2 2/3 + -1 1/2=
7/6
to make the process clear:
8/3 - 3/2 = 16/6 - 9/6 = 7/6
To add mixed numbers, you first need to convert them into improper fractions. Let's convert 2 2/3 and -1 1/2 into improper fractions.
To convert 2 2/3 into an improper fraction:
Multiply the whole number (2) by the denominator (3), then add the numerator (2).
2 * 3 = 6
6 + 2 = 8
So, 2 2/3 as an improper fraction is 8/3.
Similarly, to convert -1 1/2 into an improper fraction:
Multiply the whole number (-1) by the denominator (2), then add the numerator (1).
-1 * 2 = -2
-2 + 1 = -1
So, -1 1/2 as an improper fraction is -1/2.
Now that we have both mixed numbers converted into improper fractions, we can add them.
8/3 + (-1/2) =
To add fractions, you need a common denominator. In this case, the common denominator is 6 (the least common multiple of 3 and 2).
Multiply the numerator and denominator of the first fraction (8/3) by 2 to get a common denominator:
(8/3) * (2/2) = 16/6
Now, we can add the fractions:
16/6 + (-1/2) =
Since the fractions have the same denominator, we can combine the numerators while keeping the same denominator:
(16 - 1)/6 = 15/6
Before we finalize the sum, let's simplify the fraction:
15/6 can be reduced to its lowest terms. Both the numerator and denominator are divisible by 3:
(15/3) / (6/3) = 5/2
Therefore, 2 2/3 + -1 1/2 = 5/2 or 2 1/2.