Proportion Calculator – Solve a:b = c:d
Leave exactly one box blank; we’ll solve it and show the steps.
- Solved value:
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- Simplified left (a:b):
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- Simplified right (c:d):
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- Check (ad vs bc):
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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.