Meaning of Quantitative Reasoning

Quantitative reasoning is the ability to understand and use numbers and mathematical concepts to solve problems in real life. It helps us make sense of numerical information, analyze data, and make decisions based on calculations.

It is used in everyday life, school, work, and many practical situations, such as shopping, budgeting, cooking, and planning.

1. To solve real-life problems using numbers.


2. To analyze and interpret data correctly.


3. To make decisions based on calculations.


4. To improve logical thinking and problem-solving skills.


5. To prepare for exams that involve word problems.

Ratio

A ratio shows the relationship between two or more quantities.

Example: If a classroom has 12 boys and 8 girls, the ratio of boys to girls = 12:8 = 3:2

Proportion

Proportion is an equation that shows two ratios are equal.

Example: If 3 pencils cost ₦60, how much do 5 pencils cost?

3/60 = 5/x ⇒ x = (5 × 60) / 3 = ₦100

Percentage

Percentage shows a part of 100.

Example: A student scored 45 out of 60 marks. What is the percentage?

Percentage = (45 ÷ 60) × 100 = 75%

Profit and Loss

Profit = Selling Price − Cost Price

Loss = Cost Price − Selling Price

Percentage Profit = (Profit ÷ Cost Price) × 100

Percentage Loss = (Loss ÷ Cost Price) × 100

Simple Interest

Formula: SI = (P × R × T) ÷ 100

• P = Principal (amount borrowed or invested)


• R = Rate of interest per year


• T = Time in years

Speed, Distance, and Time

Formula: Speed = Distance ÷ Time

Rearranged formulas:

• Distance = Speed × Time


• Time = Distance ÷ Speed

Estimation

Making approximate calculations to simplify problems.

Example: 198 + 205 ≈ 200 + 200 = 400

Ratio of Quantities in Recipes or Mixtures

Example: To make juice, 3 litres of water is mixed with 2 litres of sugar syrup. The ratio is 3:2.

Scaling Up or Scaling Down

Example: A recipe for 4 people needs 200g flour. How much is needed for 6 people?

Amount = (200 × 6) ÷ 4 = 300g

Average / Mean

Formula: Average = Sum of quantities ÷ Number of quantities

Example: The scores of 5 students are 40, 45, 50, 55, 60. Average = (40+45+50+55+60) ÷ 5 = 50

1. A shop sold 120 pencils in 4 days. How many pencils did they sell per day?
   
   Step 1: Identify total pencils and number of days. Total pencils = 120, Days = 4.
   
   Step 2: Use the formula: Pencils per day = Total pencils ÷ Number of days.
   
   Step 3: Substitute the values: 120 ÷ 4.
   
   Step 4: Calculate: 120 ÷ 4 = 30.
   
   Answer: 30 pencils/day


2. A classroom has 18 boys and 12 girls. Find the ratio of boys to girls.
   
   Step 1: Identify numbers: Boys = 18, Girls = 12.
   
   Step 2: Write the ratio: Boys : Girls = 18 : 12.
   
   Step 3: Simplify the ratio by dividing both numbers by their GCD (6): 18 ÷ 6 : 12 ÷ 6 = 3 : 2.
   
   Answer: 3 : 2


3. A man bought a bag of rice for ₦25,000 and sold it for ₦28,500. Find profit and percentage profit.
   
   Step 1: Identify Cost Price (C.P.) = 25,000 and Selling Price (S.P.) = 28,500.
   
   Step 2: Calculate profit: Profit = S.P. − C.P. = 28,500 − 25,000 = ₦3,500.
   
   Step 3: Calculate percentage profit: Percentage Profit = (Profit ÷ C.P.) × 100 = (3,500 ÷ 25,000) × 100.
   
   Step 4: Calculate: 3,500 ÷ 25,000 = 0.14 → 0.14 × 100 = 14%.
   
   Answer: Profit = ₦3,500; Percentage Profit = 14%


4. A student scored 48 out of 60. Find the percentage.
   
   Step 1: Identify marks obtained = 48, total marks = 60.
   
   Step 2: Use the formula: Percentage = (Marks obtained ÷ Total marks) × 100.
   
   Step 3: Substitute: (48 ÷ 60) × 100.
   
   Step 4: Calculate: 48 ÷ 60 = 0.8 → 0.8 × 100 = 80%.
   
   Answer: 80%


5. A loan of ₦50,000 was borrowed at 5% per year for 3 years. Find simple interest.
   
   Step 1: Identify principal (P) = 50,000, rate (R) = 5%, time (T) = 3 years.
   
   Step 2: Use formula: SI = (P × R × T) ÷ 100.
   
   Step 3: Substitute: (50,000 × 5 × 3) ÷ 100.
   
   Step 4: Calculate: 50,000 × 5 = 250,000 → 250,000 × 3 = 750,000 → 750,000 ÷ 100 = 7,500.
   
   Answer: ₦7,500


6. A car travels 180 km in 3 hours. Find its speed.
   
   Step 1: Identify distance = 180 km, time = 3 hours.
   
   Step 2: Use formula: Speed = Distance ÷ Time.
   
   Step 3: Substitute: 180 ÷ 3.
   
   Step 4: Calculate: 180 ÷ 3 = 60.
   
   Answer: 60 km/h


7. A recipe for 4 people needs 200 g sugar. How much for 10 people?
   
   Step 1: Identify original quantity = 200 g, original servings = 4, new servings = 10.
   
   Step 2: Use formula: Amount for new servings = (Original quantity × New servings) ÷ Original servings.
   
   Step 3: Substitute: (200 × 10) ÷ 4.
   
   Step 4: Calculate: 200 × 10 = 2000 → 2000 ÷ 4 = 500 g.
   
   Answer: 500 g


8. Estimate 198 + 307.
   
   Step 1: Round numbers to nearest convenient values: 198 ≈ 200, 307 ≈ 300.
   
   Step 2: Add rounded numbers: 200 + 300 = 500.
   
   Answer: Approximately 500


9. Find the average of these numbers: 12, 15, 18, 20, 25.
   
   Step 1: Add all numbers: 12 + 15 + 18 + 20 + 25 = 90.
   
   Step 2: Count how many numbers: 5.
   
   Step 3: Divide sum by count: 90 ÷ 5 = 18.
   
   Answer: 18


10. A store sells 3 pens for ₦90. How much for 7 pens?
    
    Step 1: Find unit price: Unit price = Total cost ÷ Number of items = 90 ÷ 3 = ₦30 per pen.
    
    Step 2: Multiply unit price by number of pens: 30 × 7 = ₦210.
    
    Answer: ₦210

1. Calculating prices when shopping.


2. Planning family budgets.


3. Comparing quantities in recipes.


4. Determining profits, losses, and taxes.


5. Estimating distances, speed, and travel time.


6. Making predictions based on data.

1. Confusing ratio with percentage.


2. Forgetting to divide before multiplying in scaling problems.


3. Ignoring units (e.g., km, litres, naira).


4. Not rounding answers properly.


5. Mixing up formulas for profit/loss and simple interest.