A ratio is a COMPARISON of two quantities

by division

Part-to-Part: Compares one part to another part

Example: 3 boys to 5 girls → 3:5

Part-to-Whole: Compares one part to the total

Example: 3 boys out of 8 total students → 3:8

Equivalent ratios express the SAME relationship

They simplify to the same ratio

Multiply or Divide BOTH terms by the SAME number

Example: Simplify 12:18

A ratio table shows equivalent ratios in an organized way

Each column represents an equivalent ratio

Each column shows equivalent ratios: 3:5 = 6:10 = 9:15 = 12:20

A unit rate compares a quantity to ONE unit

The denominator is always 1

Unit Rate = Total Amount ÷ Number of Units

Example 1: $12 for 3 pounds. Find unit rate.

Example 2: 150 miles in 3 hours. Find unit rate.

Speed = Distance ÷ Time

Distance = Speed × Time

Time = Distance ÷ Speed

DST Triangle:

Cover what you're finding!

Example 1: A car travels 240 miles in 4 hours. Find speed.

Example 2: How far can you travel in 3 hours at 55 mph?

A proportion is an equation stating

that two ratios are EQUAL

a/b = c/d

If a/b = c/d, then a × d = b × c

Problem: 3/4 = x/12

A scale is a ratio that compares:

Drawing measurement : Actual measurement

• 1:50 means 1 cm on drawing = 50 cm in real life

• 1 inch : 10 feet means 1 inch = 10 feet

• 1/4 inch = 1 foot means ¼ inch represents 1 foot

Problem: A map has scale 1 inch : 20 miles. If two cities are 3 inches apart on the map, what's the actual distance?

Method 1: Convert both to unit rates and compare

Method 2: Find equivalent ratios with common denominator

Method 3: Convert to decimals and compare

Problem: Store A: $6 for 2 pounds OR Store B: $10 for 4 pounds

Step 1: Identify what's being compared

Step 2: Write the ratio in correct order

Step 3: Set up proportion if needed

Step 4: Solve using cross-multiplication

Step 5: Check your answer

Problem: A recipe needs 2 cups of flour for 3 cups of sugar. If you use 8 cups of flour, how much sugar do you need?

A visual model using bars (tape) to represent quantities

Helps visualize ratio relationships

Ratio 2:3 shown visually

✓ Order matters in ratios - 2:3 ≠ 3:2

✓ Equivalent ratios: Multiply or divide both parts by same number

✓ Unit rate: Denominator is always 1

✓ Speed formula: Distance ÷ Time

✓ Cross-multiply to solve proportions

✓ Scale drawings: Set up proportion with same units

✓ Comparing rates: Convert to unit rates first

✓ Always simplify ratios to lowest terms

✓ Label your units in rate problems

✓ Check your answer - does it make sense?

Ratio vs Rate:

"Ratios compare same units, rates compare different units!"

Equivalent Ratios:

"Times or divide, keep them alive - both parts change to keep ratio the same!"

Speed Formula:

"Distance divided by time, that's speed every time!"

Cross-Multiplication:

"Cross and multiply, then divide - that's how proportions are solved!"

Unit Rate:

"Per one is what you see, that's a unit rate for me!"

Proportion Check:

"Cross products equal, ratios are sequel!"