-3 5/9 plus 2 - 4 1/9
To add these mixed numbers, we first need to convert them into improper fractions.
For -3 5/9:
-3 can be written as -27/9
So, -3 5/9 can be written as -27/9 + 5/9
For 2 - 4 1/9:
4 can be written as 36/9
So, 2 - 4 1/9 can be written as 2 - 36/9 - 1/9
Now we can add them:
-27/9 + 5/9 = -22/9
2 - 36/9 - 1/9 = 2 - 37/9
To subtract -37/9 from 2, we need a common denominator:
2 can be written as 18/9
18/9 - 37/9 = -19/9
Therefore, -3 5/9 plus 2 - 4 1/9 equals -19/9.
To solve this expression, we need to perform the addition and subtraction of mixed numbers. Here are the step-by-step calculations:
Firstly, let's convert the mixed numbers into improper fractions:
-3 5/9 = (-3 * 9 + 5) / 9 = (-27 + 5) / 9 = -22/9
2 - 4 1/9 = 2 - (4 * 9 + 1) / 9 = 2 - (36 + 1) / 9 = 2 - 37/9
Now, let's perform the addition and subtraction:
-22/9 + (2 - 37/9)
To combine the numbers with the same denominator (-9), we need to find a common denominator:
-22/9 + (2 * 9 - 37) / 9
Simplifying:
-22/9 + (18 - 37) / 9
-22/9 + (-19) / 9
To add/subtract fractions, the denominators must be the same. So, we can directly combine the numerators:
(-22 - 19) / 9
-41/9
Therefore, the result of -3 5/9 plus 2 - 4 1/9 is -41/9.