Multiplication Property of Equality Calculator
Use this calculator to solve for an unknown variable 'x' in an equation of the form x / A = B, applying the multiplication property of equality.
Enter the number that 'x' is being divided by.
Enter the value on the other side of the equality sign.
Calculation Result:
Given the equation:x / ${variableDivisorA} = ${equationRightSideB}
To isolate 'x', we apply the multiplication property of equality by multiplying both sides of the equation by ${variableDivisorA}:
(x / ${variableDivisorA}) * ${variableDivisorA} = ${equationRightSideB} * ${variableDivisorA}
This simplifies to:
x = ${equationRightSideB * variableDivisorA}
Therefore, the Value of x is: ${valueOfX}
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Understanding the Multiplication Property of Equality
The Multiplication Property of Equality is a fundamental concept in algebra that states if you multiply both sides of an equation by the same non-zero number, the equality remains true. In simpler terms, whatever you do to one side of an equation, you must do to the other side to keep the equation balanced.
The Principle
Consider a basic equation: A = B. If this statement is true, then multiplying both sides by any non-zero number C will result in another true statement: A * C = B * C.
This property is incredibly useful for solving equations, especially when an unknown variable is being divided by a number. Its primary application is to "undo" division and isolate the variable.
How It Works in Practice
Let's say you have an equation where a variable, 'x', is being divided by a constant, and you want to find the value of 'x'. For example:
x / 5 = 10
To solve for 'x', you need to get 'x' by itself on one side of the equation. Since 'x' is being divided by 5, the inverse operation is multiplication by 5. According to the multiplication property of equality, if we multiply the left side by 5, we must also multiply the right side by 5:
(x / 5) * 5 = 10 * 5
On the left side, the division by 5 and multiplication by 5 cancel each other out, leaving just 'x'. On the right side, 10 multiplied by 5 equals 50:
x = 50
Thus, the value of 'x' is 50.
Why is the "Non-Zero" Condition Important?
It's crucial that the number you multiply by is non-zero. If you multiply both sides of an equation by zero, you would always get 0 = 0, which is true but doesn't help in solving for a specific variable. For instance, if you had x / 5 = 10 and multiplied by 0, you'd get 0 = 0, losing the original information about 'x'.
Using the Calculator
Our Multiplication Property of Equality Calculator simplifies this process for equations of the form x / A = B:
- Variable's Divisor (A): Enter the number that the unknown variable 'x' is being divided by. For example, if your equation is
x / 7 = 3, you would enter7. - Equation's Right Side (B): Enter the value that appears on the right side of the equality sign. In the example
x / 7 = 3, you would enter3. - Click "Calculate 'x'". The calculator will then display the step-by-step application of the multiplication property and the final value of 'x'.
Examples:
- Example 1: If you have
x / 3 = 12- Variable's Divisor (A):
3 - Equation's Right Side (B):
12 - Calculation:
x = 12 * 3 = 36
- Variable's Divisor (A):
- Example 2: If you have
y / 0.5 = 8- Variable's Divisor (A):
0.5 - Equation's Right Side (B):
8 - Calculation:
y = 8 * 0.5 = 4
- Variable's Divisor (A):
- Example 3: If you have
z / -4 = 6- Variable's Divisor (A):
-4 - Equation's Right Side (B):
6 - Calculation:
z = 6 * -4 = -24
- Variable's Divisor (A):
This property is a cornerstone of algebraic manipulation, allowing you to solve for unknown quantities in a wide range of mathematical and real-world problems.