Ratios & Proportions • Topic 1 of 3

Writing Ratios - Three Forms

What is a Ratio?

A ratio is a comparison of two quantities. It tells us how much of one thing there is compared to another.

Example: In a fruit bowl with 3 apples and 2 oranges:

  • The ratio of apples to oranges is 3 to 2

Three Ways to Write a Ratio:

FormExampleHow to Read
Colon form3:2"3 to 2"
Fraction form3/2"3 halves" or "3 to 2"
Word form3 to 2"3 to 2"

Part-to-Part vs. Part-to-Whole:

TypeMeaningExample (3 apples, 2 oranges, total 5 fruits)
Part-to-PartCompare one part to another partApples to oranges = 3:2
Part-to-WholeCompare one part to the totalApples to total fruits = 3:5
RATIO VISUAL REPRESENTATION:

    Apples:  🍎 🍎 🍎
    Oranges: 🍊 🍊
    
    Apples : Oranges = 3 : 2
    
    ┌─────────────────────────────────────┐
    │  Part-to-Part:     Part-to-Whole:   │
    │                                     │
    │  Apples : Oranges   Apples : Total  │
    │     3    :   2         3    :   5   │
    │                                     │
    │  Oranges : Apples   Oranges : Total │
    │     2    :   3         2    :   5   │
    └─────────────────────────────────────┘


RATIO BAR MODEL:

    Part-to-Part (Apples : Oranges = 3:2)
    
    Apples   │■■■│
    Oranges  │■■│
    
    Part-to-Whole (Apples : Total = 3:5)
    
    Apples   │■■■│
    Total    │■■■■■│


RATIO IN REAL LIFE:

    Recipe: 2 cups flour : 1 cup sugar
    
    Paint: 4 parts blue : 1 part white
    
    Class: 5 boys : 7 girls
    
    Map: 1 inch : 10 miles
Solved Examples
1
Worked Example

In a bag, there are 6 red marbles, 4 blue marbles, and 10 green marbles. Write the ratio of red to blue in all three forms.

Solution
  • Red = 6, Blue = 4
  • Colon: 6:4 (simplifies to 3:2)
  • Fraction: 6/4 (simplifies to (3)/(2))
  • Word: 6 to 4 (or 3 to 2)
  • Answer: 6:4, 6/4, 6 to 4
2
Worked Example

In the same bag, write the ratio of blue marbles to total marbles.

Solution
  • Blue = 4, Total = 6+4+10 = 20
  • Part-to-whole = 4:20
  • Simplify: divide both by 4 = 1:5
  • Answer: 4:20 or 1:5
3
Worked Example

A class has 12 girls and 8 boys. Write the ratio of boys to girls in simplest form.

Solution
  • Boys = 8, Girls = 12
  • Ratio = 8:12
  • Divide both by 4 = 2:3
  • Answer: 2:3

Key Points

  • Ratio compares two quantities
  • Three forms: colon (:), fraction (/), word (to)
  • Part-to-part = one part vs. another part
  • Part-to-whole = one part vs. total
  • Always simplify ratios like fractions
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.A ratio compares:
Explanation: Two quantities.
Q2.The ratio "$3$ to $4$" can be written as:
Explanation: $3:4$ or $\tfrac34$.
Q3.In a ratio, the order of the numbers:
Explanation: Order matters.
Q4.The ratio $6:9$ in simplest form is:
Explanation: Divide by $3$.
Practice more MCQs → 📝 Assignment · 35 marks