Problem 24 - Prealgebra

Question

Find the value of each expression. $$(9-7) \cdot 13$$

Step-by-Step Solution

Answer

The value of the expression is 26.

Step 1: Identify the components of the expression

The given expression is \((9-7) \cdot 13\). In this expression, we have a subtraction inside the parentheses \((9-7)\), and then the result of that subtraction is multiplied by 13.

Step 2: Perform the operation inside the parentheses

Calculate the result of the expression inside the parentheses, which is \(9 - 7\). This equals \(2\).

Step 3: Multiply the result by 13

Take the result from Step 2, which is \(2\), and multiply it by 13. Calculate \(2 \cdot 13 = 26\).

Key Concepts

Order of Operations

When we solve arithmetic expressions, following the correct order of operations is crucial. This ensures that everyone calculates expressions the same way and gets the same result. In mathematics, this is often remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (also from left to right).

In the expression \((9-7) \cdot 13\), the parentheses tell us to do the subtraction first. Therefore, we solve \(9 - 7\)=2
before doing any multiplication. Ignoring the correct order can lead to incorrect results, so always keep PEMDAS in mind.

Basic Arithmetic

Basic arithmetic refers to the simplest and most common mathematical operations: addition, subtraction, multiplication, and division. These operations are the building blocks for all other math topics.

Here's a quick overview of each operation:

• Addition: Combining numbers to get a sum
• Subtraction: Taking away one number from another to get the difference
• Multiplication: Combining sets of equal sizes
• Division: Splitting into equal parts

The original exercise uses basic subtraction and multiplication. With subtraction, we calculated \(9 - 7 = 2\). Then, the result was multiplied by 13, another basic arithmetic operation.

Multiplication

Multiplication is one of the most used arithmetic operations besides addition, subtraction, and division. It essentially involves adding a number to itself a certain number of times. For example, \(2 \cdot 13\) means you add 13 to itself 2 times, which is \(13 + 13\).

Multiplication helps in quickly finding out how many things are there if you have equal groups of items. It's an efficient way of combining numbers, which is why it's used so often.

From our exercise, after solving the parentheses, we multiplied the result by 13 to get 26. Multiplication like this is fundamental and something you'll use in many different areas of math and everyday life.