Cross-multiply is symmetry
If \(a/b = c/d\), then \(ad = bc\). That “X” pattern is just clearing denominators—algebra’s version of balancing a scale.
Balance trick
Proportion Calculator — Solve a:b = c:d
When to use a proportion (and not just a ratio)
- Cross-multiply a:b = c:d to find the missing term with an equality between two ratios.
- Sanity-check ad vs bc to verify the proportion holds after scaling recipes, maps, or mix ratios.
- Direct proportion only: this tool focuses on “together” scaling (inverse proportion needs a different model).
Inputs & Options
Privacy: Everything runs in your browser. Nothing is uploaded.
Result
- Solved value:
- Results will appear here.
- Simplified left (a:b):
- —
- Simplified right (c:d):
- —
- Check (ad vs bc):
- —
How to Read the Diagram
Think of each side as a little fraction:
\( \displaystyle \frac{a}{b} = \frac{c}{d} \)
If one box is empty, we use cross-multiplication (\( a\cdot d = b\cdot c \)) and solve for the missing value.
What Are Proportions?
A proportion is a statement that two ratios are equal. In math notation, we often write it as:
\( \dfrac{a}{b} = \dfrac{c}{d} \)
This means that the relationship between a and b is the same as the relationship between c and d. If one of the four values is missing, we can solve for it using a simple technique called cross-multiplication.
Cross-Multiplication Explained
To solve a proportion, multiply across the equal sign diagonally:
\( a \cdot d = b \cdot c \)
This equation allows us to find the missing value. For example, if we know that \( \tfrac{2}{3} = \tfrac{4}{?} \), cross-multiplication gives us \( 2 \cdot ? = 3 \cdot 4 \). Dividing both sides by 2 shows that the missing value is 6.
Everyday Uses of Proportions
Proportions are more than just abstract math problems—they are tools we use constantly in real life. Recipes are one of the clearest examples: if a cake recipe serves 4 but you need to serve 8, you can double the ratio of each ingredient using proportions. Maps and scale drawings are another common case: the ratio of distances on paper to real-world distances is a proportion. Unit conversions (like inches to centimeters) and even probability problems also rely on proportional reasoning.
Why Proportions Matter
Understanding proportions builds strong number sense and problem-solving skills. They connect fractions, ratios, and algebra in a way that feels natural. By mastering proportions, students can confidently approach word problems, compare quantities, and recognize patterns in data. Whether you are scaling a recipe, reading a map, or interpreting scientific data, proportions help ensure accuracy and fairness.
5 Fun Facts about Proportions
Direct vs inverse
Some relationships scale together (direct), others flip (inverse: \(x \propto 1/y\)). Knowing which saves you from upside-down answers.
Pick the right kind
Maps are just proportions
A 1:50,000 map means 1 cm equals 50,000 cm in reality (500 m). Every map legend is a proportion in disguise.
Scale everywhere
Mixers talk in “parts”
1:3 syrup to soda means any matching units work—teaspoons or litres. Proportions free you from fixed units.
Unit freedom
Check with products
To verify A:B = C:D, compare AD and BC. One quick multiply spots typos before you scale up a design or recipe.
Sanity check
Proportion FAQs
What does a:b = c:d mean?
It says two ratios are equal. Cross-multiplication gives a×d = b×c—that’s the check this tool shows.
Which values can be zero?
b and d cannot be zero (they’re denominators). a or c can be zero as long as the proportion still holds.
Direct vs inverse proportion?
Direct proportion scales together (y ∝ x) and fits a:b = c:d. Inverse proportion flips (y ∝ 1/x) and needs a different setup.
Does it simplify ratios?
Yes. It divides each side by the greatest common divisor (GCD) to show the simplest equivalent ratios.