10 2/9-(-3 1/3)
92/9+10/3
(92+30)/9 = 122/9
13 5/9
To subtract two mixed numbers, you'll need to first convert them into improper fractions. Then you can perform the subtraction.
Let's convert the mixed numbers to improper fractions:
10 2/9 = (10 * 9 + 2)/9 = 92/9
-3 1/3 = (-3 * 3 + 1)/3 = (-9 + 1)/3 = -8/3
Now subtract the two improper fractions:
92/9 - (-8/3)
To remove the double negative, we can multiply -8/3 by -1:
92/9 - (-1 * 8/3)
Now we can apply the subtraction:
92/9 - 8/3
To subtract fractions, we need a common denominator. In this case, the common denominator is 9 * 3 = 27.
Now let's make sure both fractions have a denominator of 27:
92/9 = (92/9) * (3/3) = 276/27
8/3 = (8/3) * (9/9) = 72/27
Now we can subtract the fractions:
276/27 - 72/27 = (276 - 72)/27 = 204/27
The result is 204/27, which can be simplified as a mixed number. Divide the numerator (204) by the denominator (27):
204 รท 27 = 7 remainder 15
The fraction is equivalent to 7 15/27. Since 15 is divisible by 3 and 27 is also divisible by 3, we can simplify the fraction further:
7 15/27 = 7 5/9
Therefore, 10 2/9 - (-3 1/3) equals to 7 5/9.