Problem 583 - Prealgebra

Question

Simplify. $$45+23$$

Step-by-Step Solution

Answer

68

Step 1: Write the Expression

Start by writing down the given expression: 45 + 23

Step 2: Add the Numbers

Add the two numbers together: 45 + 23 = 68

Key Concepts

Addition

Addition is one of the four fundamental arithmetic operations. It involves combining two or more numbers to get a total sum. When you are adding whole numbers, align them by their rightmost digits and add each column, carrying over any value that exceeds ten to the next left column. For example, with the problem given in the exercise:

First, align the numbers vertically:

45
+ 23
__

Then add each column, starting from the rightmost digit (units):

5 (units) + 3 (units) = 8
4 (tens) + 2 (tens) = 6

So the final result is 68.

Arithmetic

Arithmetic is the branch of mathematics dealing with basic number operations including addition, subtraction, multiplication, and division. It is foundational for more complex mathematical concepts. In our example, the primary operation is addition. Understanding how different operations interact with numbers helps to simplify various mathematical problems.

Key points to remember:

• Addition is commutative, meaning the order of the numbers doesn't change the result, i.e., 45 + 23 = 23 + 45.
• Addition is associative, so you can group the numbers in any way, e.g., (45 + 23) + 0 = 45 + (23 + 0).

Using these properties can sometimes make calculations easier.

Simplification

Simplification means reducing a mathematical expression to its simplest form. For arithmetic operations, it involves performing the operations in accordance with the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents (or Orders), Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Although our given problem involves just simple addition, in more complex problems you might follow these steps:

• Identify and perform any operations contained within parentheses first.
• Apply any exponents.
• Carry out multiplication and division operations from left to right.
• Finally, execute addition and subtraction operations from left to right.

By following this order, you ensure that you simplify expressions correctly. In the example of 45 + 23, since no other operations are involved, we directly add the numbers to get the simplified result of 68.