Ratios & Proportions • Topic 3 of 3

Ratio Tables and Double Number Lines

What is a Ratio Table?

A ratio table is an organized way to list equivalent ratios. It helps you see patterns and solve problems.

Example: Ratio of apples to oranges = 3:2

Apples3691215
Oranges246810

What is a Double Number Line?

A double number line shows two quantities on parallel lines. It's great for visualizing ratios!

Example: 3 cups flour : 2 cups sugar

Flour:    0    3    6    9    12   15
          ├────┼────┼────┼────┼────┤
Sugar:    0    2    4    6    8    10
RATIO TABLE - BUILDING EQUIVALENTS:

 Start with 3:2
 
 ×2 → 6:4
 ×3 → 9:6
 ×4 → 12:8
 ×5 → 15:10
 
 As a table:
 
 ┌─────────┬────┬────┬────┬────┬────┐
 │ Apples │ 3 │ 6 │ 9 │ 12 │ 15 │
 ├─────────┼────┼────┼────┼────┼────┤
 │ Oranges │ 2 │ 4 │ 6 │ 8 │ 10 │
 └─────────┴────┴────┴────┴────┴────┘
 
 +3 each time +2 each time


DOUBLE NUMBER LINE - STEP BY STEP:

 Problem: A car travels 30 miles per 1 hour.
 How far in 2.5 hours?
 
 Miles: 0 15 30 45 60 75
 ├─────┼─────┼─────┼─────┼─────┤
 Hours: 0 0.5 1 1.5 2 2.5
 
 Answer: At 2.5 hours → 75 miles


FINDING MISSING VALUES USING RATIO TABLE:

 Problem: 5 tickets cost 20. How much for 8 tickets?
 
 ┌─────────┬────┬────┬────┬────┐
 │ Tickets │ 5 │ 1 │ 8 │ │
 ├─────────┼────┼────┼────┼────┤
 │ Cost() │ 20 │ 4 │ 32 │ │
 └─────────┴────┴────┴────┴────┘
 
 Step 1: Find unit rate (÷5): 4 per ticket
 Step 2: Multiply for 8 tickets (×8): 32
Solved Examples
1
Worked Example

Complete the ratio table for the ratio 4:7

First48121620
Second7?21?35
Solution
  • Multiply both by 2: 8 → 14
  • Multiply both by 4: 16 → 28
  • Answer: 14 and 28
2
Worked Example

Use a double number line to solve: A recipe uses 2 eggs for every 3 cups of flour. How many eggs for 9 cups of flour?

Solution

``` Eggs: 0 2 4 6 ├────┼────┼────┼────┤ Flour: 0 3 6 9 ```

  • Answer: 6 eggs
3
Worked Example

A store sells 3 shirts for 45. Use a ratio table to find the cost of 7 shirts.

Solution
Shirts317
Cost4515105
  • Unit rate: 15 per shirt
  • 7 shirts: 7 × 15 = 105
  • Answer: 105

Key Points

  • Ratio tables list equivalent ratios in rows/columns
  • Multiply or divide both quantities by same number
  • Double number lines show two quantities on parallel lines
  • Both methods help find missing values
  • Unit rate = value of 1 unit (divide by first term)
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A ratio table lists:
Explanation: Equivalent ratios.
Q2.A double number line shows:
Explanation: Two related quantities.
Q3.Each column of a ratio table keeps the same:
Explanation: Same ratio.
Q4.In the table $2:6,\ 4:?$, the missing number is:
Explanation: $\times2$ of $6$.
Practice more MCQs → 📝 Assignment · 35 marks