Order of operations Knowledge-Based Study

Study notes

1. When an arithmetic expression contains both multiplication and division, a standard rule dictates the sequence of calculation to ensure consistent results.

   Equal Priority Rule

   Multiplication and division share the same level of precedence. Neither operation naturally outranks the other.

   • When both operations appear together without grouping symbols, evaluate them strictly from left to right.
   • Do not perform all multiplications before divisions; execute whichever operation appears first when scanning the expression from left to right.

   Consider the expression:

   $24 \div 4 \times 3$

   Follow the steps from left to right:

   1. Evaluate the first operation encountered on the left: $24 \div 4 = 6$.
   2. Substitute this value back into the expression: $6 \times 3$.
   3. Perform the remaining operation: $6 \times 3 = 18$.

   If multiplication were mistakenly performed first, the calculation would yield $24 \div 12 = 2$, which is incorrect.

   The left-to-right rule applies continuously across longer chains of multiplication and division.

   Example

   Evaluate: $40 \div 5 \times 2 \div 4$

   • Step 1: Compute $40 \div 5 = 8$. The expression simplifies to $8 \times 2 \div 4$.
   • Step 2: Compute $8 \times 2 = 16$. The expression simplifies to $16 \div 4$.
   • Step 3: Compute $16 \div 4 = 4$.

   The correct value of the expression is 4.

   Key Takeaway

   Always remember that multiplication does not precede division by default. Treat them as a single tier evaluated in sequential order from left to right.

   Self-Check

   Evaluate the following expression on your own before verifying:

   $36 \div 6 \div 2 \times 5$

   1. $36 \div 6 = 6$
   2. $6 \div 2 = 3$
   3. $3 \times 5 = 15$

   Final Result: 15