What We Mean by “Word Problems Leading to Simple Algebraic Fractions”

A word problem is a story or real-life situation written in words, which must be converted into mathematical form.
A simple algebraic fraction means a fraction whose numerator or denominator includes algebraic terms (letters or variables).
So, this topic teaches us how to read a problem, write it as an algebraic fraction, and then solve it.

Example:
“One-third of a number is 10.” → Equation: (1/3)x = 10
“Amanda spent 2/5 of her money and has ₦60 left.” → Equation: (2/5)x + 60 = x

1. To use algebra in real life problems.


2. To practice translating words into algebraic fractions.


3. To improve equation-solving skills involving fractions.


4. To understand fractions better through applications.


5. Because it is an important topic for exams (BECE, school tests).

1. Identify the unknown in a problem and represent it with a letter.


2. Translate the word problem into an algebraic fraction or equation.


3. Solve for the unknown and simplify if needed.


4. Check that the answer makes sense in the context of the problem.

1. Read the problem carefully and understand what is given and required.


2. Let the unknown quantity be represented by a variable (x, y, n, etc.).


3. Translate the problem into an algebraic equation (often with fractions).


4. Manipulate the equation and clear denominators if necessary.


5. Simplify and solve for the unknown.


6. Substitute back to verify the correctness of the answer.


7. Write the final answer in words.

1. “One-third of x” means (1/3)x.


2. Multiply both sides by the denominator to clear fractions.


3. Look out for words like “left,” “spent,” “remaining,” etc.


4. Denominators must not be zero.


5. Always check your answer by substitution.

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problems Examples (with Steps)

Example 1: One-third of a number is 10. What is the number?

1. Let the number be x.


2. Equation: (1/3)x = 10.


3. Multiply both sides by 3 → x = 30.


4. Answer: 30.

Example 2: Amanda spent (2/5) of her money and has ₦60 left. How much did she have originally?

1. Let her original money be x.


2. Equation: x - (2/5)x = 60.


3. Simplify: (3/5)x = 60.


4. Multiply both sides by 5 → 3x = 300.


5. Divide by 3 → x = 100.


6. Answer: ₦100.

Example 3: A pipe can fill 1/6 of a tank in one hour. How long to fill the whole tank?

1. Let time = t hours.


2. (1/6)t = 1.


3. Multiply both sides by 6 → t = 6.


4. Answer: 6 hours.

Example 4: (3/4) of a number minus 5 equals 7. Find the number.

1. Let the number be x.


2. (3/4)x - 5 = 7.


3. (3/4)x = 12.


4. Multiply both sides by 4 → 3x = 48.


5. x = 16.


6. Answer: 16.

Example 5: A total of ₦x is shared so that 1/3 goes to A, 1/4 to B, and ₦30 remains for C. Find x.

1. Let total = x.


2. Equation: x - [(1/3)x + (1/4)x] = 30.


3. Find LCM of 3 and 4 = 12 → (4/12)x + (3/12)x = (7/12)x.


4. x - (7/12)x = 30 → (5/12)x = 30.


5. Multiply both sides by 12 → 5x = 360.


6. x = 72.


7. Answer: ₦72.

Example 6: (2/5) of a number plus 8 equals 20. Find the number.

1. Let the number be x.


2. (2/5)x + 8 = 20.


3. (2/5)x = 12.


4. Multiply both sides by 5 → 2x = 60.


5. x = 30.


6. Answer: 30.

Common Pitfalls / Mistakes Students Make

1. Misreading key words like “of,” “left,” or “remaining.”


2. Forgetting to multiply both sides when clearing fractions.


3. Leaving denominators zero or answers unsimplified.


4. Failing to check the final answer in the problem.