The Multiplication Property of Equality
The Multiplication Property of Equality states that multiplying both sides of an equation by the same non-zero number keeps the equation true, allowing you to undo division to isolate a variable. For x/4 = 7, multiply both sides by 4 to get x = 28. This Grade 7 math skill from Saxon Math, Course 2 is one of the four properties of equality (addition, subtraction, multiplication, division) that form the complete toolkit for solving algebraic equations of all types throughout middle and high school mathematics.
Key Concepts
Property For any numbers $a$, $b$, and $c$, if $a = b$, then $ac = bc$. If you multiply both sides of an equation by the same number, you still have equality. To 'undo' division in an equation, we multiply both sides by the number the variable is divided by.
Examples To solve $\frac{x}{7} = 5$, we multiply both sides by 7. This gives $7 \cdot \frac{x}{7} = 7 \cdot 5$, which simplifies to $x = 35$. To solve $\frac{m}{4} = 11$, we multiply both sides by $4$. This gives $4 \cdot \frac{m}{4} = 4 \cdot 11$, which simplifies to $m = 44$. To solve $n \div 3 = 6$, we multiply both sides by $3$. This gives $n \div 3 \times 3 = 6 \times 3$, so $n = 18$.
Explanation If two quantities are perfectly equal, multiplying both by the same amount won't change their equality. We use this trick to cancel out division and solve for a variable that is part of a fraction.
Common Questions
What is the Multiplication Property of Equality?
The Multiplication Property of Equality states that if a = b, then a times c = b times c for any number c. Multiplying both sides of an equation by the same value keeps the equation balanced.
How do I use the Multiplication Property to solve an equation?
To undo division, multiply both sides by the divisor. For x/5 = 12, multiply both sides by 5: x = 60.
Why does multiplying both sides keep the equation balanced?
An equation is like a balance scale. Multiplying the same amount to both sides maintains the balance — both sides increase (or decrease) by the same factor.
When do you use multiplication to solve an equation instead of division?
Use multiplication to solve equations where the variable is divided by a number (x/a = b). Use division to solve equations where the variable is multiplied by a number (ax = b).
When do students learn the Multiplication Property of Equality?
This property is introduced in Grade 6 and formally named and applied in Grade 7. Saxon Math, Course 2 covers it throughout the equation chapters.
What are common mistakes when using the Multiplication Property?
Students sometimes multiply only the term with the variable instead of the entire side, or multiply by the wrong value. Always multiply the complete expression on both sides.
How does the Multiplication Property connect to all four equation-solving properties?
The four properties of equality (addition, subtraction, multiplication, division) each address a different operation applied to the variable. Together they allow solving any one-step or multi-step linear equation.