Find the value of the following expression:

$\frac{5-35÷5\times 15+5}{12-2}$

The correct answer is −9.5.

We need to evaluate the expression:

\frac{5-35÷5\times 15+5}{12-2}

We handle the numerator and denominator separately, applying the BODMAS rule (Brackets → Orders → Division → Multiplication → Addition → Subtraction) to the numerator.

Step 1: Evaluate the Denominator

The denominator is straightforward:

12-2=10

Step 2: Evaluate the Numerator — Division first

Numerator: 5-35÷5\times 15+5

According to BODMAS, division and multiplication are handled from left to right. First, perform the division:

35÷5=7

The expression becomes:

5-7\times 15+5

Step 3: Evaluate the Numerator — Multiplication next

7\times 15=105

The expression becomes:

5-105+5

Step 4: Evaluate the Numerator — Addition and Subtraction (left to right)

5-105+5=-100+5=-95

Step 5: Divide Numerator by Denominator

\frac{-95}{10}=-9.5

Therefore, the value of the expression is −9.5.