Problem 8 - Elementary Algebra

Question

Use the order of operations to simplify the following. $$ 3^{2}+4 \cdot 5 $$

Step-by-Step Solution

Answer

Question: Simplify the expression: \(3^2 + 4 \cdot 5\) Answer: The simplified expression is \(29\).

Step 1: Calculate the Exponent

We have an exponent \(3^2\), which means \(3\) multiplied by itself \(2\) times. Calculate the value of the exponent: $$ 3^2 = 3 \cdot 3 = 9 $$

Step 2: Calculate the Multiplication

Next, we have a multiplication \(4 \cdot 5\). Calculate the value of the multiplication: $$ 4 \cdot 5 = 20 $$

Step 3: Perform Addition

Now that we have simplified the exponent and multiplication operations, we can perform the addition: $$ 9 + 20 = 29 $$ So, the simplified expression is \(29\).

Key Concepts

Understanding Exponents

Exponents may seem challenging at first, but they are simply a way to express repeated multiplication. When you see a number with an exponent, you are multiplying that number by itself a specific number of times.
For instance, in the expression \(3^2\), the number 3 is called the base, and the number 2 is the exponent. What this means is we need to multiply the base, 3, by itself 2 times.
So, \(3^2\) is calculated as:

• 3 multiplied by 3
• which is 9

Remember, the exponent tells you how many times to use the base in a multiplication. Mastering this concept will help you solve more complicated math problems with ease.

Basics of Multiplication

Multiplication is one of the basic operations in math, just like addition and subtraction. It is a quick way of adding the same number several times.
When multiplying numbers, you have two numbers: the multiplicand and the multiplier. The order does not affect the outcome, making multiplication a commutative operation.
In the problem \(4 \cdot 5\), the number 4 is multiplied by 5, which can be thought of as adding 4, five times.

• This results in 20
• It's the same as 4 + 4 + 4 + 4 + 4

Understanding multiplication is crucial as it lays the foundation for more advanced mathematical operations.

The Role of Addition

Addition is a fundamental mathematical operation that combines two numbers to make a larger one. It forms the basis of many other math concepts, such as algebra and arithmetic.
In the expression \(9 + 20\), we simply add two numbers together to find the sum, which is straightforward and common in everyday math problems.

• Calculate 9 plus 20
• The result is 29

Addition is simple yet essential. It helps in understanding how to build numbers up and contributes to the broader concept of number operations, which include subtraction, multiplication, and division.