6 - (5/6+ { 3 7/8 - 2 1/3 + 1 7/9 } )
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To solve this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to simplify it step by step:
First, we need to simplify the expression inside the parentheses:
3 7/8 - 2 1/3 + 1 7/9
To do this, we need to convert all mixed numbers to improper fractions:
31/8 - 7/3 + 16/9
We can find a common denominator for all three fractions, which is 72:
(31/8) * 9/9 = 279/72
(7/3) * 24/24 = 168/72
(16/9) * 8/8 = 128/72
Now we can combine the fractions:
279/72 - 168/72 + 128/72 = 239/72
So, the expression inside the parentheses simplifies to 239/72.
Now we can substitute this value back into the original expression:
6 - (5/6 + 239/72)
Next, we need to simplify the addition of the two fractions inside the parentheses:
(5/6 + 239/72)
To do this, we find a common denominator for both fractions, which is 72:
(5/6) * 12/12 = 60/72
(239/72)
Now we can combine the fractions:
60/72 + 239/72 = 299/72
Substituting this value back into the original expression, we get:
6 - (299/72)
To subtract a fraction from a whole number, we need to find a common denominator:
6 * 72/72 = 432/72
Now we can subtract the fraction:
432/72 - 299/72 = 133/72
Therefore, the final solution to the expression 6 - (5/6+ { 3 7/8 - 2 1/3 + 1 7/9 } ) is 133/72.
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