Solve a : b = c : d (leave one blank).
a / b = c / d → a × d = b × c
A proportion is an equation that states two ratios are equal:
a / b = c / d
To solve for any unknown, use cross-multiplication: multiply the value diagonally opposite the unknown, then divide by its diagonal partner.
a = (b × c) / db = (a × d) / cc = (a × d) / bd = (b × c) / aAll four forms are algebraically equivalent and derived from the single cross-multiplication rule: a × d = b × c.
Using the cross-multiplication formula: d = (b × c) / a d = (4 × 9) / 3 d = 36 / 3 d = 12
Result: **d = 12** — The full proportion is 3/4 = 9/12, which simplifies to 3/4 = 3/4. ✓
The calculator found d = 12, meaning the proportion 3/4 = 9/12 holds true. You can verify this by simplifying 9/12: divide numerator and denominator by 3 to get 3/4, which matches the left side. Cross-check: 3 × 12 = 36 and 4 × 9 = 36 — both cross-products are equal, confirming the solution is correct.
A proportion is a statement that two ratios (fractions) are equal. Ratios compare two quantities, and when two ratios are equal, they form a proportion.
Example of equal ratios: 1/2 = 3/6 (both equal 0.5)
The most reliable method to solve a proportion is cross-multiplication. Given a/b = c/d, multiply the numerator of each fraction by the denominator of the other:
a × d = b × c
This eliminates the fractions and gives a simple equation you can solve with basic arithmetic.
Cross-multiply both ratios. If a/b and c/d are proportional, then a × d must equal b × c. If the two products are equal, the ratios are in proportion; if not, they are not proportional.
A unit rate expresses a ratio with a denominator of 1 (e.g., 60 miles per 1 hour). It is a simplified form of a ratio. Proportions can be solved by first finding the unit rate and then scaling up or down.
In similar triangles, corresponding side lengths are proportional. If triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF. You can use the proportion calculator to find any unknown side length.
The 'rule of three' is a classic arithmetic technique for solving a proportion when three values are known and one is unknown — exactly what this calculator does. It's another name for setting up and solving a/b = c/d by cross-multiplication.
Set up a proportion where a = original ingredient amount, b = original recipe yield, c = unknown new ingredient amount, and d = desired new yield. Solve for c: c = (a × d) / b. For example, if a recipe uses 2 cups of flour for 12 cookies and you want 30 cookies: c = (2 × 30) / 12 = 5 cups.
A proportion is an equation showing that two ratios are equal, written as a/b = c/d. It means the relationship between a and b is the same as the relationship between c and d.
Use cross-multiplication: multiply the two numbers that are diagonal from each other (across the equals sign) and set them equal. For example, if a/b = c/d and d is unknown, then d = (b × c) / a.
Yes. You can enter decimal numbers (e.g., 2.5, 0.75) in any of the four fields. If you need to enter a fraction like 1/2, convert it to its decimal equivalent (0.5) before entering.
A **ratio** is a comparison of two quantities (e.g., 3:4 or 3/4). A **proportion** is a statement that two ratios are *equal* (e.g., 3/4 = 9/12). Every proportion contains two ratios.
Yes. Percent problems are a special case of proportions. For example, 'What is 30% of 80?' can be written as 30/100 = x/80. Enter a=30, b=100, c=x (unknown), d=80 to get x = 24.
This happens when a denominator value (b or d) equals zero, or when the equation has no unique solution. Check that you've entered exactly three non-zero values and left only one field blank.
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