Find the value of 21 – 18 ÷ 3 · 2.
The correct answer and explanation is:
Let’s solve the expression step-by-step:
Expression:
21 – 18 ÷ 3 · 2
Step 1: Understand the order of operations (PEMDAS/BODMAS)
- Parentheses/Brackets
- Exponents/Orders
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Here, there are no parentheses or exponents, so we handle division and multiplication first, from left to right.
Step 2: Perform division and multiplication from left to right
- The division: 18 ÷ 3 = 6
- Now multiply the result by 2: 6 · 2 = 12
So, the middle part 18 ÷ 3 · 2 simplifies to 12.
Step 3: Substitute back into the expression
Now the expression is:
21 – 12
Step 4: Perform subtraction
21 – 12 = 9
Final answer: 9
Explanation in detail
Mathematical expressions must be evaluated using the correct order of operations to avoid ambiguity. This order ensures everyone solves problems the same way. The acronym PEMDAS or BODMAS helps us remember:
- P/B: Parentheses or brackets first
- E/O: Exponents or orders (powers and roots) next
- MD: Multiplication and division are next and are equal in priority — solve them as they appear from left to right
- AS: Finally, addition and subtraction, also solved left to right.
In the expression 21 – 18 ÷ 3 · 2, no parentheses or exponents exist. So you handle division and multiplication first:
- Divide 18 by 3, yielding 6.
- Multiply 6 by 2, yielding 12.
Once all division and multiplication are done, the only remaining operation is subtraction: 21 – 12 = 9.
If you tried to multiply 3 by 2 first before dividing, you’d get a different answer, which would be incorrect because multiplication and division must be handled from left to right, not simply multiplication before division.
Summary:
Correctly applying the order of operations gives the answer 9.