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Chapter 5: Problem 33

Solve. $$ \frac{x}{3}=\frac{0}{9} $$

Short Answer

Expert verified
x = 0

Step by step solution

01

- Understand the Equation

The given equation is \( \frac{x}{3} = \frac{0}{9} \). Notice that \( \frac{0}{9} = 0 \) because any non-zero number divided by another number (9 in this case) equals 0.
02

- Set Up the Equality

Since \( \frac{x}{3} \) is equal to 0 (from Step 1), we can set up the equation as \( \frac{x}{3} = 0 \).
03

- Solve for x

To find the value of \( x \), multiply both sides of the equation by 3 (the denominator of the fraction). This gives us \( x = 0 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Fractions
Fractions can sometimes look tricky, but they are just another way to represent division. In the equation \( \frac{x}{3} = \frac{0}{9} \), notice that \( \frac{0}{9} \) simplifies to 0. This is because any number divided by 9 (or any other number) that is zero, will give zero. Thus, the equation becomes \( \frac{x}{3} = 0 \). Understanding this simplification helps demystify fractions.
When solving fraction equations:
  • Simplify the fraction on one or both sides if possible.
  • Look for common denominators or ways to simplify the expression.
Remember, fractions show the relationship between the numerator (top number) and the denominator (bottom number).
Understanding Equations
Equations are mathematical statements that show the equality between two expressions. In our exercise, \( \frac{x}{3} = \frac{0}{9} \) means that the expression \( \frac{x}{3} \) on the left is equal to the expression \( \frac{0}{9} \) on the right.
Starting from the given step-by-step solution:
  • First understand both sides of the equation.
  • Recognize that \( \frac{0}{9} \) simplifies to 0.
  • The equation now simplifies to \( \frac{x}{3} = 0 \).
This reveals that equations often need simplification before they can be solved easily.
If we think of equations as balance scales, what we do to one side must be done to the other to keep it balanced. Maintaining this balance is key to solving equations.
Multiplication to Solve Equations
To solve equations involving fractions, multiplication can be a very useful tool. For our simplified equation: \( \frac{x}{3} = 0 \), we use multiplication to clear the fraction.
Here are the steps using multiplication:
  • Identify the denominator of the fraction (in this case, 3).
  • Multiply both sides of the equation by this denominator.
  • This gives us \( 3 * \frac{x}{3} = 3 * 0 \).
  • The left side simplifies to \( x \) because \( 3 * \frac{x}{3} = x \).
  • The right side simplifies to 0.
This results in \( x = 0 \), which is our solution.
Multiplication helps eliminate the denominator, transforming the fraction into a whole number or simpler expression. This makes it easier to solve the equation.

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