Question

Evaluate each expression.

$\frac{11-8}{1+7\cdot 2}$

Short answer

The value of the expression $\frac{\mathbf{11}\mathbf{-}\mathbf{8}}{\mathbf{1}\mathbf{+}\mathbf{7}\mathbf{\cdot }\mathbf{2}}$is $\frac{\mathbf{1}}{\mathbf{5}}$.

Step-by-step solution

Step 1. Order of operations.

In order to evaluate an expression, the order of operations must be followed, which is:

1. Evaluate the expressions inside the bracket
2. Evaluate the powers
3. Multiply and/or divide
4. Add and/ or subtract

The evaluation takes place from left to right.

Step 2. Multiply 7 by 2 in the denominator.

As per the order of operations, first, multiply 7 by 2 which is in the denominator.

$\frac{11-8}{1+7\cdot 2}=\frac{11-8}{1+14}$

Step 3. Apply subtraction and addition operations.

Subtract 8 from 11 in the numerator and add 1 and 14 in the denominator simultaneously.

$\begin{array}{l}\frac{11-8}{1+7\cdot 2}=\frac{11-8}{1+14}\\ =\frac{3}{15}\\ =\frac{1}{5}\end{array}$

Therefore, the expression is equal to $\frac{1}{5}$.