Meaning of Quantitative Reasoning

Quantitative reasoning means using what you know about numbers—fractions, ratios, decimals, percentages—to solve problems.

It isn’t just doing the conversions; it’s using them to interpret, compare, decide, or solve real-life problems.

It often involves situations like sharing, comparing amounts, finding parts of a whole, finding best buys, growth, decrease etc.

What You Need to Know First

1. Express fractions as ratios, decimals, percentages and vice versa.


2. Simplify fractions, ratios.


3. Find common denominators, LCM or simplify ratio.


4. Multiply and divide.


5. Compare sizes of fractions, decimals, percentages.

Types of Problems You May Meet

1. Distribution / sharing in given ratio.


2. Finding portions: e.g. “What is ⅖ of ₦1200?”


3. Comparing two quantities: e.g. “Which is greater: 40% of 200 or ⅓ of 300?”


4. Working backwards: e.g. “If 30% of something is 60, what is the whole?”


5. Mixture of conversions and operations: fractions + percentages etc.

Steps to Solve Quantitative Reasoning Problems

1. Read carefully: Understand what is being asked. Identify which form is given (fraction, ratio, percent, decimal).


2. Convert: Move all quantities to a common form (fraction / decimal / percent) if needed.


3. Set up the relationship: Express what you need in equation or ratio.


4. Calculate: Use division, multiplication, or conversion rules.


5. Interpret answer: Make sure answer is in correct form, simplified, and matches what was asked.

Worked Examples

Example 1

Problem: A classroom has 30 pupils. If ⅖ of them are girls, how many girls are there?

Solution:

1. ⅖ = 2 ÷ 5 = 0.4


2. 0.4 × 30 = 12


3. Check: (2/5) × 30 = 12

Answer: 12 girls.

Example 2

Problem: If 25% of a number is 150, what is the number?

Solution:

1. (25 ÷ 100) × number = 150


2. number = 150 ÷ (25/100) = 150 × 4 = 600


3. Check: 25% of 600 = 150

Answer: The number is 600.

Example 3

Problem: The ratio of sugar to flour in a recipe is 2 : 5. If you have 700 g of flour, how much sugar do you need?

Solution:

1. Ratio = 2 : 5


2. Total parts = 2 + 5 = 7


3. Flour corresponds to 5 parts → 700 ÷ 5 = 140


4. Sugar (2 parts) = 2 × 140 = 280

Answer: 280 g sugar.

Example 4

Problem: Compare which is larger: ⅗ of 120 or 40% of 150

Solution:

1. ⅗ of 120 = (3/5) × 120 = 72


2. 40% of 150 = (40 ÷ 100) × 150 = 60


3. Compare: 72 > 60

Answer: ⅗ of 120 is larger (72).

Example 5

Problem: A shop discounts an item by 15%. If the original price is ₦5,000, what is the discounted price?

Solution:

1. 15% of 5,000 = 750


2. Discounted price = 5,000 − 750 = 4,250

Answer: ₦4,250.

Example 6

Problem: A survey says 30% of people speak Yoruba, 45% speak Hausa, rest speak Igbo. If population is 2000, how many speak Igbo?

Solution:

1. Remaining percentage = 100 − (30 + 45) = 25%


2. 25% of 2000 = (25 ÷ 100) × 2000 = 500

Answer: 500 people speak Igbo.

Example 7

Problem: A paint can covers ¾ of a wall. Another full can covers how many such walls?

Solution:

1. 1 ÷ (¾) = 4/3 = 1⅓ walls.

Answer: 1⅓ walls.

Example 8

Problem: Rats are in ratio 3 : 7 : 10 in three houses. If there are total 200 rats, how many are in the second house?

Solution:

1. Total parts = 3 + 7 + 10 = 20


2. Second house = (7 ÷ 20) × 200 = 70

Answer: 70 rats in second house.

Applications & Word Problems

1. Sharing profits or expenses in given ratios.


2. Population surveys, demographics, composition (e.g. percent hobbies, percent voters etc).


3. Cooking, mixtures (ratios of ingredients).


4. Price discounts, tax, commission.


5. Comparing deals: which shop gives better discount, or which pack is cheaper.

Common Mistakes Students Make

1. Forgetting to convert percent to fraction or decimal correctly.


2. Mixing up numerator/denominator when using fractions.


3. Not simplifying ratios (or mixing units).


4. Using wrong operations (e.g. adding percents incorrectly).


5. Misreading “of” or “what is …% of …” statements.


6. Getting whole values incorrect when working backwards.

Practice Questions

1. If ⅖ of a book’s pages are coloured, and there are 300 pages, how many pages are coloured?


2. 20% of a certain amount is ₦600; what is the full amount?


3. The ratio 4 : 9 : 7 is used to share ₦4,000 among three people. How much does the first person get?


4. Compare 5/8 of 80 and 60% of 90. Which is larger?


5. A shirt sells for ₦8,000 after 25% discount. What was its original price?


6. In a class, 45% passed Maths, 30% passed English, rest failed. If class has 60 students, how many failed?


7. Water and juice are mixed in ratio 3:2. If total is 25 litres, how much water is used?


8. A runner completed 60% of a race; ⅕ of what remains, how much of the race has she run so far?

Conclusion

Quantitative reasoning with fractions, ratios and percentages is very important. It helps in daily life: budgeting, cooking, shopping, distributing, comparing, etc.

Being able to convert between forms, set up problems correctly, do operations and interpret the answers is what gives confidence in math.

Always check your setup, simplify, and make sure your result answers what was asked.