Fractions Solve for Unknown X

How the Fractions Solve for Unknown X Works:

The calculator operates by applying the concept of cross-multiplication to solve for the unknown variable $x$. This is based on the mathematical property that two fractions are equal if their cross-products are equal:

$$\frac{a}{b} = \frac{c}{d} \implies a \cdot d = b \cdot c$$

Given any three known values and one unknown $x$, the calculator rearranges the equation and solves for $x$ using cross-multiplication.

Steps to Use:

1. Input the Known Values: Enter three known values among the four: two numerators and two denominators.
2. Enter the Unknown Variable: Use “x” (or any other letter) for the position of the unknown variable.
3. Calculate: Click “Calculate” to find the value of $x$.
4. View the Answer: The calculator will display the answer as a fraction formula and the simplified numerical value of $x$.

Examples and Formulas:

1. Example 1: Solving for a Missing Numerator

   $$\frac{x}{6} = \frac{4}{12}$$

   Here, the missing value is $x$ in the first fraction’s numerator.

   Step 1: Cross Multiply

   $$x \times 12 = 6 \times 4$$$$12x = 24$$

   Step 2: Solve for $x$

   $$x = \frac{24}{12} = 2$$

   Result: $x = 2$
   

2. Example 2: Solving for a Missing Denominator

   $$\frac{3}{x} = \frac{5}{15}$$

   Here, $x$ is the unknown denominator of the first fraction.

   Step 1: Cross Multiply

   $$3 \times 15 = x \times 5$$$$45 = 5x$$

   Step 2: Solve for $x$

   $$x = \frac{45}{5} = 9$$

   Result: $x = 9$
   

3. Example 3: Solving for $x$ in Any Position Suppose you have:

   $$\frac{8}{10} = \frac{x}{15}$$

   Here, $x$ is the unknown numerator of the second fraction.

   Step 1: Cross Multiply

   $$8 \times 15 = 10 \times x$$$$120 = 10x$$

   Step 2: Solve for $x$

   $$x = \frac{120}{10} = 12$$

   Result: $x = 12$