Equivalent Ratios
Learn how to find and create ratios that represent the same relationship.
Definition
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Worked Examples
Find three ratios equivalent to .
Multiply both parts by 2
and →
Multiply both parts by 3
and →
Multiply both parts by 4
and →
Answer: Three equivalent ratios are , , and
Common Mistakes
Adding the same number to both parts instead of multiplying
Why it's wrong: Adding changes the ratio's value. If becomes (adding 2), these are NOT equivalent.
Correct: Always multiply or divide both parts by the SAME number. (multiplying by 2).
Multiplying only one part of the ratio
Why it's wrong: To keep ratios equivalent, you must apply the same operation to BOTH parts.
Correct: , not or .
Thinking larger numbers mean larger ratios
Why it's wrong: looks bigger than , but they represent the same relationship.
Correct: The size of the numbers does not determine the ratio's value. Always simplify to compare.
Interactive Visual
Ratio Tape Diagram
Adjust the ratio parts using + and - buttons.
Click on the circle to change the fraction
Interactive Sandbox
Expression Calculator
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Practice Problems
16 problemsWhich ratio is equivalent to ?
Why It Matters
- Cooking: If a recipe calls for 2 cups of flour to 3 cups of sugar, you can double it to 4 cups of flour and 6 cups of sugar
- Maps: A scale of 1:100 means 1 cm on the map equals 100 cm in real life
- Mixing: If paint requires a 3:1 ratio of white to blue, you need to keep this ratio no matter how much paint you make
- Shopping: Comparing unit prices uses equivalent ratios to find the best deal
Real World Applications
Scaling Recipes
Chefs use equivalent ratios to adjust recipes for different numbers of servings.
Example:
A recipe for 4 people uses 3 eggs and 2 cups of flour. For 8 people, use 6 eggs and 4 cups of flour (multiply by 2).
A smoothie recipe uses 2 bananas for every 3 cups of milk. You want to make enough for 6 bananas.
How many cups of milk do you need?
Step 1: Write the mathematical expression
If 2 bananas need 3 cups, find the multiplier:
Map Scales
Maps use ratios to represent real distances. A scale of 1:50,000 means 1 cm on the map equals 50,000 cm (or 500 m) in reality.
Example:
On a 1:100 scale map, 5 cm represents 500 cm (5 meters) in real life.
A map has a scale of 1:25,000. Two cities are 8 cm apart on the map.
What is the real distance in kilometers?
Step 1: Write the mathematical expression
Calculate the real distance:
Mixing Paint
Artists mix colors using specific ratios to get consistent shades.
Example:
To make light green, mix blue and yellow in a 1:4 ratio. For 20 ml total, use 4 ml blue and 16 ml yellow.
A shade of orange requires red and yellow paint in a 2:5 ratio. You have 10 ml of red paint.
How much yellow paint do you need?
Step 1: Write the mathematical expression
Find the equivalent ratio:
Key Takeaways
- 1Equivalent ratios express the same relationship between quantities
- 2To create equivalent ratios, multiply or divide BOTH parts by the same number
- 3You can check if ratios are equivalent by simplifying them to lowest terms
- 4Ratio tables help organize and find multiple equivalent ratios
- 5Never add or subtract to find equivalent ratios - only multiply or divide
Frequently Asked Questions
Glossary
- Equivalent ratios
- Two or more ratios that represent the same relationship between quantities
- Ratio table
- A table showing pairs of numbers that all form equivalent ratios
- Simplest form
- A ratio where both terms have no common factors other than 1
- Scale factor
- The number you multiply both parts of a ratio by to get an equivalent ratio