Ratio and Proportion

Ratio, rate and proportion are important concepts in mathematics that involve comparing quantities and establishing relationships between them. They have many practical applications in various fields. 

1. What is a Ratio? – A Way to Compare Two Things

A ratio compares two amounts to show how much of one thing is compared to another.

We write ratios in three ways:

• 3 to 2

• 3:2

• 3/2

📌 Important: The order of the words matters in a ratio!
If it says “cats to dogs,” write cats first, then dogs.

Real-Life Examples of Ratios:

Example 1: In a classroom, there are 6 boys and 4 girls.

The ratio of boys to girls is: 6:4

Now simplify the ratio: 6:4 (divide both by 2)

✅ Final Ratio: 3:2

This means that for every 3 boys, there are 2 girls.

🟨 Practice Time: There are 10 apples and 5 oranges. What’s the ratio of apples to oranges?

✅ Answer: 10:5 → 2:1 (simplified)

2. What is a Rate? – A Comparison with Different Units

A rate is like a ratio, but it compares two things with different units.

📌 Think of:

• Miles per hour (mph)

• Dollars per item

• Heartbeats per minute
  
  

You see rates all the time in daily life!

✅ Real-Life Example of a Rate:

Example 2:  You drive 120 miles in 3 hours. What’s your rate?

120 miles /3 hours = 40 miles per hour

✅ Final Answer: 40 mph

Example 3:  You buy 6 bananas for $3. What’s the price per banana?

3 dollars/6 bananas = 0.50 dollars per banana

✅ Final Answer: $0.50 per banana

Practice Time: A box of 8 pens costs $4. What’s the cost per pen?

✅ Answer: $4 ÷ 8 = $0.50 per pen

3. What is a Proportion? – Two Equal Ratios

A proportion is when two ratios or rates are equal to each other. We often use proportions to find missing numbers in word problems.