Evaluate the expression. 7.2 + 6.3(5.4 – 6)
The correct answer and explanation is:
Let’s evaluate the expression step by step:
Expression:
7.2+6.3(5.4−6)7.2 + 6.3(5.4 – 6)
Step 1: Evaluate the parentheses
Calculate the value inside the parentheses first: 5.4−6=−0.65.4 – 6 = -0.6
Step 2: Multiply
Now multiply 6.3 by the result from Step 1: 6.3×(−0.6)=−3.786.3 \times (-0.6) = -3.78
Step 3: Add
Finally, add 7.2 to the product from Step 2: 7.2+(−3.78)=7.2−3.78=3.427.2 + (-3.78) = 7.2 – 3.78 = 3.42
Final answer:
3.42\boxed{3.42}
Explanation (300 words)
When evaluating mathematical expressions, it is important to follow the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
Here, the expression involves addition and multiplication, with a subtraction inside parentheses. According to the order of operations, we first simplify the expression inside the parentheses: 5.4−65.4 – 6. Subtraction here yields −0.6-0.6.
Next, multiplication must be done before addition. We multiply 6.3 by −0.6-0.6, which results in −3.78-3.78. Multiplying a positive number by a negative number results in a negative product, hence the negative sign.
Finally, we add 7.2 to the product −3.78-3.78. Addition of a negative number is equivalent to subtraction, so this becomes 7.2−3.787.2 – 3.78, which equals 3.42.
Understanding how to apply the order of operations ensures accurate results. Mistakes commonly occur if one tries to perform addition before multiplication or ignores the parentheses, leading to incorrect answers.
This expression also shows the importance of handling decimal numbers carefully, ensuring precise arithmetic to get the right answer.
In summary, by following the proper steps—simplify parentheses, multiply, then add—we correctly evaluate the expression as 3.42.