Fractions — Mastery

Q1. Which of the following is the correct list of fractional units (also called unit fractions)?

• A. 2/3, 3/4, 4/5, 5/6
• B. 1, 2, 3, 4, 5
• C. 1/2, 1/3, 1/4, 1/5
• D. 2, 3, 4, 5, 6

Q2. Asha says: 'For two unit fractions 1/a and 1/b, the one with the bigger denominator is the bigger fraction.' What is the best evaluation of Asha's rule?

• A. The rule is correct; bigger denominator means bigger fraction always.
• B. The rule is correct only for fractions less than 1/2.
• C. The rule is wrong; for unit fractions, the bigger denominator gives the smaller fraction.
• D. The rule depends on whether the numerator is 1 or more.

Q3. A whole chikki is divided into 8 equal parts. One such part is shown to the class. What fraction of the whole chikki is this one part?

• A. 1/4
• B. 1/16
• C. 8
• D. 1/8

Q4. Start with a paper strip of length 1 unit. After folding it once into two equal parts and then folding again into two equal parts, how many equal parts does the strip now have and what is the length of each part?

• A. 2 parts of length 1/2 unit each
• B. 3 parts of length 1/3 unit each
• C. 4 parts of length 1/4 unit each
• D. 8 parts of length 1/8 unit each

Q5. How many times must the fractional unit 1/8 be added to itself to make exactly 1 whole?

• A. 4
• B. 8
• C. 16
• D. 2

Q6. Ravi draws 5 pieces of 1/4 of a roti. The total roti he has shown is

• A. 5/20
• B. 5/4 = 1 + 1/4
• C. 1/5
• D. 5

Q7. On a number line, the segment from 0 to 1 is divided into 3 equal parts. The mark just before reaching 1 stands for which fraction?

• A. 1/3
• B. 1/2
• C. 2/3
• D. 3/3

Q8. On a number line, the gap between 0 and 1 is divided into two equal parts. A black line is drawn from 0 to the point one mark beyond 1 (i.e., 3 such half-units long). The length of the black line is

• A. 1/2 unit
• B. 2/3 unit
• C. 1 unit
• D. 3/2 units

Q9. How many whole units are there in 11/5?

• A. 1
• B. 5
• C. 2
• D. 11

Q10. Can all fractions greater than 1 be written as mixed numbers? The answer is

• A. No, only fractions whose numerator is twice the denominator can be mixed.
• B. Yes, every fraction greater than 1 can be written as a whole part plus a fractional part less than 1.
• C. Only fractions with a denominator of 2 can be mixed.
• D. No, only fractions whose denominator is a prime number can be mixed.

Q11. From the fraction wall which of the following is a correct equality of equivalent fractions?

• A. 1/2 = 1/4 = 1/8
• B. 1/2 = 3/4 = 5/8
• C. 1/2 = 2/3 = 4/6
• D. 1/2 = 2/4 = 4/8

Q12. Which pair below gives two correct equivalent fractions of 2/6?

• A. 4/12 and 1/3
• B. 2/3 and 3/9
• C. 1/2 and 4/8
• D. 2/3 and 6/12

Q13. 2/3 is also the simplest form of 4/6 and of 6/9. The best reason for this is

• A. 2/3 has the smallest numerator possible.
• B. 2 and 3 have no common factor other than 1, and 4/6 and 6/9 both reduce to 2/3.
• C. 2/3 is less than 1.
• D. 2 + 3 = 5 is prime.

Q14. Reduce 64/144 to lowest terms by dividing in steps.

• A. 32/72
• B. 16/36
• C. 4/9
• D. 8/18

Q15. In which group will each child get more chikki? Group A: 1 chikki divided equally between 2 children. Group B: 5 chikkis divided equally among 8 children.

• A. Group A, because 1/2 > 5/8
• B. Group B, because 5/8 > 1/2
• C. Both groups give the same share
• D. Group A, because fewer children always means a bigger share

Q16. Compare 1/2 and 4/7 using common denominators.

• A. 4/7 > 1/2
• B. 1/2 > 4/7
• C. 1/2 = 4/7
• D. Cannot be decided

Q17. Write the fractions 3/4, 12/5, 7/12, 5/4 in descending order.

• A. 12/5, 5/4, 3/4, 7/12
• B. 5/4, 12/5, 3/4, 7/12
• C. 3/4, 5/4, 7/12, 12/5
• D. 12/5, 3/4, 5/4, 7/12

Q18. Sunita teaches her class: 'When two fractions have the same numerator, the one with the larger denominator is the smaller fraction.' Which of the following is the most accurate evaluation of Sunita's rule?

• A. The rule is fully correct and follows directly from the smaller-share rule.
• B. The rule is correct only when the numerator is 1.
• C. The rule is incorrect; a larger denominator always means a bigger fraction.
• D. The rule is correct only when both fractions are less than 1/2.

Q19. Add 4/7 + 6/7 and write the answer as a mixed number.

• A. 1 3/7
• B. 10/14
• C. 1 1/7
• D. 10/49

Q20. Geeta bought 2/5 metre of lace and Shamim bought 3/4 metre of the same lace to cover a tablecloth border of perimeter 1 metre. How much lace did they together buy, and will it cover the border?

• A. 5/9 metre; not enough.
• B. 6/20 metre; not enough.
• C. Cannot decide without metre stick.
• D. 23/20 metre; yes, enough (with some left over).

Q21. What is 10/3 − 13/4?

• A. 1/12
• B. 3/1
• C. −3/12
• D. 23/12

Q22. Jeevika takes 10/3 minutes to run one round of the park. Namit takes 13/4 minutes for the same round. Who is faster and by how much?

• A. Jeevika; she is faster by 1/12 minute.
• B. Namit; he is faster by 1/12 minute.
• C. Both take the same time.
• D. Jeevika; she is faster by 1/4 minute.

Q23. The general method for adding fractions used today was first explicitly described by which Indian mathematician, in which year?

• A. Aryabhata, 499 CE
• B. Sridharacharya, c. 750 CE
• C. Brahmagupta, 628 CE
• D. Mahaviracharya, c. 850 CE

Q24. A Class 6 teacher in Rampur wants to introduce fractions to children for the first time, using the approach of Ganita Prakash Chapter 7. The best first activity is

• A. Write the symbol 1/2 on the board and ask the class to copy it twenty times.
• B. Cut one roti into two equal parts and ask the children what each child will get when one roti is shared between two children.
• C. Drill the formula a/b + c/d = (ad + bc)/bd on the board.
• D. Ask the class to memorise the multiplication table of 12.

Q25. A student in Class 6 writes 2/3 + 1/4 = 3/7. What is the best remedial step a teacher can take?

• A. Tell the student the answer is wrong and ask them to copy the correct answer twenty times.
• B. Use a paper-strip or fraction-wall demonstration that 2/3 and 1/4 do not share the same fractional unit, then convert to a common denominator and re-add.
• C. Tell the student that fractions cannot be added.
• D. Ignore the error; the student will figure it out by Class 8.

Q26. Examine the order in which Chapter 7 develops a child's understanding of fractions: I. Number-line marking and Brahmagupta's symbolic method. II. Paper-strip folding and rectangular-strip diagrams. III. Sharing one roti among children in everyday language. Which sequence of teaching mirrors the chapter's order?

• A. I, II, III
• B. III, II, I
• C. II, III, I
• D. III, I, II

Q27. A teacher uses paper strips of equal length to make a 'fraction wall'. What is the strongest learning outcome this manipulative supports?

• A. Memorising the multiplication table of fractions.
• B. Seeing visually that 1/2 = 2/4 = 4/8 — i.e., recognising equivalent fractions.
• C. Practising long division of fractions.
• D. Learning the formula for the area of a rectangle.

Q28. Meena ate 1/2 of a chikki and her younger brother ate 1/4 of the same chikki. How much of the chikki did they eat together?

• A. 2/6 of the chikki
• B. 1/2 of the chikki
• C. 1/8 of the chikki
• D. 3/4 of the chikki

Q29. Following the previous problem, Meena ate 1/2 and her brother ate 1/4 of one chikki. What fraction of the chikki is left?

• A. 1/4 of the chikki
• B. 1/2 of the chikki
• C. 3/4 of the chikki
• D. 0 — nothing is left

Q30. There is only one way to write 1 as the sum of three different fractional units. Which sum is it?

• A. 1/2 + 1/3 + 1/6 = 1
• B. 1/2 + 1/4 + 1/4 = 1
• C. 1/3 + 1/3 + 1/3 = 1
• D. 1/2 + 1/3 + 1/5 = 1