📖Definition
A proportion is an equation stating that two ratios are equal. It shows that two fractions or ratios have the same value. Proportions are written as a/b = c/d or a:b = c:d, and can be solved using cross multiplication.
📐Formula
When two ratios are equal, their cross products are equal. If a/b = c/d, then ad = bc. This is called cross multiplication and is used to solve for unknown values.
📝Step-by-Step Guide
Set Up the Proportion
Write the two ratios as equal fractions. Make sure corresponding quantities are in the same positions.
Cross Multiply
Multiply the numerator of one fraction by the denominator of the other.
Solve for the Unknown
Use algebra to isolate the variable.
Check Your Answer
Substitute back to verify both ratios are equal.
⚠️Common Mistakes to Avoid
- Setting up ratios with quantities in wrong positions
- Cross multiplying incorrectly
- Mixing up units in word problems
- Not checking if the answer makes sense
- Confusing proportions with simple equations
✏️Practice Problems
Solve for x: 3/4 = x/12
Answer: x = 9
If 5 apples cost $3, how much do 8 apples cost?
Answer: $4.80
A map scale is 1 inch : 50 miles. Two cities are 3.5 inches apart on the map. How far apart are they?
Answer: 175 miles
Printable Proportions practice
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