The problem is to evaluate the sum of three numbers: $+(1/2)$, $+(2/3)$, and $-(1\frac{1}{6})$.

ArithmeticFractionsAdditionSubtractionMixed NumbersSimplification
2025/5/19

1. Problem Description

The problem is to evaluate the sum of three numbers: +(1/2)+(1/2), +(2/3)+(2/3), and (116)-(1\frac{1}{6}).

2. Solution Steps

First, we can rewrite the expression as:
12+23116\frac{1}{2} + \frac{2}{3} - 1\frac{1}{6}
Next, we convert the mixed number to an improper fraction:
116=1×6+16=761\frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6}
So the expression becomes:
12+2376\frac{1}{2} + \frac{2}{3} - \frac{7}{6}
Now, we find a common denominator for the three fractions, which is

6. We convert each fraction to an equivalent fraction with a denominator of 6:

12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
76\frac{7}{6} remains as is.
So the expression now becomes:
36+4676\frac{3}{6} + \frac{4}{6} - \frac{7}{6}
Now, we can add and subtract the fractions:
3+476=776=06=0\frac{3+4-7}{6} = \frac{7-7}{6} = \frac{0}{6} = 0

3. Final Answer

0

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