let's simplify the expression step by step.
First, let's add the mixed numbers 2 3/4 and 9 7/6. To do this, we need to find a common denominator, which is 12 in this case.
2 3/4 + 9 7/6 = (2 * 4 + 3) / 4 + (9 * 6 + 7) / 6
= (8 + 3) / 4 + (54 + 7) / 6
= 11 / 4 + 61 / 6
Next, let's convert these fractions to have a common denominator of 12.
11 / 4 = (11 * 3) / (4 * 3) = 33 / 12
61 / 6 = (61 * 2) / (6 * 2) = 122 / 12
Now we can add these fractions together:
33 / 12 + 122 / 12 = (33 + 122) / 12 = 155 / 12
Finally, let's subtract the mixed number 7 9/9 from the result. To do this, we need to find a common denominator, which is 9 in this case.
155 / 12 - 7 9/9 = (155 / 12) - (7 * 9 + 9) / 9
= 155 / 12 - (63 + 9) / 9
= 155 / 12 - 72 / 9
To subtract these fractions, we need a common denominator of 36.
155 / 12 = (155 * 3) / (12 * 3) = 465 / 36
72 / 9 = (72 * 4) / (9 * 4) = 288 / 36
Now we can subtract these fractions:
465 / 36 - 288 / 36 = (465 - 288) / 36 = 177 / 36
Finally, we can simplify this fraction:
177 / 36 = (177 / 9) / (36 / 9) = 19 9/36
So, the simplified result of (2 3/4 + 9 7/6) - 7 9/9 is 19 9/36.
