Use a calculator to evaluate:
[tex]$\frac{1.5 \times 3 \div 2.4 \times 0.6+2.44}{1.2 \div 12}$[/tex]
Answer (2)
First, calculate the numerator: 1.5 × 3 \tdiv 2.4 × 0.6 + 2.44 = 3.565 .
Then, calculate the denominator: 1.2 \tdiv 12 = 0.1 .
Finally, divide the numerator by the denominator: 0.1 3.565 = 35.65 .
The result of the expression is 35.65 .
Explanation
Understanding the Expression We are asked to evaluate the expression 1.2 \tdiv 12 1.5 × 3 \tdiv 2.4 × 0.6 + 2.44 using a calculator. We will follow the order of operations (PEMDAS) to simplify the expression.
Evaluating the Numerator First, we evaluate the numerator: 1.5 × 3 \tdiv 2.4 × 0.6 + 2.44 . We perform multiplication and division from left to right.
First Multiplication 1.5 × 3 = 4.5
Division 4.5 \tdiv 2.4 = 1.875
Second Multiplication 1.875 × 0.6 = 1.125
Addition 1.125 + 2.44 = 3.565
Evaluating the Denominator Next, we evaluate the denominator: 1.2 \tdiv 12 = 0.1
Final Division Finally, we divide the numerator by the denominator: 0.1 3.565 = 35.65
Examples
In physics, when calculating the overall resistance of a complex circuit, you might need to evaluate a similar expression involving multiple multiplication, division, addition, and subtraction operations. Correctly evaluating such expressions ensures accurate results in circuit analysis and design. Also, when calculating the total cost of items with discounts and taxes, you may need to evaluate expressions with multiple operations to get the final amount.
The evaluated expression gives a result of 35.65. First, the numerator is calculated as 3.565, and the denominator as 0.1, leading to the final division. This process highlights the importance of following the order of operations in mathematics.
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