Simplify $15-3(6-4)$
A) 9
B) 3
C) 24
D) 68
Answer (2)
First, evaluate the expression inside the parentheses: 6 − 4 = 2 .
Next, perform the multiplication: 3 × 2 = 6 .
Then, perform the subtraction: 15 − 6 = 9 .
The simplified expression is 9 .
Explanation
Understanding the problem We are asked to simplify the expression 15 − 3 ( 6 − 4 ) . To do this, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Simplifying parentheses First, we simplify the expression inside the parentheses: ( 6 − 4 ) = 2 .
Performing multiplication Next, we perform the multiplication: 3 ( 6 − 4 ) = 3 ( 2 ) = 6 .
Performing subtraction Finally, we perform the subtraction: 15 − 3 ( 6 − 4 ) = 15 − 6 = 9 .
Final Answer Therefore, the simplified expression is 9.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a series of actions. For instance, if you are buying items at a store with a discount and then paying sales tax, the order in which you apply the discount and tax matters. If an item costs $20, has a 20% discount, and then a 5% sales tax, you first calculate the discount: $20 \times 0.20 = $4, so the discounted price is $20 - $4 = $16. Then, you apply the sales tax: $16 \times 0.05 = $0.80, so the final price is $16 + $0.80 = $16.80. Following the correct order ensures you pay the correct amount.
The simplified expression of 15 − 3 ( 6 − 4 ) is 9. By following the order of operations, we first evaluate the parentheses, then perform multiplication, and finally carry out the subtraction. Therefore, the correct answer is option A) 9.
;
