Multiplication Property of Equality
Use the multiplication property of equality in Grade 9 algebra. Multiply both sides of an equation by the same nonzero value to isolate variables and solve fractional equations.
Key Concepts
Property Both sides of an equation can be multiplied by the same number, and the statement will still be true. $a=b$, so $ac=bc$.
Examples To solve $\frac{x}{6} = 8$, multiply both sides by 6: $6 \cdot \frac{x}{6} = 8 \cdot 6$, which simplifies to $x = 48$. For $ 11 = \frac{1}{4}w$, multiply both sides by 4: $4 \cdot 11 = 4 \cdot \frac{1}{4}w$, which gives you $ 44 = w$.
Explanation Imagine an equation is a balanced scale. If you add weight to one side, you have to add the same weight to the other to keep it level. The Multiplication Property is the same idea! Multiplying both sides by the same number keeps your equation perfectly balanced and true, letting you solve for the variable.
Common Questions
What is the multiplication property of equality?
If a = b, then a × c = b × c for any nonzero c. You can multiply both sides by the same number without changing the solution — key for equations with fractions.
How do you use the multiplication property to solve equations with fractions?
Multiply both sides by the denominator or LCD to clear fractions. For x/3 = 5, multiply both sides by 3: x = 15. This eliminates fractions and simplifies solving.
When should you use multiplication vs. division to solve an equation?
Use multiplication when the variable is divided by a number (multiply to clear the denominator). Use division when the variable is multiplied by a number (divide to isolate it).