Solve proportions

key notes :

1️⃣ What is a Proportion?

  • A proportion is an equation that shows two ratios are equal.
  • Example:

a/b = c/d (where b≠0,d≠0)

  • ✅ Ratios in proportion: Cross products are equal

a×d = b×c

2️⃣ Steps to Solve Proportions

  1. Write the proportion clearly ✏️
    Example: 3/4=x/8
  2. Use cross multiplication 🔄
    3×8 = 4 × x
    24 = 4 x
  3. Solve for the unknown 🧮
    x = 24/4 = 6✅
  4. Check your solution ✔️
    Substitute x=6x = 6x=6 back into the proportion:
    3/4 = 6/8True! ✅

3️⃣ Tips & Tricks

  • Always simplify ratios first ✨
  • Remember: Cross multiplication is key! 🔑
  • If fractions are mixed numbers, convert to improper fractions first 🔢
  • Check your answer by putting it back into the original proportion ✅

4️⃣ Word Problem Strategy 📚

  1. Read carefully and identify ratios 🔍
  2. Assign letters to unknown quantities ✏️
  3. Write a proportion equation
  4. Solve using cross multiplication
  5. Check if answer makes sense 👍

5️⃣ Quick Emoji Memory Aid

  • Proportion = 🔗 Equal Ratios
  • Cross multiply = ✖️🔄
  • Solve for unknown = 🧮
  • Check = ✅

Learn with an exampl

🔔 Solve for n in the proportion.

n/12 = 12/8

n = 

Solve for n in the proportion.

n/12 = 12/8

n/12 ( 12.8 ) = 12/8 ( 12.8 ) Multiply both sides by 12 · 8

8n = 12 · 12 Simplify

8n = 144 Simplify

n = 18 Divide both sides by 8

🔔 Solve for w in the proportion.

45/39 = 30/w

w = 

Solve for w in the proportion.

45/39 = 30/w

45/39 ( 39w ) = 30/w ( 39w ) Multiply both sides by 39w

45w = 39 · 30 Simplify

45w = 1,170 Simplify

w = 26 Divide both sides by 45

Solve for g in the proportion.

15/2 = 45/g

g =

Solve for g in the proportion.

15/2 = 45/g

15/2 (2g) = 45/g (2g) Multiply both sides by 2g

15g = 2 · 45 Simplify

15g = 90 Simplify

g = 6 Divide both sides by 15

Let’s Practice!