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Chapter 4: Problem 28

Solve the equations. Write the answers as fractions or whole numbers. $$\frac{a}{4}=12$$

Short Answer

Expert verified
a = 48

Step by step solution

01

Understand the Equation

The given equation is \( \frac{a}{4} = 12 \). This means that when \( a \) is divided by 4, it equals 12.
02

Isolate the Variable

To find the value of \( a \), multiply both sides of the equation by 4. This will cancel the 4 on the left side.
03

Perform the Multiplication

Multiply both sides: \( \frac{a}{4} \times 4 = 12 \times 4 \). This simplifies to \( a = 48 \).

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Key Concepts

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

Equation Solving
Solving linear equations is a fundamental skill in algebra. Equations are math statements where two expressions are equal. For example, in the equation \( \frac{a}{4} = 12 \), we have two equal expressions: \( \frac{a}{4} \) and 12. To solve such equations, you need to find the value of the unknown variable that makes the equation true. Remember, the main goal is to 'solve' to find the value of the unknown that balances the equation. This process involves several steps which often include isolating the variable and performing calculations to simplify the equation.
Isolating Variables
Isolating the variable means rearranging the equation so that the unknown variable is on one side by itself. In the equation \( \frac{a}{4} = 12 \), the variable is 'a'.
  • Step 1: Identify the variable you need to solve for. In our example, it鈥檚 'a'.
  • Step 2: Undo any operations that are affecting the variable. Here, 'a' is divided by 4.
To undo division by 4, you multiply both sides of the equation by 4. This step helps to remove the fraction and simplifies your work. So, multiplying both sides, we get \( \frac{a}{4} \times 4 = 12 \times 4 \), which simplifies to \( a = 48 \).
Multiplication in Equations
Multiplication is a common step in solving equations, especially when trying to eliminate fractions. In the equation \( \frac{a}{4} = 12 \), to clear the fraction, multiply both sides by 4. This action helps because multiplying by 4 cancels out the division by 4 on the left side:
  • \( \frac{a}{4} \times 4 = a \) (since dividing then multiplying by the same number cancels out).
  • On the right side, \( 12 \times 4 = 48 \).
By performing this multiplication, we successfully isolate the variable: \( a = 48 \). This makes solving the equation straightforward without complex fractions. Using multiplication is key to simplifying and solving equations efficiently. Remember: always perform the same operation on both sides to maintain the equation's balance.

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