Problem 6 - Algebra 1: Concepts and Skills

Question

Write an equation for each question. Do not solve the equation. 13 is 45% of what number?

Step-by-Step Solution

Answer

The equation representing the problem is: \(13 = 0.45 * n\)

Step 1: Understand the problem

In this type of problem, we can understand that '13 is 45% of what number' means that 13 is the result of taking 45% of an unknown number. We can represent the unknown number with a variable, for example 'n'.

Step 2: Translate the problem to an algebraic equation

In mathematical terms, 'is' usually represents the equals sign (=), 'of' indicates multiplication, and the percentage should be expressed as a decimal. Therefore, the sentence '13 is 45% of what number' can be translated to '13 = 0.45 * n'.

Key Concepts

Variables

In algebra, a variable is a symbol used to represent a number that can vary or is unknown. People often use letters like \( n \), \( x \), or \( y \) to denote variables. When working with algebraic equations, variables allow us to model real-world situations where a specific value is not known. Imagine variables like placeholders that turn abstract ideas into mathematical expressions that can be manipulated.
For instance, in the exercise given, we need to find an unknown number, so we use a variable \( n \). This helps in setting up the equation and performing further operations to eventually find the value of \( n \). Using variables makes equations versatile and capable of representing many different scenarios.

Percentages

Percentages are a way of expressing a number as a fraction of 100. The term "percent" comes from the Latin for "per hundred." If you have a percentage, you are essentially dealing with a number divided by 100.
In algebra and the problem we are examining, translating percentages into decimals is a crucial step. For example, 45% is written as '45 per 100' which is equal to 0.45 in decimal form.
This conversion is important because in mathematical equations, decimals are much easier to work with than percentages. Remember these quick tips:

• To convert a percentage to a decimal, divide by 100. So, 45% becomes 0.45.
• Decimals allow for smoother arithmetic operations within an equation.
• Understanding percentages can help bridge the gap between mathematical models and real-life applications.

Translating Words to Equations

Translating words to algebraic equations is like learning a new language. It requires understanding how words often used in everyday language map to mathematical symbols and operations.
Let's break it down using the given problem: '13 is 45% of what number?'

• 'Is' translates to the equals sign \( (=) \).
• '45%' becomes 0.45, turning a percentage into a decimal as previously explained.
• 'Of' indicates multiplication, implying the need to multiply 0.45 by the unknown number.
• The phrase 'what number' refers to our variable \( n \).

This understanding leads us to set up the equation: \( 13 = 0.45 \times n \). By systematically translating each word to its mathematical equivalent, you create a powerful tool for solving real-world problems effectively.