Navigation
Learning how to find ratios that represent the same relationship and organizing them in tables.
Have you ever wondered how a baker makes a tiny cupcake and a giant wedding cake taste exactly the same? It’s not magic—it’s the power of equivalent ratios!
Equivalent ratios are ratios that represent the same relationship between two quantities. Think of them like equivalent fractions; they look different but have the same 'value' or 'flavor.' To find an equivalent ratio, you must multiply or divide both parts of the ratio by the same non-zero number. This is often called the 'Golden Rule' of ratios: whatever you do to one side, you must do to the other! For example, the ratio is the same as or because the relationship (the second number is double the first) never changes.
A recipe for chocolate milk uses scoop of cocoa for every cups of milk. How much do you need for a large party if you want to use scoops of cocoa?
1. Start with the original ratio: . 2. Identify the change: To get from scoop to scoops, you multiply by . 3. Apply the 'Golden Rule': Multiply the milk by as well. 4. Calculate: . 5. The equivalent ratio is ( scoops for cups of milk).
Quick Check
If a ratio is , what is an equivalent ratio if you multiply both parts by ?
Answer
A ratio table is a tool used to organize equivalent ratios. It helps you see patterns and find missing information quickly. Each column (or row) in the table represents an equivalent ratio. You can move from one column to another by multiplying or dividing. For instance, if you know that movie tickets cost $\$2012105$). Ratio tables keep your work neat and prevent mistakes when dealing with multiple sets of numbers.
A car travels miles for every gallons of gas. Let's find how far it goes on gallon and gallons.
Quick Check
In a ratio table, if the ratio of blue paint to yellow paint is , and you use units of blue paint, how much yellow paint do you need?
Answer
units
Sometimes we need to know which ratio is 'better' or 'stronger.' For example, which store has a better deal on soda? To compare ratios, you can use a table to find a common value. If Store A sells cans for $\$25\, you can extend both tables until you find a common number of cans (like ) and then compare the prices. This allows you to make fair comparisons even when the starting numbers are totally different.
Mix A uses cups of concentrate for cups of water. Mix B uses cups of concentrate for cups of water. Which mix is stronger (more concentrate)?
1. Find a common amount of water for both: cups (since ). 2. Scale Mix A: To get cups of water, multiply the ratio by . Result: . 3. Scale Mix B: To get cups of water, multiply the ratio by . Result: . 4. Compare: Mix A has cups of concentrate for cups of water, while Mix B only has . Mix A is stronger!
Which of the following ratios is equivalent to ?
In a ratio table, the first row is and . If the first number in the second row is , what is the second number?
You can create an equivalent ratio by adding the same number to both sides of the ratio.
Review Tomorrow
Tomorrow morning, try to remember the 'Golden Rule' of ratios. If you have a ratio of , what are three other ratios that mean the same thing?
Practice Activity
Next time you are at the grocery store, look at the 'Price per Ounce' on the shelf tags. That is a ratio table in real life! See if you can calculate the price for 10 ounces of your favorite snack.