Question

Evaluate: 3/7+-4/9--11/7-7/9

Answer 1

To evaluate the expression
`\displaystyle\sf (3)/(7) + (-4)/(9) - (-11)/(7) - (7)/(9)`, we can follow these steps:

Step 1: Find a common denominator for all the fractions. In this case, the common denominator is 63, which is the least common multiple of 7 and 9.

Step 2: Convert all the fractions to have the common denominator of 63.

`\displaystyle\sf (3)/(7) = (3 * 9)/(7 * 9) = (27)/(63)`

`\displaystyle\sf (-4)/(9) = (-4 * 7)/(9 * 7) = (-28)/(63)`

`\displaystyle\sf (-11)/(7) = (-11 * 9)/(7 * 9) = (-99)/(63)`

`\displaystyle\sf (7)/(9) = (7 * 7)/(9 * 7) = (49)/(63)`

Step 3: Substitute the converted fractions back into the original expression and simplify:

`\displaystyle\sf (27)/(63) + (-28)/(63) - (-99)/(63) - (49)/(63)`

Combining the numerators over the common denominator:

`\displaystyle\sf (27 - 28 + 99 - 49)/(63)`

Simplifying the numerator:

`\displaystyle\sf (49)/(63)`

The resulting fraction is already in simplest form. Therefore, the expression
`\displaystyle\sf (3)/(7) + (-4)/(9) - (-11)/(7) - (7)/(9)` evaluates to
`\displaystyle\sf (49)/(63)`.