Question

Evaluate the given expression. 2 6/7 - 5/7 + 1 4/7

Answer 1

To evaluate the expression \( 2 \frac{6}{7} - \frac{5}{7} + 1 \frac{4}{7} \), we will perform the operations step by step.

First, we convert the mixed numbers to improper fractions.

1. Convert \( 2 \frac{6}{7} \) to an improper fraction:
\[
2 \frac{6}{7} = \frac{2 \times 7 + 6}{7} = \frac{14 + 6}{7} = \frac{20}{7}
\]

2. Convert \( 1 \frac{4}{7} \) to an improper fraction:
\[
1 \frac{4}{7} = \frac{1 \times 7 + 4}{7} = \frac{7 + 4}{7} = \frac{11}{7}
\]

Now we substitute these values back into the expression:
\[
\frac{20}{7} - \frac{5}{7} + \frac{11}{7}
\]

Next, we can perform the subtraction and addition using a common denominator (which is already 7):
\[
\frac{20 - 5 + 11}{7} = \frac{20 + 11 - 5}{7} = \frac{26}{7}
\]

Finally, we can convert the improper fraction \( \frac{26}{7} \) back to a mixed number:
\[
\frac{26}{7} = 3 \frac{5}{7} \quad \text{(since \( 26 \div 7 = 3 \) remainder \( 5 \))}
\]

Thus, the final result of the expression \( 2 \frac{6}{7} - \frac{5}{7} + 1 \frac{4}{7} \) is:
\[
\boxed{3 \frac{5}{7}}
\]