Question

Translate to an equation and solve. What percent of 120 is \(48 ?\)

Short answer

Answer: 40%

Step-by-step solution

Formulate the equation

Since we are looking for a percentage, we'll call the percentage "x". To represent the problem as an equation, we can write it in the form: (x / 100) * Total_Number = Given_Number. In this case, "Total_Number" is 120, and "Given_Number" is 48. The equation becomes: (x / 100) * 120 = 48.

Solve for x

We are now solving the equation (x / 100) * 120 = 48 for x. We can multiply both sides by 100 to get rid of the fraction: x * 120 = 4800. Then divide both sides by 120 to isolate x: x = 4800 / 120

Calculate x

Calculate the value of x by dividing 4800 by 120. x = 4800 / 120 = 40. So, x = 40%. Therefore, 48 is 40% of 120.

Key concepts

Understanding Equations

Equations are the foundation of understanding relationships between different mathematical quantities. An equation is a statement that shows the equality between two expressions by linking them with an equals sign ( = ).
In our example, the equation is \((x / 100) \times 120 = 48\), which links the unknown percentage \(x\) with the known total number 120 and the given number 48. Here are some key points to remember about equations:

• Equations can have a variable, like \(x\), representing an unknown value we're trying to find.
• Balancing an equation means making sure the expressions on both sides of the equals sign are equal.
• Operations can be performed on both sides of the equation to isolate the variable.

Understanding how to set up and manipulate equations is crucial in all branches of math, including prealgebra.

How to Solve for x

Solving for \(x\) means finding the value of the variable that makes an equation true. In our example, the equation is \((x / 100) \times 120 = 48\). To solve for \(x\), let's break it down into steps:

• Step 1: Eliminate Fractions
  Multiply both sides of the equation by 100 to remove the fraction: \(x \times 120 = 4800\).
• Step 2: Isolate x
  Divide both sides by 120 to solve for \(x\): \(x = 4800 / 120\).
• Step 3: Calculate
  Perform the division to find \(x = 40\). So, 48 is 40% of 120.

When solving for \(x\), focus on reversing operations to isolate the variable, working through multiplication, division, addition, or subtraction as needed.

Basics of Prealgebra

Prealgebra serves as the bridge between basic arithmetic and algebra. It introduces fundamental algebraic concepts while still relying on basic number operations. Here's a brief overview:

• Introduction to Variables: Prealgebra introduces the idea of variables as symbols that represent numbers. This helps in forming equations and understanding expressions.
• Basic Arithmetic: Core operations like addition, subtraction, multiplication, and division are essential. For example, solving our exercise required multiplication and division to solve for \(x\).
• Understanding Percentages: Prealgebra includes learning how to work with percentages, understanding them as parts of 100, and translating them into equations.

This foundation is crucial as it teaches logical thinking and problem-solving skills that are needed for more advanced algebraic topics.