Fractions — Hard

Q1. Consider the statements: I. If the same whole is shared among more people, each share is smaller. II. The fraction 1/200 is greater than 1/100 because 200 > 100. III. Two fractional units with the same numerator follow: larger denominator means smaller fraction. Which of the statements are correct?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q2. Assertion (A): Two pieces cut from one chikki into 6 equal parts in different ways are equal in size, even if shapes differ. Reason (R): If a whole is split into n equal parts, each part is 1/n of the whole, irrespective of shape.

• 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, R is false.
• D. A is false, R is true.

Q3. Express 47/9 as a mixed number.

• A. 4 7/9
• B. 5 2/9
• C. 5 1/9
• D. 4 11/9

Q4. Express the mixed number 7 2/3 as an improper fraction.

• A. 9/3
• B. 21/3
• C. 14/3
• D. 23/3

Q5. From the 'Figure it Out' 5 glasses of juice shared equally among 4 friends is the same as ____ glasses of juice shared equally among 8 friends. So 5/4 =?/8.

• A. 9
• B. 1
• C. 20
• D. 10

Q6. Express 17/51 in its lowest terms.

• A. 17/51
• B. 17/3
• C. 1/17
• D. 1/3

Q7. Express 126/147 in its lowest terms.

• A. 9/11
• B. 6/7
• C. 18/21
• D. 126/147

Q8. Compare 7/9 and 17/21. Which relation is correct?

• A. 7/9 < 17/21
• B. 7/9 = 17/21
• C. 7/9 > 17/21
• D. Cannot be decided

Q9. Group 1 has 3 glasses of sugarcane juice divided equally among 4 children. Group 2 has 7 glasses divided equally among 10 children. In which group does each child get a larger share?

• A. Group 2, because 7 + 10 > 3 + 4
• B. Group 2, because 7 > 3
• C. Both are equal, because 3/4 = 7/10
• D. Group 1, because 30/40 > 28/40

Q10. Write the fractions 7/10, 11/15, 2/5 in ascending order using a common denominator.

• A. 2/5, 7/10, 11/15
• B. 11/15, 7/10, 2/5
• C. 2/5, 11/15, 7/10
• D. 7/10, 11/15, 2/5

Q11. Using Brahmagupta's method, what is 2/3 + 1/5?

• A. 3/8
• B. 3/15
• C. 13/15
• D. 2/15

Q12. Using Brahmagupta's method, what is 3/4 − 2/3?

• A. 1/1
• B. 1/7
• C. 5/12
• D. 1/12

Q13. Jaya's school is 7/10 km from her home. She takes an auto for 1/2 km and walks the rest. How far does she walk daily?

• A. 6/8 km
• B. 1/5 km
• C. 1/10 km
• D. 2/10 km

Q14. Consider these steps for adding fractions I. Convert to equivalent fractions with a common denominator. II. Add the numerators and keep the same denominator. III. Express the result in lowest terms if needed. Which are part of Brahmagupta's method?

• A. I and II only
• B. II and III only
• C. I and III only
• D. All three

Q15. A Class 6 student writes 1/2 + 1/3 = 2/5. Which of the following is the correct evaluation of this student's work?

• A. The answer 2/5 is correct, because we add numerator with numerator and denominator with denominator.
• B. The answer is wrong; the correct sum 5/6 is obtained by first converting to common denominator 6.
• C. The answer is wrong; the correct sum is 2/6, found by adding numerators only.
• D. The answer is wrong; the correct sum is 3/5, since 1 + 1 = 2 in the numerator and 2 + 3 = 5 in the denominator.