Question

Use a calculator to evaluate the expression. (Round to two decimal places.)$\frac{11.46-5.37}{3.91}$

Short answer

The answer is 1.56

Step-by-step solution

Perform the Subtraction

The first step is to subtract 5.37 from 11.46. This should give a result of 6.09.

Perform the Division

The next step is to divide this result by 3.91. This would provide the final answer.

Round to Two Decimal Places

The final step is to round the result to two decimal places, if necessary. However, the answer from the division is already a number with two decimal places, so it doesn't require rounding.

Key concepts

Subtraction

Understanding subtraction is essential, as it is one of the fundamental arithmetic operations in mathematics. Subtraction involves finding the difference between two numbers. In the context of our exercise, we subtract the smaller number, 5.37, from the larger one, 11.46.
When subtracting decimals, it's important to align the decimal points vertically before proceeding with the subtraction. You subtract each digit in the column, starting from the right and moving towards the left, borrowing from the neighbor if needed:

• Write down the numbers, one under the other, with the decimal points aligned.
• Subtract each digit, starting from the rightmost digit, moving towards the left.
• If a number you are subtracting is larger than the number above, you need to 'borrow' from the next left digit in the minuend.

The result of our subtraction process is 6.09, which is now used in the subsequent division step in the exercise.

Division

Division is another crucial arithmetic operation, representing a method to split a set into equal parts or groups. In our case, we divide 6.09 by 3.91. Division may seem intimidating with decimals, but it follows the same basic principles as whole number division.
To divide decimals:

• Make sure the divisor (3.91) is a non-decimal number by multiplying both the divisor and dividend (6.09) by a power of 10 that turns the divisor into a whole number.
• Proceed with the typical long division process after that.

For the sake of simplicity with calculators, we often just key in the numbers as they are and rely on the calculator to execute these steps automatically. The resulting quotient from our exercise would be the final value we consider for rounding.

Rounding Decimals

Rounding decimals is a form of approximating to make numbers easier to work with, especially if we don't need an exact figure. Rounding to two decimal places is common in financial calculations or physical measurements where precision beyond hundredths is not necessary.
Here's how to round a number to two decimal places:

• Identify the third decimal place. If this digit is five or higher, add one to the second decimal place.
• If this digit is four or lower, leave the second decimal place as it is.
• Eliminate all digits after the second decimal place.

The exercise's final division result didn't require rounding as it was already to two decimal places. However, knowing how to round is beneficial when dealing with more intricate calculations.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. They are the bedrock of mathematical calculations and play a pivotal role in nearly every field of study and real-world application. Becoming proficient in these basic operations is essential as they form the building blocks for more advanced concepts in mathematics like algebra, calculus, and beyond.
Here are key points about arithmetic operations:

• Understand the correct order to perform operations (order of operations): parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
• Each operation has specific rules and properties that can help simplify calculations, such as the commutative, associative, and distributive properties.

Through the exercise, we used subtraction and division, both vital arithmetic operations, to reach our final answer. Practice with these concepts helps build mathematical fluency.