Simplify
(
4
+
2
�
3
)
+
(
5
�
3
+
2
)
(4+2n
3
)+(5n
3
+2). Write the answer in standard form.
To simplify the expression, we'll first simplify the expressions inside each set of parentheses.
In the first set of parentheses, we have 4 + 2 ÷ 3. Dividing 2 by 3 gives us 2/3. Adding 4 and 2/3 gives us 4 2/3.
In the second set of parentheses, we have 5 ÷ 3 + 2. Dividing 5 by 3 gives us 5/3. Adding 5/3 and 2 gives us 5/3 + 2.
So now we have (4 2/3) + (5/3 + 2).
To add 5/3 and 2, we need to find a common denominator. The least common multiple of 3 and 1 (from 2) is 3, so we'll multiply 2 by 3/3 to get 6/3. Adding 5/3 and 6/3 gives us 11/3.
So now we have (4 2/3) + (11/3).
To add mixed numbers, we need to convert them to improper fractions first. 4 2/3 is equivalent to (3 * 4) + 2/3, which is 14/3.
So now we have (14/3) + (11/3).
Adding 14/3 and 11/3 gives us 25/3.
Therefore, the simplified expression is 25/3 or 8 1/3 in mixed number form.