Do the ratios form a proportion?

Key notes:

🔢 What is a Ratio?

  • A ratio compares two quantities using : , / , or words
  • Example: 2 : 4, 2/4, or 2 to 4 🍎🍎🍎🍎

⚖️ What is a Proportion?

  • A proportion says two ratios are equal
  • Example: 2 : 4 = 3 : 6 ✅

❓ How to Check if Ratios Form a Proportion?
👉 Use cross multiplication ✖️

🧮 If

a/b = c/d

Then check:

a×d = b×c

✅ If both products are equal → They form a proportion 🎉
❌ If not equal → They do NOT form a proportion 🚫

📘 Example 1 (Forms a Proportion)

2/3 = 4/6

👉 Cross multiply:

  • 2×6=12
  • 3×4=12
    ✅ Yes! It is a proportion 😊

📕 Example 2 (Does NOT Form a Proportion)

3/4 = 5/6

👉 Cross multiply:

  • 3×6=18
  • 4×5=20
    ❌ No! Not a proportion 😕

🧠 Quick Tip to Remember
✨ Equal cross products = Proportion ✨

🎯 Real-Life Examples

  • Speed 🚗 (distance : time)
  • Recipes 🍰 (ingredients ratios)
  • Maps 🗺️ (scale drawings)

🌈 Fun Check!

  • Always simplify ratios first if possible ✂️
  • Or use cross multiplication for quick checking ⚡

📚 You’re Ready!

Practice more and proportions will be easy-peasy! 😄📊

Learn with an example

👉 Do the ratios 3/2 and 15/10  form a proportion?

  • yes
  • no

To determine whether the two ratios 3/2 and 15/10 form a proportion, you can compare them using a common denominator.

The denominators are 2 and 10. You can use 10 as the common denominator since 10 is a multiple of 2.

Write 3/2 with a denominator of 10.

3/2 = 3 . 5 / 2 .5 = 15 / 10

So, 3/2 and 15/10 are equal.

This means that the ratios form a proportion.

👉 Do the ratios 1/2 and 7/14 form a proportion?

  • yes
  • no

To determine whether the two ratios 1/2 and 7/14 form a proportion, you can compare them using a common denominator.

The denominators are 2 and 14. You can use 14 as the common denominator since 14 is a multiple of 2.

Write 1/2 with a denominator of 14.

1/2 = 1 . 7 / 2 . 7 = 7/14

So,  1/2 and 7/14 are equal.

This means that the ratios 1/2 and 7/14 form a proportion.

👉 Do the ratios 2/1 and 16/8 form a proportion?

  • yes
  • no

To determine whether the two ratios 2/1 and 16/8 form a proportion, you can compare them using a common denominator.

The denominators are 1 and 8. You can use 8 as the common denominator since 8 is a multiple of 1.

Write 2/1 with a denominator of 8.

2/1 = 2 . 8 / 1 . 8 = 16/8

So, 2/1 and 16/8  are equal.

This means that the ratios 2/1 and 16/8 form a proportion.

let’s practice! 🖊️