Meaning of Quantitative Reasoning

Quantitative Reasoning means using numbers, calculation, and mathematics to think clearly and solve real-life problems. It is about understanding quantities (how much, how many), comparing them, making decisions with numbers, and applying maths in everyday situations (not just theoretical maths).

It is more about applying what we know — operations, algebra, fractions, percentages, measurement — to things that happen in real life.

Students learn Quantitative Reasoning because:

1. It helps you solve problems outside school (shopping, cooking, budgeting).


2. It builds skills in thinking with numbers and making sound decisions.


3. It strengthens your ability to use algebra, fractions, percentages, etc., in practical situations.


4. It prepares you for exams that have word problems and real-life scenarios.


5. It supports other subjects (science, economics, geography) that use numbers.

Quantitative Reasoning usually involves several skills:

1. Interpreting word problems: reading, understanding what is asked.


2. Translating real-life situations into mathematical expressions or equations.


3. Using operations (addition, subtraction, multiplication, division) correctly.


4. Working with fractions, decimals, ratios, percentages.


5. Applying algebraic expressions (simple ones) to represent situations.


6. Estimating, checking if answers make sense.


7. Comparing quantities, ordering, proportions.

Here is a simple procedure students are taught to follow when working Quantitative Reasoning questions:

1. Read carefully: Understand every part of the problem (what quantities, what is given, what is asked).


2. Identify the numbers and operations needed (what to add, subtract, multiply, divide).


3. Translate into mathematical form: expressions, equations, or operations.


4. Solve the mathematical form step by step.


5. Check answer: Does it make sense in the real situation? Is the unit correct (e.g. cm, hours, naira)?


6. Write full solution clearly, showing steps so others can follow.

Here are typical kinds of questions / examples used. These reflect what is usually expected:

1. If a bag of rice costs ₦1,600 and you bought 3 bags, how much do you spend?


2. Jane had ₦5,000. She spent ₦1,250 on books and ₦375 on transport. How much money remains?


3. A class has 30 students. If 2/5 of them are girls, how many girls are there?


4. Hong’s salary is increased by 15%. If his old salary was ₦20,000, what is his new salary?


5. If a rectangle has length 12 cm and width 7 cm, what is its perimeter and area?


6. If one kilogram of sugar costs ₦450, how much do 2.5 kg cost?

1. Misreading the question: forgetting some details (e.g. "per", "each").


2. Doing operations in wrong order.


3. Mixing up units (meters vs centimetres; naira vs kobo; hours vs minutes).


4. Using wrong conversion: e.g. decimals and percentages.


5. Giving answers without showing steps.


6. Not checking if the answer makes sense (too big, too small).

How Teachers Can Teach It Well

Some methods that work:

1. Use many real life examples (market, money, cooking, time).


2. Encourage students to explain their reasoning out loud (why they chose a particular operation).


3. Give gradual increase in difficulty: start simple, then more complex word problems.


4. Use group work so students can share ways of solving.


5. Provide worked examples in class with full steps.


6. Give practice questions labeled “Quantitative Reasoning” frequently, and mark explicit parts (read, translate, solve, check).

Assessment and Learning Outcomes

By the end of studying Quantitative Reasoning , students should be able to:

1. Solve word problems involving whole numbers, fractions, decimals, percentages with confidence.


2. Translate everyday situations into algebraic expressions or equations.


3. Use quantitative reasoning to check reasonableness of answers.


4. Apply quantitative reasoning in other areas of mathematics and in other subjects.

Worked Examples — Quantitative Reasoning (Using Algebraic Expressions)

1. Buying Apples

   Problem: A bag of apples costs ₦x. If Bola buys 4 bags and pays ₦2,000 in total, write the expression and find x.

   Translate: Total cost = 4 × price of one bag → 4x.

   Equation: 4x = 2000.

   1. Step 1: Divide both sides by 4 to get x: x = 2000 ÷ 4.
   
   
   2. Step 2 (arithmetic): 2000 ÷ 4 = 500.
   
   
   3. Answer: x = 500. So each bag costs ₦500.
   
   


2. Age Problem

   Problem: Tunde is 5 years older than twice his sister’s age. If the sister’s age is y and Tunde is 19 years, find y.

   Translate: Tunde’s age = 2y + 5.

   Equation: 2y + 5 = 19.

   1. Step 1: Subtract 5 from both sides: 2y = 19 − 5 = 14.
   
   
   2. Step 2: Divide both sides by 2: y = 14 ÷ 2 = 7.
   
   
   3. Answer: Sister is 7 years old.
   
   


3. Sharing Money Equally

   Problem: A man has ₦x. He gives ₦150 to each of his 3 children and has ₦50 left. Write equation and find x.

   Translate: Money given to children = 3 × 150 = 450. Remaining plus given equals total: 450 + 50 = x. Or equation: x − 3(150) = 50.

   1. Step 1: Use x − 450 = 50.
   
   
   2. Step 2: Add 450 to both sides: x = 50 + 450 = 500.
   
   
   3. Answer: x = 500. He had ₦500.
   
   


4. Book and Pen Cost (Expression)

   Problem: A book costs ₦x and a pen costs ₦y. Write an expression for buying 3 books and 4 pens.

   Translate: Cost = 3 × x + 4 × y.

   Answer / Expression: 3x + 4y.

   (If x = 200 and y = 50, evaluate: 3(200) + 4(50) = 600 + 200 = 800.)



5. Distance = Speed × Time

   Problem: A car moves at v km/h for 3 hours. Write expression for distance and evaluate if v = 60.

   Translate: Distance = v × 3 = 3v.

   1. If v = 60: Distance = 3 × 60 = 180 km.
   
   
   2. Answer: Expression: 3v. When v = 60, distance = 180 km.
   
   


6. Perimeter of Rectangle

   Problem: Length = l cm, width = w cm. Write expression for perimeter. If l = 12 and w = 7, find perimeter.

   Translate: Perimeter = 2(l + w).

   1. If values: 2(12 + 7).
   
   
   2. Step 1: Compute inside bracket: 12 + 7 = 19.
   
   
   3. Step 2: Multiply by 2: 2 × 19 = 38.
   
   
   4. Answer: Perimeter = 38 cm.
   
   


7. Simple Profit Problem

   Problem: A trader buys an item for ₦x and sells it for ₦(x + 200). Write expression for profit and find profit when x = 800.

   Translate: Profit = Selling price − Cost price = (x + 200) − x.

   1. Simplify: Profit = 200 (this is constant).
   
   
   2. If x = 800: Profit = 200.
   
   
   3. Answer: Profit = ₦200.
   
   


8. Fraction & Algebraic Expression

   Problem: 1/3 of a number is 10. Let the number be n. Find n.

   Translate: 1/3 · n = 10.

   1. Step 1: Multiply both sides by 3: n = 10 × 3.
   
   
   2. Step 2: n = 30.
   
   
   3. Answer: n = 30.
   
   


9. Using Algebra to Compare Quantities

   Problem: A is x years old. B is 4 years younger than A. Write expression for B’s age. If A is 15, find B.

   Translate: B = x − 4.

   1. If x = 15: B = 15 − 4 = 11.
   
   
   2. Answer: B is 11 years old.
   
   


10. Combining Like Terms in a Problem

    Problem: Mary has x pens. She buys 3 more and then gives 2 to a friend. Write an expression for how many pens she has now. If x = 5, how many?

    Translate: New number = x + 3 − 2.

    1. Simplify expression: x + 1.
    
    
    2. If x = 5: 5 + 1 = 6.
    
    
    3. Answer: Expression x + 1; with x = 5, Mary has 6 pens.
    
    


11. Simple Equation from Word Problem

    Problem: Sum of two consecutive whole numbers is 25. Let the smaller be n. Write equation and find the numbers.

    Translate: Consecutive numbers: n and n + 1. Sum: n + (n + 1) = 25.

    1. Step 1: Combine like terms: 2n + 1 = 25.
    
    
    2. Step 2: Subtract 1: 2n = 24.
    
    
    3. Step 3: Divide by 2: n = 12. Numbers: 12 and 13.
    
    
    4. Answer: The numbers are 12 and 13.
    
    


12. Percent Increase with Algebra

    Problem: A salary is increased by 10% and becomes ₦x. If original salary was ₦20,000, write expression for new salary and check if new salary is ₦22,000.

    Translate: New salary = Original + 10% of original = 20000 + 0.10 × 20000 or 20000(1 + 0.10) = 20000 × 1.10.

    1. Step 1: 20000 × 1.10 = 20000 + 2000 = 22000 (compute: 10% of 20000 = 20000 ÷ 10 = 2000; add gives 22000).
    
    
    2. Answer: New salary = ₦22,000. So yes, x = 22,000.
    
    

Short Tips for Students

1. Always translate words to algebra first: identify unknown (use a letter), write the expression, then solve.


2. Show each step (translate → form expression/equation → manipulate → compute → check).


3. Check answers: plug solutions back if needed to see they fit the problem.