NCERT Class 5 Mathematics • New NEP 2020 / NCF 2023

Chapter 2: Fractions

Q: In each of the following figures, identify the fraction represented by the shaded region:(a) A circle divided into 8 equal sectors with 3 shaded.(b) A

Fraction Identification: • (a) Circle: Total parts = 8, Shaded = 3. Fraction = 3/8 (three-eighths). • (b) Rectangle: Total parts = 12, Shaded = 7. Fraction = 7/12 (seven-twelfths). • (c) Strip: Total parts = 10. Shaded parts = 10 - 4 = 6. Fraction = 6/10 = 3/5 (three-fifths).

Q: Find three equivalent fractions for each of the following:(a) 3/4(b) 2/7(c) 18/24 (using division/simplification)

Finding Equivalent Fractions: • (a) 3/4: - (3 × 2)/(4 × 2) = 6/8 - (3 × 3)/(4 × 3) = 9/12 - (3 × 4)/(4 × 4) = 12/16. • (b) 2/7: - (2 × 2)/(7 × 2) = 4/14 - (2 × 3)/(7 × 3) = 6/21 - (2 × 5)/(7 × 5) = 10/35. • (c) 18/24: - Divide by 2: (18 ÷ 2)/(24 ÷ 2) = 9/12 - Divide by 3: (18 ÷ 3)/(24 ÷ 3) = 6/8 - D

Q: Compare the following pairs of fractions using > or (a) 3/5 and 4/7(b) 5/8 and 7/12(c) 2/3 and 8/12

Comparison by Cross Multiplication: • (a) 3/5 vs 4/7: Cross multiply: 3 × 7 = 21, and 5 × 4 = 20. Since 21 > 20, 3/5 > 4/7. • (b) 5/8 vs 7/12: Cross multiply: 5 × 12 = 60, and 8 × 7 = 56. Since 60 > 56, 5/8 > 7/12. • (c) 2/3 vs 8/12: Cross multiply: 2 × 12 = 24, and 3 × 8 = 24. Since 24 = 24, 2/3 =

Q: Draw a number line from 0 to 1 and locate the points representing: 1/4, 2/4, 3/4, and 4/4. What is another name for 2/4 and 4/4?

Number Line Representation: 1. Divide the segment from 0 to 1 into 4 equal segments. 2. Mark points at 1/4, 2/4, 3/4, and 4/4. • Another name for 2/4: Simplifying gives 1/2 (One-Half). • Another name for 4/4: 4 ÷ 4 = 1 (One Whole).

Q: Rohan has a chocolate bar with 16 equal pieces. He gives 1/4 of it to his sister, 1/2 of it to his mother, and keeps the rest for himself.(a) How many

Calculations (Total = 16 pieces): • (a) Sister's Share: 1/4 of 16 = 16 ÷ 4 = 4 pieces. • (b) Mother's Share: 1/2 of 16 = 16 ÷ 2 = 8 pieces. • (c) Rohan's Share: - Pieces left = 16 - (4 + 8) = 16 - 12 = 4 pieces. - Fraction = 4/16 = 1/4 of the chocolate bar.

Q: Solve the following additions and express in simplest form:(a) 2/9 + 4/9(b) 3/10 + 5/10(c) 7/15 + 8/15

Step-by-Step Addition: • (a) 2/9 + 4/9: (2 + 4)/9 = 6/9 = 2/3. • (b) 3/10 + 5/10: (3 + 5)/10 = 8/10 = 4/5. • (c) 7/15 + 8/15: (7 + 8)/15 = 15/15 = 1 (Whole).

Q: Solve the following subtractions:(a) 7/8 - 3/8(b) 11/12 - 5/12(c) 1 - 3/5

Calculations: • (a) 7/8 - 3/8: (7 - 3)/8 = 4/8 = 1/2. • (b) 11/12 - 5/12: (11 - 5)/12 = 6/12 = 1/2. • (c) 1 - 3/5: Write 1 as 5/5: 5/5 - 3/5 = (5 - 3)/5 = 2/5.

Q: Calculate:(a) 3/4 of 24 apples(b) 2/5 of 45 students(c) 5/6 of 60 minutes

Calculations: • (a) 3/4 of 24: (24 ÷ 4) × 3 = 6 × 3 = 18 apples. • (b) 2/5 of 45: (45 ÷ 5) × 2 = 9 × 2 = 18 students. • (c) 5/6 of 60: (60 ÷ 6) × 5 = 10 × 5 = 50 minutes.

Q: (a) Convert the improper fraction 14/3 into a mixed fraction.(b) Convert the mixed fraction $3\frac{2}{5}$ into an improper fraction.(c) Which is grea

Conversions & Comparison: • (a) 14/3: 14 ÷ 3 gives quotient 4 with remainder 2 → $4\frac{2}{3}$. • (b) $3\frac{2}{5}$: (3 × 5 + 2)/5 = (15 + 2)/5 = 17/5. • (c) Comparison: Convert $2\frac{1}{2}$ to improper: 5/2 = 10/4. Since 10/4 > 9/4, $2\frac{1}{2} > 9/4$.

Q: A vegetable farmer divides his rectangular plot into 12 equal beds. He plants tomatoes in 4 beds, potatoes in 3 beds, spinach in 2 beds, and carrots i

Analysis (Total = 12 beds): • (a) Tomatoes: 4/12 = 1/3 of the field. • (b) Carrots: Beds left = 12 - (4 + 3 + 2) = 12 - 9 = 3 beds. Fraction = 3/12 = 1/4 of the field. • (c) Potatoes + Spinach: 3/12 + 2/12 = 5/12. Half the field is 6/12. Since 5/12 No, they occupy less than half of the field.

भिन्न (अंश, हर, तुल्य भिन्न एवं भिन्नों की तुलना) | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts

Fraction as part of a whole: Fraction = Numerator (parts taken)/Denominator (total equal parts).
Fraction Kits: Combining unit fractions: two 1/6 pieces make 1/3, two 1/4 pieces make 1/2.
Equivalent Fractions: Fractions that have the same value: a/b = a × k/b × k.
Cross-multiplication rule for comparing fractions: a/b vs c/d ⇒ compare a × d and b × c.
Addition and subtraction of fractions with common denominators.

All Textbook Exercises & In-Text Tasks (24 Questions)

100% Complete Ingestion

Q1 Visual Fractions • Shaded Parts

In each of the following figures, identify the fraction represented by the shaded region:
(a) A circle divided into 8 equal sectors with 3 shaded.
(b) A rectangle divided into 12 equal squares with 7 shaded.
(c) A strip of 10 equal parts with 4 unshaded. What fraction is shaded?

[3 Marks]

✅ Step-by-Step Solution & Working

Fraction Identification:
• (a) Circle: Total parts = 8, Shaded = 3. Fraction = 3/8 (three-eighths).
• (b) Rectangle: Total parts = 12, Shaded = 7. Fraction = 7/12 (seven-twelfths).
• (c) Strip: Total parts = 10. Shaded parts = 10 - 4 = 6. Fraction = 6/10 = 3/5 (three-fifths).

CBSE Step-by-Step Marking Scheme

Part (a): 3/8 1.0 M

Part (b): 7/12 1.0 M

Part (c): 6/10 or 3/5 1.0 M

Q2 Equivalent Fractions • Multiplication & Division

Find three equivalent fractions for each of the following:
(a) 3/4
(b) 2/7
(c) 18/24 (using division/simplification)

[3 Marks]

✅ Step-by-Step Solution & Working

Finding Equivalent Fractions:
• (a) 3/4:
- (3 × 2)/(4 × 2) = 6/8
- (3 × 3)/(4 × 3) = 9/12
- (3 × 4)/(4 × 4) = 12/16.
• (b) 2/7:
- (2 × 2)/(7 × 2) = 4/14
- (2 × 3)/(7 × 3) = 6/21
- (2 × 5)/(7 × 5) = 10/35.
• (c) 18/24:
- Divide by 2: (18 ÷ 2)/(24 ÷ 2) = 9/12
- Divide by 3: (18 ÷ 3)/(24 ÷ 3) = 6/8
- Divide by 6: (18 ÷ 6)/(24 ÷ 6) = 3/4 (simplest form).

CBSE Step-by-Step Marking Scheme

Part (a) equivalent fractions 1.0 M

Part (b) equivalent fractions 1.0 M

Part (c) simplified equivalent fractions 1.0 M

Q3 Comparing Fractions • Cross Multiplication

Compare the following pairs of fractions using > or < signs:
(a) 3/5 and 4/7
(b) 5/8 and 7/12
(c) 2/3 and 8/12

[3 Marks]

✅ Step-by-Step Solution & Working

Comparison by Cross Multiplication:
• (a) 3/5 vs 4/7: Cross multiply: 3 × 7 = 21, and 5 × 4 = 20. Since 21 > 20, 3/5 > 4/7.
• (b) 5/8 vs 7/12: Cross multiply: 5 × 12 = 60, and 8 × 7 = 56. Since 60 > 56, 5/8 > 7/12.
• (c) 2/3 vs 8/12: Cross multiply: 2 × 12 = 24, and 3 × 8 = 24. Since 24 = 24, 2/3 = 8/12 (they are equal equivalent fractions).

CBSE Step-by-Step Marking Scheme

Part (a): 3/5 > 4/7 1.0 M

Part (b): 5/8 > 7/12 1.0 M

Part (c): 2/3 = 8/12 1.0 M

Q4 Fractions on a Number Line

Draw a number line from 0 to 1 and locate the points representing: 1/4, 2/4, 3/4, and 4/4. What is another name for 2/4 and 4/4?

[3 Marks]

✅ Step-by-Step Solution & Working

Number Line Representation:
1. Divide the segment from 0 to 1 into 4 equal segments.
2. Mark points at 1/4, 2/4, 3/4, and 4/4.
• Another name for 2/4: Simplifying gives 1/2 (One-Half).
• Another name for 4/4: 4 ÷ 4 = 1 (One Whole).

CBSE Step-by-Step Marking Scheme

Correct subdivision into 4 equal parts 1.5 M

Identification of 2/4 = 1/2 and 4/4 = 1 1.5 M

Q5 Word Problem • Sharing Food

Rohan has a chocolate bar with 16 equal pieces. He gives 1/4 of it to his sister, 1/2 of it to his mother, and keeps the rest for himself.
(a) How many pieces does his sister get?
(b) How many pieces does his mother get?
(c) What fraction and how many pieces are left for Rohan?

[3 Marks]

✅ Step-by-Step Solution & Working

Calculations (Total = 16 pieces):
• (a) Sister's Share: 1/4 of 16 = 16 ÷ 4 = 4 pieces.
• (b) Mother's Share: 1/2 of 16 = 16 ÷ 2 = 8 pieces.
• (c) Rohan's Share:
- Pieces left = 16 - (4 + 8) = 16 - 12 = 4 pieces.
- Fraction = 4/16 = 1/4 of the chocolate bar.

CBSE Step-by-Step Marking Scheme

Sister: 4 pieces 1.0 M

Mother: 8 pieces 1.0 M

Rohan: 4 pieces (1/4) 1.0 M

Q6 Addition of Like Fractions

Solve the following additions and express in simplest form:
(a) 2/9 + 4/9
(b) 3/10 + 5/10
(c) 7/15 + 8/15

[3 Marks]

✅ Step-by-Step Solution & Working

Step-by-Step Addition:
• (a) 2/9 + 4/9: (2 + 4)/9 = 6/9 = 2/3.
• (b) 3/10 + 5/10: (3 + 5)/10 = 8/10 = 4/5.
• (c) 7/15 + 8/15: (7 + 8)/15 = 15/15 = 1 (Whole).

CBSE Step-by-Step Marking Scheme

Part (a): 6/9 = 2/3 1.0 M

Part (b): 8/10 = 4/5 1.0 M

Part (c): 15/15 = 1 1.0 M

Q7 Subtraction of Like Fractions

Solve the following subtractions:
(a) 7/8 - 3/8
(b) 11/12 - 5/12
(c) 1 - 3/5

[3 Marks]

✅ Step-by-Step Solution & Working

Calculations:
• (a) 7/8 - 3/8: (7 - 3)/8 = 4/8 = 1/2.
• (b) 11/12 - 5/12: (11 - 5)/12 = 6/12 = 1/2.
• (c) 1 - 3/5: Write 1 as 5/5: 5/5 - 3/5 = (5 - 3)/5 = 2/5.

CBSE Step-by-Step Marking Scheme

Part (a): 1/2 1.0 M

Part (b): 1/2 1.0 M

Part (c): 2/5 1.0 M

Q8 Fraction of a Set / Collection

Calculate:
(a) 3/4 of 24 apples
(b) 2/5 of 45 students
(c) 5/6 of 60 minutes

[3 Marks]

✅ Step-by-Step Solution & Working

Calculations:
• (a) 3/4 of 24: (24 ÷ 4) × 3 = 6 × 3 = 18 apples.
• (b) 2/5 of 45: (45 ÷ 5) × 2 = 9 × 2 = 18 students.
• (c) 5/6 of 60: (60 ÷ 6) × 5 = 10 × 5 = 50 minutes.

CBSE Step-by-Step Marking Scheme

Part (a): 18 apples 1.0 M

Part (b): 18 students 1.0 M

Part (c): 50 minutes 1.0 M

Q9 Mixed Fractions & Improper Fractions

(a) Convert the improper fraction 14/3 into a mixed fraction.
(b) Convert the mixed fraction $3\frac{2}{5}$ into an improper fraction.
(c) Which is greater: $2\frac{1}{2}$ or 9/4?

[3 Marks]

✅ Step-by-Step Solution & Working

Conversions & Comparison:
• (a) 14/3: 14 ÷ 3 gives quotient 4 with remainder 2 → $4\frac{2}{3}$.
• (b) $3\frac{2}{5}$: (3 × 5 + 2)/5 = (15 + 2)/5 = 17/5.
• (c) Comparison: Convert $2\frac{1}{2}$ to improper: 5/2 = 10/4. Since 10/4 > 9/4, $2\frac{1}{2} > 9/4$.

CBSE Step-by-Step Marking Scheme

Part (a): 4 2/3 1.0 M

Part (b): 17/5 1.0 M

Part (c): 2 1/2 > 9/4 1.0 M

Q10 Ramu's Vegetable Field • Comprehensive Fractions

A vegetable farmer divides his rectangular plot into 12 equal beds. He plants tomatoes in 4 beds, potatoes in 3 beds, spinach in 2 beds, and carrots in the remaining beds.
(a) What fraction of the garden is used for tomatoes (in simplest form)?
(b) What fraction of the garden is used for carrots?
(c) Do potatoes and spinach together occupy more than half of the field? Explain.

[3 Marks]

✅ Step-by-Step Solution & Working

Analysis (Total = 12 beds):
• (a) Tomatoes: 4/12 = 1/3 of the field.
• (b) Carrots: Beds left = 12 - (4 + 3 + 2) = 12 - 9 = 3 beds. Fraction = 3/12 = 1/4 of the field.
• (c) Potatoes + Spinach: 3/12 + 2/12 = 5/12. Half the field is 6/12. Since 5/12 < 6/12, No, they occupy less than half of the field.

CBSE Step-by-Step Marking Scheme

Tomatoes = 1/3 1.0 M

Carrots = 1/4 1.0 M

Comparison: 5/12 < 6/12 (less than half) 1.0 M

Q11 Practical Application • Fuel Tank Fraction

A car fuel tank holds 40 litres when completely full. The fuel gauge needle points to 3/8.
(a) How many litres of petrol are currently in the tank?
(b) How many litres are needed to fill the tank to capacity?

[3 Marks]

✅ Step-by-Step Solution & Working

Working:
• (a) Current Petrol: 3/8 of 40 L = (40 ÷ 8) × 3 = 5 × 3 = 15 litres.
• (b) Petrol to Fill: 40 L - 15 L = 25 litres (or 5/8 of 40 = 25 L).

CBSE Step-by-Step Marking Scheme

Current: 15 litres 1.5 M

Needed: 25 litres 1.5 M

Q12 Ordering Fractions

Arrange the following fractions in ascending order (smallest to largest):
2/3, 1/6, 3/4, 5/12

[3 Marks]

✅ Step-by-Step Solution & Working

Finding Common Denominator (LCM of 3, 6, 4, 12 is 12):
• 2/3 = (2 × 4)/(3 × 4) = 8/12
• 1/6 = (1 × 2)/(6 × 2) = 2/12
• 3/4 = (3 × 3)/(4 × 3) = 9/12
• 5/12 = 5/12
Comparing numerators: 2 < 5 < 8 < 9.
Ascending Order: 1/6 < 5/12 < 2/3 < 3/4.

CBSE Step-by-Step Marking Scheme

Converting to common denominator 12 1.5 M

Correct ascending order: 1/6, 5/12, 2/3, 3/4 1.5 M

Q13 In-Text Activity • Paper Folding Fractions

Take a square paper napkin. Fold it in half horizontally, then in half vertically.
(a) How many equal parts are created?
(b) If you unfold and colour 3 of the squares, what fraction is coloured?
(c) If each small square has an area of 9 cm², what is the area of the entire napkin?

[3 Marks]

✅ Step-by-Step Solution & Working

Geometry & Fractions:
• (a) Equal Parts: 2 × 2 = 4 equal squares.
• (b) Fraction Coloured: 3 out of 4 = 3/4 (three-fourths).
• (c) Total Area: 4 × 9 cm² = 36 cm².

CBSE Step-by-Step Marking Scheme

Part (a): 4 equal parts 1.0 M

Part (b): 3/4 1.0 M

Part (c): Total area = 36 cm² 1.0 M

Q14 Unit Fractions • Concept & Property

(a) What is a unit fraction? Give two examples.
(b) Which unit fraction is larger: 1/7 or 1/9? Explain the rule.

[3 Marks]

✅ Step-by-Step Solution & Working

Unit Fractions Explanation:
• (a) Definition: A fraction with a numerator of 1 is called a unit fraction. Examples: 1/2, 1/5, 1/10.
• (b) Comparison: 1/7 > 1/9.
Rule: When two fractions have the same numerator (1), the fraction with the smaller denominator is greater, because dividing a whole into fewer parts makes each individual part larger.

CBSE Step-by-Step Marking Scheme

Definition and examples 1.5 M

1/7 > 1/9 with logical rule explanation 1.5 M

Q15 Fraction Word Problem • Library Books

In a class library of 60 books, 1/3 are science books, 2/5 are storybooks, and the rest are mathematics puzzle books.
(a) Find the number of science books.
(b) Find the number of storybooks.
(c) How many mathematics puzzle books are there?

[3 Marks]

✅ Step-by-Step Solution & Working

Working:
• (a) Science Books: 1/3 of 60 = 60 ÷ 3 = 20 books.
• (b) Storybooks: 2/5 of 60 = (60 ÷ 5) × 2 = 12 × 2 = 24 books.
• (c) Math Puzzle Books: 60 - (20 + 24) = 60 - 44 = 16 books.

CBSE Step-by-Step Marking Scheme

Science = 20 1.0 M

Story = 24 1.0 M

Math = 16 1.0 M

Q16 Decimal-Fraction Equivalence

Express each fraction as a decimal:
(a) 3/10
(b) 75/100
(c) 2/5
(d) 1/4

[3 Marks]

✅ Step-by-Step Solution & Working

Conversions:
• (a) 3/10: 0.3.
• (b) 75/100: 0.75.
• (c) 2/5: Multiply top and bottom by 2: 4/10 = 0.4.
• (d) 1/4: Multiply top and bottom by 25: 25/100 = 0.25.

CBSE Step-by-Step Marking Scheme

0.3 and 0.75 1.5 M

0.4 and 0.25 1.5 M

Q17 HOTS • Fraction Riddle

A fraction is equivalent to 2/3. The sum of its numerator and denominator is 25. Find the fraction.

[3 Marks]

✅ Step-by-Step Solution & Working

Algebraic Reasoning:
1. Let the fraction be (2 × k) / (3 × k).
2. Sum of numerator and denominator: 2k + 3k = 25.
3. 5k = 25 → k = 5.
4. Numerator = 2 × 5 = 10.
5. Denominator = 3 × 5 = 15.
The fraction is 10/15 (Check: 10 + 15 = 25 and 10/15 reduces to 2/3).

CBSE Step-by-Step Marking Scheme

Setting up proportion 2k + 3k = 25 1.5 M

Final fraction = 10/15 1.5 M

Q18 Time & Fractions • Hour Portions

How many minutes are there in:
(a) 1/4 of an hour
(b) 2/3 of an hour
(c) 1/2 of 1/2 of an hour

[3 Marks]

✅ Step-by-Step Solution & Working

1 Hour = 60 Minutes:
• (a) 1/4 of 60: 60 ÷ 4 = 15 minutes.
• (b) 2/3 of 60: (60 ÷ 3) × 2 = 20 × 2 = 40 minutes.
• (c) 1/2 of 1/2 of 60: 1/4 of 60 = 15 minutes.

CBSE Step-by-Step Marking Scheme

Part (a): 15 minutes 1.0 M

Part (b): 40 minutes 1.0 M

Part (c): 15 minutes 1.0 M

Q19 Fraction Word Problem • Money Spent

Priya had ₹240. She spent 1/3 of her money on a geometry box and 1/4 of her money on sketch pens.
(a) How much money did she spend on the geometry box?
(b) How much on sketch pens?
(c) How much money does she have left?

[3 Marks]

✅ Step-by-Step Solution & Working

Financial Calculations:
• (a) Geometry Box: 1/3 of 240 = 240 ÷ 3 = ₹80.
• (b) Sketch Pens: 1/4 of 240 = 240 ÷ 4 = ₹60.
• (c) Money Left: 240 - (80 + 60) = 240 - 140 = ₹100.

CBSE Step-by-Step Marking Scheme

Geometry box: ₹80 1.0 M

Sketch pens: ₹60 1.0 M

Remaining: ₹100 1.0 M

Q20 Simplifying Fractions to Lowest Terms

Reduce each fraction to its simplest form by dividing by their HCF:
(a) 24/36
(b) 15/45
(c) 28/70

[3 Marks]

✅ Step-by-Step Solution & Working

Simplification:
• (a) 24/36: HCF(24, 36) = 12. (24 ÷ 12)/(36 ÷ 12) = 2/3.
• (b) 15/45: HCF(15, 45) = 15. (15 ÷ 15)/(45 ÷ 15) = 1/3.
• (c) 28/70: HCF(28, 70) = 14. (28 ÷ 14)/(70 ÷ 14) = 2/5.

CBSE Step-by-Step Marking Scheme

Part (a): 2/3 1.0 M

Part (b): 1/3 1.0 M

Part (c): 2/5 1.0 M

Q21 Fraction of Weight & Mass

A baker uses 1 kg of flour. He uses 3/8 kg for biscuits and 1/2 kg for bread.
(a) Express both amounts in grams.
(b) How many grams of flour are used in total?
(c) How many grams of flour remain unused?

[3 Marks]

✅ Step-by-Step Solution & Working

1 kg = 1,000 g:
• (a) In grams:
- Biscuits: 3/8 of 1,000 = (1000 ÷ 8) × 3 = 125 × 3 = 375 g.
- Bread: 1/2 of 1,000 = 500 g.
• (b) Total Flour Used: 375 g + 500 g = 875 g.
• (c) Unused Flour: 1,000 g - 875 g = 125 g (or 1/8 kg).

CBSE Step-by-Step Marking Scheme

Part (a): 375 g and 500 g 1.0 M

Part (b): 875 g 1.0 M

Part (c): 125 g 1.0 M

Q22 Measurement Fractions • Tape Length

A tailor has a 2-metre ribbon. He cuts it into 8 equal pieces.
(a) What fraction of a metre is each piece?
(b) What is the length of each piece in centimetres?

[3 Marks]

✅ Step-by-Step Solution & Working

Calculations:
• (a) Fraction of a Metre: Total length = 2 m. Length per piece = 2 ÷ 8 = 2/8 = 1/4 of a metre.
• (b) In Centimetres: 1 m = 100 cm. 1/4 of 100 cm = 100 ÷ 4 = 25 cm.

CBSE Step-by-Step Marking Scheme

Fraction = 1/4 m 1.5 M

Length = 25 cm 1.5 M

Q23 Critical Thinking • True or False with Reason

State whether each statement is True or False. Give a mathematical justification:
(a) 2/3 of 12 is greater than 3/4 of 12.
(b) Any fraction with numerator equal to denominator equals 1.
(c) 4/6 and 6/9 are equivalent fractions.

[3 Marks]

✅ Step-by-Step Solution & Working

Justifications:
• (a) False: 2/3 of 12 = 8; 3/4 of 12 = 9. Since 8 < 9, the statement is False.
• (b) True: When numerator = denominator (e.g. 5/5, 8/8), dividing a quantity into $n$ parts and taking all $n$ parts equals exactly 1 whole.
• (c) True: 4/6 simplifies to 2/3 (divide by 2). 6/9 simplifies to 2/3 (divide by 3). Both equal 2/3, so they are equivalent.

CBSE Step-by-Step Marking Scheme

Part (a): False with calculation 1.0 M

Part (b): True with justification 1.0 M

Part (c): True with simplification 1.0 M

Q24 Comprehensive Review • Fraction Story Problem

A cricket team played 20 matches in a season. They won 3/5 of their matches, lost 1/4 of their matches, and the rest were tied.
(a) How many matches did they win?
(b) How many matches did they lose?
(c) How many matches were tied, and what fraction of the total is that?

[3 Marks]

✅ Step-by-Step Solution & Working

Working (Total Matches = 20):
• (a) Matches Won: 3/5 of 20 = (20 ÷ 5) × 3 = 4 × 3 = 12 matches.
• (b) Matches Lost: 1/4 of 20 = 20 ÷ 4 = 5 matches.
• (c) Matches Tied: 20 - (12 + 5) = 20 - 17 = 3 matches.
- Fraction tied = 3/20 of the matches.

CBSE Step-by-Step Marking Scheme

Won: 12 matches 1.0 M

Lost: 5 matches 1.0 M

Tied: 3 matches (3/20) 1.0 M

🌟 NEP 2020 Competency-Based Case Study

Competency Question: Farmer Sohan's Crop Field Partition

Farmer Sohan has a square field measuring 24 acres. He cultivates wheat on 1/3 of the land, tomatoes on 1/4 of the land, and mustard on 1/6 of the land. The remaining land is kept as grazing meadow for cattle.

Analytical Task: (a) How many acres are used for each of the three crops?
(b) How many acres remain for cattle grazing?
(c) What fraction of the total field is left for cattle?

Evaluation & Model Answer: