Class 6 Maths (Ganita Prakash) - Chapter 7 - Fractions

1. Multiple Choice Questions (MCQs)

(c) 1/4 - When a whole is divided into 4 equal parts, each part is one-fourth.
(a) 1/5 - Among unit fractions, the one with the smallest denominator is the largest.
(a) 3/8 - Total parts = 8, Shaded parts = 3. Fraction = 3/8.
(a) Proper fraction - A fraction where the numerator is less than the denominator is a proper fraction.
(b) 7/4 - An improper fraction has a numerator greater than or equal to its denominator.
(b) 7/2 - (3 × 2) + 1 = 7. So, 3½ = 7/2.
(a) Like fractions - Fractions with the same denominator are called like fractions.
(a) 1/2 and 2/4 - 1/2 = 2/4. They represent the same part of a whole.
(a) 2/3 - The HCF of 12 and 18 is 6. (12÷6)/(18÷6) = 2/3.
(b) 1/2 - The midpoint between 0 and 1 is 1/2.
(b) 3/5 - With like fractions, add the numerators: 2 + 1 = 3. So, 2/5 + 1/5 = 3/5.
(c) 4/8 - With like fractions, subtract the numerators: 7 - 3 = 4. So, 7/8 - 3/8 = 4/8.
(d) 12 - The lowest common multiple of 3 and 4 is 12.
(b) 8/4 - If 1 = 4/4, then 2 = 2 × (4/4) = 8/4.
(d) 3/4 - 'Three-quarters' means 3 parts out of 4, written as 3/4.
(b) Denominator - The number below the line in a fraction is the denominator.
(d) Both (a) and (c) - 5/1 = 5 and 5/5 = 1, both are whole numbers.
(c) 1/2 - Converting to decimals or common denominator shows 1/2 (0.5) is smaller than 2/3 (~0.66), 3/4 (0.75), and 5/6 (~0.83).
(c) 3/4 - 1/2 = 2/4. So, 2/4 + 1/4 = 3/4.
(b) 3/10 - Total parts = 10, Eaten = 7, Remaining = 10 - 7 = 3 parts. Fraction = 3/10.

2. Assertion and Reasoning Questions

(a) Both A and R are true, and R is the correct explanation of A. - The reason correctly explains why 1/2 is greater than 1/4.
(a) Both A and R are true, and R is the correct explanation of A. - The definition of an improper fraction is that the numerator is greater than the denominator.
(a) Both A and R are true, and R is the correct explanation of A. - Cross-multiplication (2×6=12 and 3×4=12) confirms they are equivalent.
(d) A is false but R is true. - The value of 1/5 depends on the whole. Without knowing the sizes of the roti and watermelon, we cannot compare. The reason is generally true.
(a) Both A and R are true, and R is the correct explanation of A. - The calculation is correct: (2 × 3) + 1 = 7, so 2⅓ = 7/3.
(a) Both A and R are true, and R is the correct explanation of A. - Two halves indeed make a whole.
(c) A is true but R is false. - Assertion A is false because 9/12 can be simplified to 3/4. Reason R is true as HCF is 3, which proves A is false.
(a) Both A and R are true, and R is the correct explanation of A. - 5/2 = 2.5, which lies between 2 and 3.
(a) Both A and R are true, and R is the correct explanation of A. - A unit fraction is defined as a fraction with 1 as the numerator.
(a) Both A and R are true, and R is the correct explanation of A. - To add fractions, they must be converted to like fractions (same denominator) first.
(a) Both A and R are true, and R is the correct explanation of A. - The calculation is correct.
(a) Both A and R are true, and R is the correct explanation of A. - Zero divided by any non-zero number is zero.
(a) Both A and R are true, and R is the correct explanation of A. - If numerators are the same, the fraction with the smaller denominator represents larger parts.
(d) A is false but R is true. - Improper fractions (e.g., 5/4) and mixed fractions (e.g., 1½) are greater than 1. The reason is true.
(b) Both A and R are true, but R is not the correct explanation of A. - Both statements are true, but the reason is too general; it doesn't specifically explain the assertion about Brahmagupta's method.
(a) Both A and R are true, and R is the correct explanation of A. - The reason is the correct definition.
(a) Both A and R are true, and R is the correct explanation of A. - All these fractions represent the same value (0.5).
(a) Both A and R are true, and R is the correct explanation of A. - 7 ÷ 5 gives 1 whole and a remainder of 2, so it is 1²/₅.
(d) A is false but R is false. - A is false (1/2+1/3=5/6, not 2/5). R is false because numerators and denominators cannot be added directly without a common denominator.
(a) Both A and R are true, and R is the correct explanation of A. - The density of fractions means there are infinitely many between any two numbers.

3. True or False

False - Among unit fractions, the one with the larger denominator is smaller. So, 1/9 < 1/7.
False - 5/4 = 1.25, which is greater than 1, so it lies to the right of 1 on the number line.
True - 2/3 = (2×3)/(3×3) = 6/9.
True - This is the definition of a mixed fraction.
False - 1/2 + 1/4 = 2/4 + 1/4 = 3/4, not 2/6.
False - In 3/8, the numerator is 3 and the denominator is 8.
True - The HCF of 12 and 15 is 3. (12÷3)/(15÷3) = 4/5.
True - With like fractions, subtract the numerators: 3 - 1 = 2. So, 3/5 - 1/5 = 2/5.
True - 1/2 (3/6) + 1/3 (2/6) + 1/6 = 6/6 = 1.
True - Bhinna is the Sanskrit word for 'broken', which was used for fractions.

4. Short Answer Type-I (2 Marks)

Shabnam will get the larger piece. Justification: When the whole is the same, 1/2 represents a larger share than 1/4 because the whole is divided into fewer parts.
Any two correct equivalent fractions, e.g., 4/6 and 6/9. (Multiply numerator and denominator by the same non-zero number).
2³/₄. (11 ÷ 4 = 2 with a remainder of 3).
Diagram: A number line from 0 to 1 divided into 5 equal parts. The point at the third mark from 0 represents 3/5.
A: 2/5, B: 4/6 (or 2/3).
5/7 > 3/7. Since the denominators are the same, the fraction with the larger numerator is greater.
12/8 or 1¹/₂ or 3/2. 5/8 + 7/8 = 12/8 = 3/2.
6/10 or 3/5. 9/10 - 3/10 = 6/10 = 3/5.
8. (2/3 = ?/12 => ? = (2×12)/3 = 8).
Yes, it is in its simplest form. Reason: The HCF of 16 and 21 is 1.
One piece = 1/6. Three pieces = 3/6 or 1/2.
1/5, 1/4, 1/3, 1/2. (Convert to decimals: 0.2, 0.25, 0.33..., 0.5).
7/10.
(4 × 7) + 2 = 30. So, 30/7.
2¹/₂ rotis. 3 - 1/2 = 2¹/₂.

5. Short Answer Type-II (3 Marks)

Fraction: 2/3 of a roti each.
Diagram: [Two rottis, each divided into 3 equal parts. Each friend gets 2 of these 1/3 pieces].
1. 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1.
2²/₃. 5 - 2¹/₃ = 5 - 7/3 = 15/3 - 7/3 = 8/3 = 2²/₃.
3/5. First, solve the bracket: 3/5 - 1/2 = 6/10 - 5/10 = 1/10. Then, 7/10 - 1/10 = 6/10 = 3/5.
Diagram: A fraction wall with one whole, then halves, thirds, fourths, fifths, sixths. The 1/2 bar and the 3/6 bar are of equal length.
11/15 of the pizza. 2/5 + 1/3 = 6/15 + 5/15 = 11/15.
Yes, they are equivalent. 5/6 = (5×3)/(6×3) = 15/18. OR Cross-multiply: 5×18=90 and 6×15=90.
3/4. 36/48 ÷ 2/2 = 18/24; 18/24 ÷ 2/2 = 9/12; 9/12 ÷ 3/3 = 3/4. (Or directly divide by HCF 12: 36/48 = 3/4).
a) 3²/₅ (17 ÷ 5 = 3 R2). b) 6²/₃ (20 ÷ 3 = 6 R2).
1/2 meter. (5/2) ÷ 5 = (5/2) × (1/5) = 5/10 = 1/2.

6. Long Answer Type (5 Marks)

a) Descending Order: 4/5, 2/3, 7/10, 8/15.
(LCM of 3,5,10,15 is 30. So, 2/3=20/30, 4/5=24/30, 7/10=21/30, 8/15=16/30).
b) Mixed Fraction: 19/5 = 3⁴/₅.
c) Number Line: Mark 0 and 1. Divide the segment between 0 and 1 into 4 equal parts. Then, extend to the right of 1 and divide the next segment (1 to 2) into 4 equal parts. Mark 7/4 at the 7th small mark from 0.
a) Sum: 4²/₃ + 3¹/₂ = 14/3 + 7/2 = 28/6 + 21/6 = 49/6 = 8¹/₆.
b) Simplify: 5¹/₄ - 2³/₈ = 21/4 - 19/8 = 42/8 - 19/8 = 23/8 = 2⁷/₈.
a) Closer: Asha lives closer.
Difference: 5/4 - 7/5 = 25/20 - 28/20 = -3/20. So, Asha is 3/20 km closer.
b) Flour needed: (1/2) × (3/4) = 3/8 cup.
a) Diagrams: [Circle divided into 4 parts, 3 shaded] + [Circle divided into 3 parts, 2 shaded].
Sum: 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1⁵/₁₂.
b) Yes, the sum is greater than 1 because 17/12 > 12/12.
a) Any three equivalent fractions: e.g., 10/14, 15/21, 20/28.
b) Simplest form: 84/98. Divide numerator and denominator by 14 (HCF). 6/7.
a) Solve: 2³/₅ + 4¹/₂ - 3³/₁₀ = 13/5 + 9/2 - 33/10 = 26/10 + 45/10 - 33/10 = 38/10 = 19/5 or 3⁴/₅.
b) Perimeter: 2 × (Length + Breadth) = 2 × (22/3 + 11/2) = 2 × (44/6 + 33/6) = 2 × (77/6) = 154/6 = 77/3 m or 25²/₃ m.
a) Explanation: Brahmagupta's method states that to add fractions, multiply the numerator and denominator of each fraction by the other denominators to get a common denominator. Then add the new numerators.
Example: 1/2 + 1/3 = (1×3)/(2×3) + (1×2)/(3×2) = 3/6 + 2/6 = 5/6.
b) Sum: 1/4 + 1/5 + 1/10 = (1×5×10 + 1×4×10 + 1×4×5) / (4×5×10) = (50 + 40 + 20)/200 = 110/200 = 11/20.
(Alternatively, using LCM 20: 5/20 + 4/20 + 2/20 = 11/20).
a) Any five fractions between 1/4 and 1/2: e.g., 3/8, 5/12, 1/2, 11/24, 5/8 (Note: 1/2 is 0.5, so any fraction between 0.25 and 0.5 is correct).
b) Number of one-sixths in 2¹/₃: 2¹/₃ = 7/3 = 14/6. So, there are 14 one-sixths.
Milk left: 5¹/₂ - 1³/₄ = 11/2 - 7/4 = 22/4 - 7/4 = 15/4 = 3³/₄ litres.
a) Compare: 3/7 and 4/9. Cross-multiply: 3×9=27, 4×7=28. Since 27 < 28, 3/7 < 4/9.
b) Simplest form: 45/75 = (45÷15)/(75÷15) = 3/5.
c) Fraction of a day: 8/24 = 1/3.

7. Case-Based Questions (CBQs)

Case 1: The School Picnic

(b) 1/3
(c) 1/6
(a) Share among 3 children (1/3 > 1/6)
(b) 1/5

Case 2: The Pizza Party

(b) 2
(b) 3
(c) 2/3 (Each child's share from two pizzas: 2 ÷ 3 = 2/3)
(b) 2/3 pizza

Case 3: The Chikki Box

Answers:

(b) 6 - 1/4 of 24 = (1/4) × 24 = 6 pieces.
(c) 18 - 24 - 6 = 18 pieces.
(a) 6 - Brother takes 1/3 of the remaining: 1/3 of 18 = (1/3) × 18 = 6 pieces.
(d) 1/2 - Total taken = 6 (Meena) + 6 (Brother) = 12 pieces. Left = 24 - 12 = 12 pieces. Fraction left = 12/24 = 1/2.

Case 4: The Ribbon Length

Answers:

(a) 1/2 m - (5/2) ÷ 5 = (5/2) × (1/5) = 5/10 = 1/2 m.
(b) 1/5 - The whole ribbon is divided into 5 pieces, so each is 1/5 of the whole.
(c) 3/5 - She used 3 out of 5 pieces = 3/5 of the original ribbon.
(a) 1/4 m - (5/2) ÷ 10 = (5/2) × (1/10) = 5/20 = 1/4 m.

Case 5: The Fraction Wall

Answers:

(d) All of these - From the wall, 1/2 = 2/4 = 3/6 = 4/8.
(b) 3 - The 1/2 strip is the same length as three 1/6 strips.
(b) 3/4 - On the wall, the strip for 3/4 is longer than the strip for 2/3.
(c) 3/4 - 1/2 = 2/4. So, 2/4 + 1/4 = 3/4.

Thursday, November 20, 2025

ANSWERKEY Class 6 – Ganita Prakash – QUESTION BANK CHAPTER 7 Fractions

Class 6 Maths (Ganita Prakash) - Chapter 7 - Fractions

1. Multiple Choice Questions (MCQs)

(c) 1/4 - When a whole is divided into 4 equal parts, each part is one-fourth.

(a) 1/5 - Among unit fractions, the one with the smallest denominator is the largest.

(a) 3/8 - Total parts = 8, Shaded parts = 3. Fraction = 3/8.

(a) Proper fraction - A fraction where the numerator is less than the denominator is a proper fraction.

(b) 7/4 - An improper fraction has a numerator greater than or equal to its denominator.

(b) 7/2 - (3 × 2) + 1 = 7. So, 3½ = 7/2.

(a) Like fractions - Fractions with the same denominator are called like fractions.

(a) 1/2 and 2/4 - 1/2 = 2/4. They represent the same part of a whole.

(a) 2/3 - The HCF of 12 and 18 is 6. (12÷6)/(18÷6) = 2/3.

(b) 1/2 - The midpoint between 0 and 1 is 1/2.

(b) 3/5 - With like fractions, add the numerators: 2 + 1 = 3. So, 2/5 + 1/5 = 3/5.

(c) 4/8 - With like fractions, subtract the numerators: 7 - 3 = 4. So, 7/8 - 3/8 = 4/8.

(d) 12 - The lowest common multiple of 3 and 4 is 12.

(b) 8/4 - If 1 = 4/4, then 2 = 2 × (4/4) = 8/4.

(d) 3/4 - 'Three-quarters' means 3 parts out of 4, written as 3/4.

(b) Denominator - The number below the line in a fraction is the denominator.

(d) Both (a) and (c) - 5/1 = 5 and 5/5 = 1, both are whole numbers.

(c) 1/2 - Converting to decimals or common denominator shows 1/2 (0.5) is smaller than 2/3 (~0.66), 3/4 (0.75), and 5/6 (~0.83).

(c) 3/4 - 1/2 = 2/4. So, 2/4 + 1/4 = 3/4.

(b) 3/10 - Total parts = 10, Eaten = 7, Remaining = 10 - 7 = 3 parts. Fraction = 3/10.

2. Assertion and Reasoning Questions

(a) Both A and R are true, and R is the correct explanation of A. - The reason correctly explains why 1/2 is greater than 1/4.

(a) Both A and R are true, and R is the correct explanation of A. - The definition of an improper fraction is that the numerator is greater than the denominator.

(a) Both A and R are true, and R is the correct explanation of A. - Cross-multiplication (2×6=12 and 3×4=12) confirms they are equivalent.

(d) A is false but R is true. - The value of 1/5 depends on the whole. Without knowing the sizes of the roti and watermelon, we cannot compare. The reason is generally true.

(a) Both A and R are true, and R is the correct explanation of A. - The calculation is correct: (2 × 3) + 1 = 7, so 2⅓ = 7/3.

(a) Both A and R are true, and R is the correct explanation of A. - Two halves indeed make a whole.

(c) A is true but R is false. - Assertion A is false because 9/12 can be simplified to 3/4. Reason R is true as HCF is 3, which proves A is false.

(a) Both A and R are true, and R is the correct explanation of A. - 5/2 = 2.5, which lies between 2 and 3.

(a) Both A and R are true, and R is the correct explanation of A. - A unit fraction is defined as a fraction with 1 as the numerator.

(a) Both A and R are true, and R is the correct explanation of A. - To add fractions, they must be converted to like fractions (same denominator) first.

(a) Both A and R are true, and R is the correct explanation of A. - The calculation is correct.

(a) Both A and R are true, and R is the correct explanation of A. - Zero divided by any non-zero number is zero.

(a) Both A and R are true, and R is the correct explanation of A. - If numerators are the same, the fraction with the smaller denominator represents larger parts.

(d) A is false but R is true. - Improper fractions (e.g., 5/4) and mixed fractions (e.g., 1½) are greater than 1. The reason is true.

(b) Both A and R are true, but R is not the correct explanation of A. - Both statements are true, but the reason is too general; it doesn't specifically explain the assertion about Brahmagupta's method.

(a) Both A and R are true, and R is the correct explanation of A. - The reason is the correct definition.

(a) Both A and R are true, and R is the correct explanation of A. - All these fractions represent the same value (0.5).

(a) Both A and R are true, and R is the correct explanation of A. - 7 ÷ 5 gives 1 whole and a remainder of 2, so it is 1²/₅.

(d) A is false but R is false. - A is false (1/2+1/3=5/6, not 2/5). R is false because numerators and denominators cannot be added directly without a common denominator.

(a) Both A and R are true, and R is the correct explanation of A. - The density of fractions means there are infinitely many between any two numbers.

3. True or False

False - Among unit fractions, the one with the larger denominator is smaller. So, 1/9 < 1/7.

False - 5/4 = 1.25, which is greater than 1, so it lies to the right of 1 on the number line.

True - 2/3 = (2×3)/(3×3) = 6/9.

True - This is the definition of a mixed fraction.

False - 1/2 + 1/4 = 2/4 + 1/4 = 3/4, not 2/6.

False - In 3/8, the numerator is 3 and the denominator is 8.

True - The HCF of 12 and 15 is 3. (12÷3)/(15÷3) = 4/5.

True - With like fractions, subtract the numerators: 3 - 1 = 2. So, 3/5 - 1/5 = 2/5.

True - 1/2 (3/6) + 1/3 (2/6) + 1/6 = 6/6 = 1.

True - Bhinna is the Sanskrit word for 'broken', which was used for fractions.

4. Short Answer Type-I (2 Marks)

Shabnam will get the larger piece. Justification: When the whole is the same, 1/2 represents a larger share than 1/4 because the whole is divided into fewer parts.

Any two correct equivalent fractions, e.g., 4/6 and 6/9. (Multiply numerator and denominator by the same non-zero number).

2³/₄. (11 ÷ 4 = 2 with a remainder of 3).

Diagram: A number line from 0 to 1 divided into 5 equal parts. The point at the third mark from 0 represents 3/5.

A: 2/5, B: 4/6 (or 2/3).

5/7 > 3/7. Since the denominators are the same, the fraction with the larger numerator is greater.

12/8 or 1¹/₂ or 3/2. 5/8 + 7/8 = 12/8 = 3/2.

6/10 or 3/5. 9/10 - 3/10 = 6/10 = 3/5.

8. (2/3 = ?/12 => ? = (2×12)/3 = 8).

Yes, it is in its simplest form. Reason: The HCF of 16 and 21 is 1.

One piece = 1/6. Three pieces = 3/6 or 1/2.

1/5, 1/4, 1/3, 1/2. (Convert to decimals: 0.2, 0.25, 0.33..., 0.5).

7/10.

(4 × 7) + 2 = 30. So, 30/7.

2¹/₂ rotis. 3 - 1/2 = 2¹/₂.

5. Short Answer Type-II (3 Marks)

Fraction: 2/3 of a roti each.Diagram: [Two rottis, each divided into 3 equal parts. Each friend gets 2 of these 1/3 pieces].

1. 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1.

2²/₃. 5 - 2¹/₃ = 5 - 7/3 = 15/3 - 7/3 = 8/3 = 2²/₃.

3/5. First, solve the bracket: 3/5 - 1/2 = 6/10 - 5/10 = 1/10. Then, 7/10 - 1/10 = 6/10 = 3/5.

Diagram: A fraction wall with one whole, then halves, thirds, fourths, fifths, sixths. The 1/2 bar and the 3/6 bar are of equal length.

11/15 of the pizza. 2/5 + 1/3 = 6/15 + 5/15 = 11/15.

Yes, they are equivalent. 5/6 = (5×3)/(6×3) = 15/18. OR Cross-multiply: 5×18=90 and 6×15=90.

Fraction: 2/3 of a roti each.
Diagram: [Two rottis, each divided into 3 equal parts. Each friend gets 2 of these 1/3 pieces].

a) Sum: 4²/₃ + 3¹/₂ = 14/3 + 7/2 = 28/6 + 21/6 = 49/6 = 8¹/₆.
b) Simplify: 5¹/₄ - 2³/₈ = 21/4 - 19/8 = 42/8 - 19/8 = 23/8 = 2⁷/₈.

a) Closer: Asha lives closer.
Difference: 5/4 - 7/5 = 25/20 - 28/20 = -3/20. So, Asha is 3/20 km closer.
b) Flour needed: (1/2) × (3/4) = 3/8 cup.

a) Diagrams: [Circle divided into 4 parts, 3 shaded] + [Circle divided into 3 parts, 2 shaded].
Sum: 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1⁵/₁₂.
b) Yes, the sum is greater than 1 because 17/12 > 12/12.

a) Any three equivalent fractions: e.g., 10/14, 15/21, 20/28.
b) Simplest form: 84/98. Divide numerator and denominator by 14 (HCF). 6/7.

a) Solve: 2³/₅ + 4¹/₂ - 3³/₁₀ = 13/5 + 9/2 - 33/10 = 26/10 + 45/10 - 33/10 = 38/10 = 19/5 or 3⁴/₅.
b) Perimeter: 2 × (Length + Breadth) = 2 × (22/3 + 11/2) = 2 × (44/6 + 33/6) = 2 × (77/6) = 154/6 = 77/3 m or 25²/₃ m.

a) Any five fractions between 1/4 and 1/2: e.g., 3/8, 5/12, 1/2, 11/24, 5/8 (Note: 1/2 is 0.5, so any fraction between 0.25 and 0.5 is correct).
b) Number of one-sixths in 2¹/₃: 2¹/₃ = 7/3 = 14/6. So, there are 14 one-sixths.

a) Compare: 3/7 and 4/9. Cross-multiply: 3×9=27, 4×7=28. Since 27 < 28, 3/7 < 4/9.
b) Simplest form: 45/75 = (45÷15)/(75÷15) = 3/5.
c) Fraction of a day: 8/24 = 1/3.