Solving Word Problems Involving Fractions in Equations


This lesson shows how to solve real-world problems where fractions are involved in the equation. It builds directly from Lesson 12 on dividing fractions.


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🔍 Steps to Solve:


1. Read the word problem carefully.


2. Let the unknown number be x.


3. Translate the words into a fraction-based equation.


4. Solve by multiplying by the reciprocal or using the LCM method.


5. State your final answer clearly.


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📘 Example 1:


Problem:

One-third of a number is 9. What is the number?


Solution:

Let the number be x.

(1/3) × x = 9

Multiply both sides by 3:

x = 9 × 3 = 27


✅ Final Answer: 27


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📘 Example 2:


Problem:

Half a number minus 2 equals 3. Find the number.


Solution:

(1/2) × x - 2 = 3

Add 2 to both sides:

(1/2) × x = 5

Multiply both sides by 2:

x = 10


✅ Final Answer: 10


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📘 Example 3:


Problem:

Two-thirds of a number equals 16. What is the number?


Solution:

(2/3) × x = 16

Multiply both sides by 3/2:

x = 16 × (3/2) = 48/2 = 24


✅ Final Answer: 24


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📝 Practice Questions:


1. One-fourth of a number is 5. What is the number?


2. A number divided by 2/5 is 10. Find the number.


3. Three-fifths of a number plus 1 is 7. What is the number?


4. Half of a number equals 12. What is the number?


5. A number divided by 3/4 is 8. What is the number?


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✅ Answers:


1. x = 20


2. x = 10 × (2/5)⁻¹ = 10 × (5/2) = 25


3. x = (7 - 1) × (5/3) = 6 × (5/3) = 10


4. x = 24


5. x = 8 × (3/4) = 6


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📘 Lesson Summary:

These types of problems help apply fraction skills to real situations. Mastering this prepares you for percentages, ratios, and advanced algebra.


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📍 For more lessons visit:

🌐 Blog: https://easymathsteps.blogspot.com

🌐 Website: https://www.easymathsguid.com.ng



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