Cross Multiply Calculator
Enter three known values of a proportion (a/b = c/x) to find the unknown value (x).
Understanding the Cross Multiply Calculator
The Cross Multiply Calculator is a tool designed to solve proportions, which are equations stating that two ratios are equal. A common way to represent a proportion is a/b = c/x, where 'a', 'b', and 'c' are known values, and 'x' is the unknown value you want to find.
What is Cross Multiplication?
Cross multiplication is a mathematical technique used to solve for an unknown variable in a proportion. When you have two fractions set equal to each other, a/b = c/x, you can "cross-multiply" by multiplying the numerator of one fraction by the denominator of the other fraction, and setting these products equal to each other. This results in the equation a * x = b * c.
How Does It Work?
Once you have the equation a * x = b * c, you can isolate 'x' by dividing both sides of the equation by 'a'. This gives you the formula: x = (b * c) / a. Our calculator uses this exact formula to quickly find the unknown value 'x' based on the three values you provide.
When to Use Cross Multiplication
Cross multiplication is incredibly useful in various real-world scenarios and mathematical problems:
- Scaling Recipes: If a recipe for 4 people calls for 2 cups of flour, how much flour do you need for 6 people? (2 cups / 4 people = x cups / 6 people)
- Unit Conversions: If 1 inch equals 2.54 centimeters, how many centimeters are in 5 inches? (1 inch / 2.54 cm = 5 inches / x cm)
- Map Scales: If a map scale is 1:10,000 (1 cm on map = 10,000 cm in reality), and two points are 3 cm apart on the map, what's the actual distance? (1 cm / 10,000 cm = 3 cm / x cm)
- Chemistry: Calculating concentrations or stoichiometry in chemical reactions.
- Physics: Solving problems involving ratios, such as force, distance, or time relationships.
Example Calculation
Let's say you have the proportion: 5/10 = 15/x
Here:
- Value A (Numerator 1) = 5
- Value B (Denominator 1) = 10
- Value C (Numerator 2) = 15
Using the cross-multiplication formula x = (b * c) / a:
x = (10 * 15) / 5
x = 150 / 5
x = 30
So, the unknown value 'x' is 30. This means 5/10 = 15/30, which simplifies to 1/2 = 1/2, confirming the proportion is correct.
Use the calculator above to quickly solve your own proportion problems!