Question

Evaluate each expression. $$ (5-3) \frac{1}{2} $$

Short answer

1

Step-by-step solution

Calculate inside the parentheses

First, evaluate the expression inside the parentheses. In this case, subtract 3 from 5.

Subtract the Numbers

Perform the subtraction: 5 - 3 = 2.

Multiply by \frac{1}{2}

Now, multiply the result from Step 2 by \frac{1}{2}\[2 \times \frac{1}{2} = 1\]

Key concepts

Understanding Parentheses in Arithmetic

Parentheses are used in arithmetic to group parts of an expression that should be evaluated first. This is crucial for following the correct order of operations, often remembered by the acronym PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In the given exercise, \((5 - 3) \frac{1}{2} \), parentheses tell us to first calculate the result of \ 5 - 3 \. This helps in simplifying the expression step-by-step and ensures accuracy in complex calculations.

When you see parentheses in an expression, always perform the calculations inside them first before moving on to the rest. This practice will make solving arithmetic problems easier and more manageable.

Performing Subtraction Step-by-Step

Subtraction is one of the basic arithmetic operations, and it's essential to get it right to ensure the accuracy of your calculations. It involves taking one number away from another, resulting in a difference. In the original exercise, the step inside the parentheses is the subtraction of 3 from 5: \(5 - 3\).

Here are key points to remember about subtraction:

• Start from the right-most digit and move left.
• If the digit you subtract is larger than the digit from which you subtract, you may need to borrow from the next digit.

In our example, 5 minus 3 equals 2. This straightforward operation paves the way for subsequent steps, such as multiplication, as seen in the next part of the exercise.

Basics of Multiplication in Arithmetic

Multiplication is another fundamental operation in arithmetic, symbolized by an 'x' or often by juxtaposition (placing numbers together) as in our exercise. Multiplication involves scaling one number by another. In the exercise, after performing the subtraction \(5 - 3 = 2\), we then multiply the result by \ \frac{1}{2} \.

To multiply by a fraction, you can think of it as dividing by the denominator (bottom number of the fraction) or scaling down the number. So, \ 2 \ times \ \frac{1}{2} \is the same as dividing 2 by 2:

• Consider \ 2 \ as being divided into 2 equal parts by \ \frac{1}{2} \.
• This results in 1 since \ 2 \ divided by 2 equals 1.

Thus, \ 2 \times \frac{1}{2} = 1 \.

Multiplication by fractions often simplifies calculations and helps in breaking down complex problems into manageable steps.