How do you solve a proportion like 2/5 = x/20?

Using cross-multiplication: 1. (2 * 20) = (5 * x) 2. 40 = 5x 3. Divide both sides by 5: x = 40 / 5 4. x = 8

What is a statistical proportion calculator?

A statistical proportion is a different concept. It refers to the fraction of a population that has a certain characteristic (e.g., 60% of voters). Statistical proportion calculators are used to find confidence intervals or appropriate sample sizes for surveys, not to solve algebraic ratios.

Proportion Calculator

Q: What is a proportion?

A proportion is an equation that states that two ratios are equal. A ratio is a comparison of two numbers (e.g., A/B or A:B). A proportion sets two of these ratios equal, such as A/B = C/D.

Q: What is the formula for solving a proportion?

The main method for solving a proportion is called cross-multiplication (or the Means-Extremes Property). For the proportion A/B = C/D, the formula is A * D = B * C. You can then solve for any of the four variables.

Q: What is a real-life example of a proportion?

A common example is scaling a recipe. If a recipe for 12 cookies requires 2 cups of flour, and you want to make 36 cookies, you can set up a proportion: (12 cookies) / (2 cups) = (36 cookies) / (x cups) 12 * x = 2 * 36 12x = 72 x = 6 cups of flour.

This calculator solves algebraic proportions, which are equations involving two equal ratios. To use it, enter three known values and one unknown value (use 'x' or leave the box blank) in the format $A/B = C/D$. The calculator will solve for the missing variable and show the steps.

Enter three numbers and 'x' (or leave one box blank) for the unknown.

What is a Proportion?

A proportion is a statement that two ratios or fractions are equal. It is an equation that can be written in two forms:

Fraction Form: $\frac{A}{B} = \frac{C}{D}$
Ratio Form: $A : B = C : D$

In both forms, $A$ and $D$ are called the "extremes," and $B$ and $C$ are called the "means." A proportion is used to find a missing value when two quantities scale up or down at the same rate. For example, if you are scaling a recipe or reading a map, you are using proportions.

How to Solve a Proportion (Cross-Multiplication)

The easiest way to solve a proportion is by using **cross-multiplication**. This is also known as the "Means-Extremes Property."

For any proportion $\frac{A}{B} = \frac{C}{D}$, the product of the means equals the product of the extremes:

$A \times D = B \times C$

To solve for an unknown value (like $x$), you can rearrange this formula.

Example: Solve for $x$ in $\frac{2}{5} = \frac{x}{20}$

Set up the equation: $A=2$, $B=5$, $C=x$, $D=20$
Cross-multiply: $2 \times 20 = 5 \times x$
Simplify: $40 = 5x$
Isolate $x$: $x = \frac{40}{5}$
Solve: $x = 8$

Example: Solve for $x$ in $\frac{3}{10} = \frac{15}{x}$

Set up the equation: $A=3$, $B=10$, $C=15$, $D=x$
Cross-multiply: $3 \times x = 10 \times 15$
Simplify: $3x = 150$
Isolate $x$: $x = \frac{150}{3}$
Solve: $x = 50$

Algebraic vs. Statistical Proportions

It's important to know that this calculator solves **algebraic proportions** (ratios). This is different from **statistical proportions**, which relate to percentages or fractions of a population (e.g., "60% of voters"). Calculators for statistical proportions are used to find things like confidence intervals or the sample size needed for a survey.

Proportion Calculator

Result

Step-by-Step Calculation

What is a Proportion?

How to Solve a Proportion (Cross-Multiplication)

Example: Solve for $x$ in $\frac{2}{5} = \frac{x}{20}$

Example: Solve for $x$ in $\frac{3}{10} = \frac{15}{x}$

Algebraic vs. Statistical Proportions

Frequently Asked Questions (FAQ)

What is the formula for solving a proportion?

How do you solve a proportion with x on the bottom?

What is a real-life example of a proportion?

What is the difference between a ratio and a proportion?