Class 6 Maths (Ganita Prakash) - Chapter 7 - Fractions
1. Multiple Choice Questions (1 Mark Each)
1. If one roti is divided equally among 4 children, how much will each child get?
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/5
(Competency: Conceptual Understanding)
2. Which of the following fractions is the largest?
(a) 1/5
(b) 1/7
(c) 1/9
(d) 1/11
(Competency: Problem Solving)
3. The fraction representing the shaded portion in the figure is:
[Image: A circle divided into 8 equal parts, with 3 parts shaded]
(a) 3/8
(b) 5/8
(c) 3/5
(d) 8/3
(Competency: Visual Representation)
4. A fraction whose numerator is less than its denominator is called a:
(a) Proper fraction
(b) Improper fraction
(c) Mixed fraction
(d) Unit fraction
(Competency: Conceptual Understanding)
5. Which of the following is an improper fraction?
(a) 2/3
(b) 7/4
(c) 1/5
(d) 4/4
(Competency: Conceptual Understanding)
6. The mixed fraction 3½ can be expressed as an improper fraction:
(a) 5/2
(b) 7/2
(c) 3/2
(d) 9/2
(Competency: Problem Solving)
7. Fractions with the same denominator are called:
(a) Like fractions
(b) Unlike fractions
(c) Equivalent fractions
(d) Unit fractions
(Competency: Conceptual Understanding)
8. Which of the following is a pair of equivalent fractions?
(a) 1/2 and 2/4
(b) 1/3 and 3/1
(c) 2/3 and 2/5
(d) 1/7 and 1/8
(Competency: Problem Solving)
9. The simplest form of 12/18 is:
(a) 2/3
(b) 3/2
(c) 4/6
(d) 6/9
(Competency: Problem Solving)
10. Which fraction is shown on the number line between 0 and 1, exactly at the midpoint?
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1/3
(Competency: Visual Representation)
11. The sum of 2/5 + 1/5 is:
(a) 3/10
(b) 3/5
(c) 2/5
(d) 1/5
(Competency: Problem Solving)
12. The result of 7/8 - 3/8 is:
(a) 4/0
(b) 10/8
(c) 4/8
(d) 1/2
(Competency: Problem Solving)
13. To add 1/3 and 1/4, we need to find a common denominator, which is:
(a) 3
(b) 4
(c) 7
(d) 12
(Competency: Conceptual Understanding)
14. If 1 = 4/4, then 2 is equal to:
(a) 4/4
(b) 8/4
(c) 2/4
(d) 6/4
(Competency: Reasoning)
15. The fraction 'three-quarters' is written as:
(a) 3/2
(b) 4/3
(c) 2/3
(d) 3/4
(Competency: Conceptual Understanding)
16. In the fraction 5/9, the number 9 is the:
(a) Numerator
(b) Denominator
(c) Divisor
(d) Mixed number
(Competency: Conceptual Understanding)
17. A fraction that represents a whole number is:
(a) 5/1
(b) 1/5
(c) 5/5
(d) Both (a) and (c)
(Competency: Reasoning)
18. Which of the following fractions is the smallest?
(a) 2/3
(b) 3/4
(c) 1/2
(d) 5/6
(Competency: Problem Solving)
19. The value of 1/2 + 1/4 is:
(a) 2/6
(b) 1/6
(c) 3/4
(d) 2/4
(Competency: Problem Solving)
20. If a cake is divided into 10 equal pieces and 7 pieces are eaten, the fraction of the cake remaining is:
(a) 7/10
(b) 3/10
(c) 10/7
(d) 10/3
(Competency: Problem Solving)
2. Assertion and Reasoning Questions (1 Mark Each)
Directions: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
1. Assertion (A): The fraction 1/2 is greater than 1/4.
Reason (R): When the whole is divided into more equal parts, the size of each part becomes smaller.
(Competency: Reasoning)
2. Assertion (A): 5/3 is an improper fraction.
Reason (R): In an improper fraction, the numerator is greater than the denominator.
(Competency: Conceptual Understanding)
3. Assertion (A): The fractions 2/3 and 4/6 are equivalent.
Reason (R): Two fractions are equivalent if their cross-multiplications are equal. (2x6 = 3x4).
(Competency: Problem Solving)
4. Assertion (A): 1/5 of a roti is larger than 1/5 of a watermelon.
Reason (R): The value of a fraction depends on the whole.
(Competency: Reasoning)
5. Assertion (A): The mixed number 2⅓ is equal to 7/3.
Reason (R): To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator, then write over the original denominator.
(Competency: Problem Solving)
6. Assertion (A): The sum of 1/2 and 1/2 is 1.
Reason (R): Adding two halves makes a whole.
(Competency: Conceptual Understanding)
7. Assertion (A): 9/12 is in its simplest form.
Reason (R): The HCF of 9 and 12 is 3, so it can be simplified.
(Competency: Problem Solving)
8. Assertion (A): On a number line, 5/2 lies between 2 and 3.
Reason (R): 5/2 is equal to 2.5.
(Competency: Visual Representation)
9. Assertion (A): 1/8 is a unit fraction.
Reason (R): A unit fraction has 1 as its numerator.
(Competency: Conceptual Understanding)
10. Assertion (A): It is not possible to add 1/2 and 1/3 directly.
Reason (R): Fractions can only be added if they have the same denominator.
(Competency: Problem Solving)
11. Assertion (A): The difference between 5/4 and 1/4 is 1.
Reason (R): 5/4 - 1/4 = 4/4 = 1.
(Competency: Problem Solving)
12. Assertion (A): The fraction 0/5 is equal to 0.
Reason (R): If the numerator is zero, the fraction is zero.
(Competency: Conceptual Understanding)
13. Assertion (A): 3/7 is greater than 3/8.
Reason (R): If numerators are the same, the fraction with the smaller denominator is larger.
(Competency: Reasoning)
14. Assertion (A): All fractions are less than 1.
Reason (R): A fraction represents a part of a whole.
(Competency: Reasoning)
15. Assertion (A): The method for adding fractions with different denominators was described by Brahmagupta.
Reason (R): Ancient Indian mathematicians made significant contributions to mathematics.
(Competency: Historical Awareness)
16. Assertion (A): The fraction 10/10 is equal to 1.
Reason (R): When the numerator and denominator are equal, the fraction represents one whole.
(Competency: Conceptual Understanding)
17. Assertion (A): The fractions 1/2, 2/4, and 50/100 are all equivalent.
Reason (R): Equivalent fractions represent the same part of a whole.
(Competency: Problem Solving)
18. Assertion (A): 7/5 can be written as 1²/₅.
Reason (R): When we convert an improper fraction to a mixed number, the remainder becomes the numerator of the fractional part.
(Competency: Problem Solving)
19. Assertion (A): 1/2 + 1/3 = 2/5.
Reason (R): Numerators and denominators are added directly.
(Competency: Problem Solving)
20. Assertion (A): There are an infinite number of fractions between 0 and 1.
Reason (R): You can always find a fraction between any two given fractions.
(Competency: Reasoning)
3. True or False (1 Mark Each)
1. 1/9 is greater than 1/7. (True/False)
(Competency: Conceptual Understanding)
2. The fraction 5/4 lies to the left of 1 on the number line. (True/False)
(Competency: Visual Representation)
3. 2/3 is equivalent to 6/9. (True/False)
(Competency: Problem Solving)
4. A mixed fraction is a combination of a whole number and a proper fraction. (True/False)
(Competency: Conceptual Understanding)
5. 1/2 + 1/4 = 2/6. (True/False)
(Competency: Problem Solving)
6. The numerator of the fraction 3/8 is 8. (True/False)
(Competency: Conceptual Understanding)
7. The fraction 12/15 in its simplest form is 4/5. (True/False)
(Competency: Problem Solving)
8. 3/5 - 1/5 = 2/5. (True/False)
(Competency: Problem Solving)
9. The fractions 1/2, 1/3, and 1/6 can be added to get 1. (True/False)
(Competency: Problem Solving)
10. Fractions were called bhinna in ancient India. (True/False)
(Competency: Historical Awareness)
4. Short Answer Type-I (2 Marks Each)
1. Shabnam and Mukta have a roti. Shabnam says she wants 1/2 of it, and Mukta says she wants 1/4 of it. Who will get a larger piece? Justify your answer.
(Competency: Reasoning)
2. Write any two fractions that are equivalent to 2/3.
(Competency: Problem Solving)
3. Express 11/4 as a mixed fraction.
(Competency: Problem Solving)
4. Represent the fraction 3/5 on a number line.
(Competency: Visual Representation)
5. Identify the fractions represented by the shaded parts in the figures A and B.
[Image A: A rectangle divided into 5 parts, 2 shaded]
[Image B: A circle divided into 6 parts, 4 shaded]
(Competency: Visual Representation)
6. Compare the fractions 3/7 and 5/7.
(Competency: Problem Solving)
7. Solve: 5/8 + 7/8
(Competency: Problem Solving)
8. Solve: 9/10 - 3/10
(Competency: Problem Solving)
9. Fill in the blank: 2/3 = __ /12
(Competency: Problem Solving)
10. State whether the fraction 16/21 is in its simplest form or not. Give a reason for your answer.
(Competency: Problem Solving)
11. If a chikki bar is broken into 6 equal pieces, what fraction of the whole is one piece? What fraction would 3 such pieces represent?
(Competency: Conceptual Understanding)
12. Arrange the following fractions in ascending order: 1/2, 1/4, 1/3, 1/5
(Competency: Problem Solving)
13. Write the fraction 'seven-tenths' in numerals.
(Competency: Conceptual Understanding)
14. Convert the mixed fraction 4²/₇ into an improper fraction.
(Competency: Problem Solving)
15. If you have 3 whole rottis and you give half a roti to a friend, how much roti is left with you? Express your answer as a mixed fraction.
(Competency: Problem Solving)
5. Short Answer Type-II (3 Marks Each)
1. Three friends shared 2 identical rottis equally. What fraction of a roti did each friend get? Show the division with a diagram.
(Competency: Problem Solving & Visual Representation)
2. Find the sum: 1/2 + 1/3 + 1/6
(Competency: Problem Solving)
3. Subtract 2¹/₃ from 5.
(Competency: Problem Solving)
4. Simplify: 7/10 - ( 3/5 - 1/2 )
(Competency: Problem Solving)
5. Draw a fraction wall up to 1/6 and use it to show that 1/2 = 3/6.
(Competency: Visual Representation)
6. Rahim ate 2/5 of a pizza and his sister ate 1/3 of it. How much of the pizza did they eat altogether?
(Competency: Problem Solving)
7. Check if the fractions 5/6 and 15/18 are equivalent.
(Competency: Problem Solving)
8. Express 36/48 in its simplest form by successively dividing the numerator and denominator by common factors.
(Competency: Problem Solving)
9. Write the following fractions as mixed numbers: a) 17/5 b) 20/3
(Competency: Problem Solving)
10. A ribbon of length 5/2 m is cut into 5 pieces of equal length. What is the length of each piece?
(Competency: Problem Solving)
6. Long Answer Type (5 Marks Each)
1. (a) Arrange the following in descending order: 2/3, 4/5, 7/10, 8/15.
(b) Convert 19/5 into a mixed fraction.
(c) Show the fraction 7/4 on a number line.
(Competency: Problem Solving & Visual Representation)
2. (a) Find the sum of 4²/₃ and 3¹/₂.
(b) Simplify: 5¹/₄ - 2³/₈
(Competency: Problem Solving)
3. (a) Ritu's house is 5/4 km from school and Asha's house is 7/5 km from the same school. Who lives closer to the school and by how much?
(b) A recipe requires 3/4 cup of flour. If you are making half the recipe, how much flour do you need?
(Competency: Problem Solving)
4. (a) Draw diagrams to represent the fractions 3/4 and 2/3. Using these diagrams or otherwise, find 3/4 + 2/3.
(b) Is the sum greater than 1? Justify.
(Competency: Problem Solving & Visual Representation)
5. (a) Find three equivalent fractions of 5/7.
(b) Reduce the fraction 84/98 to its simplest form.
(Competency: Problem Solving)
6. (a) Solve: 2³/₅ + 4¹/₂ - 3³/₁₀
(b) The length of a rectangular field is 7¹/₃ m and its breadth is 5¹/₂ m. Find the perimeter of the field.
(Competency: Problem Solving)
7. (a) Explain Brahmagupta's method for adding fractions with the help of an example.
(b) Use this method to add: 1/4 + 1/5 + 1/10
(Competency: Conceptual Understanding & Problem Solving)
8. (a) Write any five fractions that lie between 1/4 and 1/2 on a number line.
(b) How many one-sixths are there in 2¹/₃?
(Competency: Problem Solving & Reasoning)
9. A vessel had 5¹/₂ litres of milk. A cat drank 1³/₄ litres from it. How much milk is left in the vessel? Express your answer as a mixed fraction.
(Competency: Problem Solving)
10. (a) Compare: 3/7 and 4/9
(b) Express 45/75 in its simplest form.
(c) What fraction of a day is 8 hours?
(Competency: Problem Solving)
7. Case-Based Questions (CBQs)
Case 1: The School Picnic
For the school picnic, the teacher brought a large chocolate bar. She divided it equally among Ravi, Priya, and Sam.
[Image: A rectangular chocolate bar divided into 3 equal parts]
1. What fraction of the chocolate bar did each child get?
(a) 1/2
(b) 1/3
(c) 1/4
(d) 1/6
(Competency: Conceptual Understanding)
2. If the teacher had divided the same chocolate bar among 6 children equally, what fraction would each get?
(a) 1/2
(b) 1/3
(c) 1/6
(d) 1/12
(Competency: Conceptual Understanding)
3. Which is greater: the share of one child among 3 children or the share of one child among 6 children?
(a) Share among 3 children
(b) Share among 6 children
(c) Both are equal
(d) Cannot be determined
(Competency: Reasoning)
4. If two more children joined the group of 3, and the chocolate was re-divided equally among all 5, what fraction would each child get now?
(a) 1/3
(b) 1/5
(c) 1/6
(d) 2/5
(Competency: Problem Solving)
Case 2: The Pizza Party
Anil, Beni, and Charu ordered two pizzas of the same size. They decided to share the pizzas equally.
[Image: Two circular pizzas]
1. How many pizzas are there in total?
(a) 1
(b) 2
(c) 3
(d) 4
(Competency: Conceptual Understanding)
2. How many children are sharing the pizzas?
(a) 2
(b) 3
(c) 4
(d) 5
(Competency: Conceptual Understanding)
3. What fraction of a pizza will each child get?
(a) 1/2
(b) 1/3
(c) 2/3
(d) 3/2
(Competency: Problem Solving)
4. What is the total amount of pizza each child gets?
(a) 1/2 pizza
(b) 2/3 pizza
(c) 3/2 pizza
(d) 1/3 pizza
(Competency: Problem Solving)
Case 3: The Chikki Box
Content:
A box contains 24 identical chikki pieces. Meena takes 1/4 of the pieces, and her brother takes 1/3 of the remaining pieces.
[Image: A grid of 24 squares representing chikki pieces]
Questions:
How many pieces did Meena take?
(a) 4
(b) 6
(c) 8
(d) 12
(Competency: Problem Solving)After Meena takes her share, how many pieces are left?
(a) 12
(b) 16
(c) 18
(d) 20
(Competency: Problem Solving)How many pieces did Meena's brother take?
(a) 6
(b) 8
(c) 4
(d) 10
(Competency: Problem Solving)What fraction of the original box is left after both have taken their shares?
(a) 1/3
(b) 1/4
(c) 1/6
(d) 1/2
(Competency: Problem Solving)
Case 4: The Ribbon Length
Content:
Riya has a ribbon that is 5/2 meters long. She cuts it into 5 equal pieces. She then uses 3 of these pieces to tie parcels.
[Image: A ribbon labeled 5/2 m, then divided into 5 equal parts]
Questions:
What is the length of each small piece?
(a) 1/2 m
(b) 1 m
(c) 2/5 m
(d) 5/2 m
(Competency: Problem Solving)What fraction of the original ribbon is one small piece?
(a) 1/10
(b) 1/5
(c) 2/5
(d) 1/2
(Competency: Conceptual Understanding)What fraction of the original ribbon did she use to tie parcels?
(a) 2/5
(b) 3/5
(c) 1/2
(d) 3/10
(Competency: Problem Solving)If she had cut the ribbon into 10 equal pieces instead, what would be the length of each piece?
(a) 1/4 m
(b) 1/2 m
(c) 2/5 m
(d) 1 m
(Competency: Reasoning)
Case 5: The Fraction Wall
Content:
The following fraction wall is made up of several strips of the same length, each divided into equal parts.
[Image: A fraction wall with strips representing 1, 1/2, 1/3, 1/4, 1/6, and 1/8]
Questions:
Using the wall, which fraction is equivalent to 1/2?
(a) 2/4
(b) 3/6
(c) 4/8
(d) All of these
(Competency: Visual Representation)How many 1/6 parts are needed to equal 1/2?
(a) 2
(b) 3
(c) 4
(d) 6
(Competency: Conceptual Understanding)Which is greater: 2/3 or 3/4? Use the wall to explain.
(a) 2/3
(b) 3/4
(c) They are equal
(d) Cannot be determined
(Competency: Visual Representation & Reasoning)What is the sum of 1/2 and 1/4?
(a) 1/6
(b) 2/6
(c) 3/4
(d) 2/8
(Competency: Problem Solving)
