To simplify the expression 4-4/15-11/15+2/23, we need to find a common denominator for the fractions. The least common denominator of 15 and 23 is 345.
Then, we rewrite the fractions with the common denominator:
4 - (4/15)*23/23 - (11/15)*23/23 + (2/23)*15/15
Simplifying the fractions:
4 - (92/345) - (253/345) + (30/345)
Combining like terms:
= 4 - 92/345 - 253/345 + 30/345
= 4 - 315/345 + 30/345
Now, we add and subtract the fractions:
= 4 - (315 - 30)/345
= 4 - 285/345
Simplifying the fraction:
= 4 - 19/23
Finally, subtracting the fractions:
= (4*23 - 19)/23
= 92 - 19/23
So, 4-4/15-11/15+2/23 simplifies to 92 - 19/23.
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