1/2a) + (4 - 7) + (-2/3b + 1/6b)
= 3/4a - 3 + (1/6 - 2/3)b
= 3/4a - 3 - 5/6b
= -1/6a + 5/12b - 3
So, the simplified sum is Negative one-sixth a + StartFraction 5 over 12 EndFraction b minus 3.