What are one-step equations using multiplication and division?

📚 What are One-Step Equations?

One-step equations are algebraic equations that can be solved in just one step. When dealing with multiplication and division, the goal is to isolate the variable (usually represented by a letter like $x$) by performing the inverse operation.

📜 A Little History

The concept of solving equations dates back to ancient civilizations. Egyptians and Babylonians used methods to solve linear equations, but the symbolic notation we use today developed gradually through the work of mathematicians like Diophantus and later, Al-Khwarizmi, who is often called the father of algebra.

🧮 Key Principles

• ⚖️ Inverse Operations: Use the opposite operation to isolate the variable. For multiplication, divide; for division, multiply.
• ➗ Division: If the equation involves multiplication, divide both sides by the coefficient of the variable.
• ✖️ Multiplication: If the equation involves division, multiply both sides by the divisor.
• 📝 Maintaining Balance: Whatever you do to one side of the equation, you must do to the other side to keep the equation balanced.

➗ Solving One-Step Equations with Division

Consider the equation $3x = 12$. To solve for $x$, we need to isolate $x$. Since $x$ is being multiplied by 3, we perform the inverse operation, which is division. Divide both sides of the equation by 3:

$\frac{3x}{3} = \frac{12}{3}$

$x = 4$

✖️ Solving One-Step Equations with Multiplication

Consider the equation $\frac{x}{5} = 6$. To solve for $x$, we need to isolate $x$. Since $x$ is being divided by 5, we perform the inverse operation, which is multiplication. Multiply both sides of the equation by 5:

$5 \cdot \frac{x}{5} = 6 \cdot 5$

$x = 30$

💡 Real-World Examples

1. 🍕 Sharing Pizza: If 4 friends want to share a pizza equally and each person gets 3 slices, how many slices were originally in the pizza? Equation: $\frac{x}{4} = 3$. Solution: $x = 12$ slices.
2. 🛍️ Buying Multiple Items: You bought 5 identical items and spent a total of $35. How much did each item cost? Equation: $5x = 35$. Solution: $x = $7 per item.

✔️ Conclusion

One-step equations involving multiplication and division are fundamental algebraic concepts. By understanding inverse operations and maintaining balance, you can easily solve these equations. Keep practicing, and you'll master them in no time!