Working with Fractions — Mastery

Q1. In the unit-square area model, what does the unit square itself represent?

• A. The fractional unit 1/2
• B. The product of the two fractions
• C. The larger of the two denominators
• D. The whole — that is, the number 1

Q2. In the unit-square model the number of columns represents which quantity?

• A. The numerator of the multiplier
• B. The denominator of the multiplicand
• C. The denominator of the multiplier
• D. The numerator of the multiplicand

Q3. In the unit-square model for 3/4 × 2/5 the number of shaded small squares equals

• A. The denominator of the product
• B. The sum of the two denominators
• C. The sum of the two numerators
• D. The numerator of the product

Q4. Using Brahmagupta's general formula the value of 3/5 × 4 is

• A. 12/5
• B. 7/5
• C. 3/20
• D. 12/20

Q5. While evaluating 8/9 × 15/16, the smallest convenient cancellation before multiplying is

• A. Divide 8 in the numerator and 16 in the denominator by 8
• B. Divide 9 in the denominator and 15 in the numerator by 9
• C. Divide 8 and 16 by 4 only
• D. No cancellation is possible

Q6. A fraction is in its 'lowest form' when

• A. Its numerator is 1
• B. Its denominator is the larger of the two original denominators
• C. Both numerator and denominator are even
• D. Its numerator and denominator have no common factor other than 1

Q7. Consider the following statements about cancellation before multiplying: I. Dividing both numerator and denominator of a fraction by the same non-zero number leaves the fraction unchanged. II. Cancelling a common factor before multiplying gives a different product than cancelling after. III. Cancelling before multiplying gives the answer directly in lowest form when only one common factor exists.

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

Q8. A shopkeeper cuts ribbon into pieces of 3/4 metre each. The total length of ribbon needed to cut 7 such pieces is

• A. 7/12 m
• B. 3/28 m
• C. 10/4 m
• D. 21/4 m

Q9. Using Brahmagupta's formula, 2/3 of 6/10 in lowest form equals

• A. 12/30
• B. 8/13
• C. 2/5
• D. 3/5

Q10. A Class 7 teacher introduces 2/3 × 3/5 using grid paper. The most effective classroom step before stating Brahmagupta's formula is to

• A. Ask students to memorise the rule '(a×c)/(b×d)' and practise 20 sums
• B. Draw a unit square on the grid, mark 3 rows and 5 columns, shade 2 × 3 small squares, and count the shaded out of total
• C. Convert both fractions to decimals on a calculator and multiply
• D. Tell students that fraction multiplication always makes numbers smaller

Q11. Asha begins her Class 7 lesson on fraction multiplication. Of the following first steps, the chapter recommends

• A. State a/b × c/d = (a×c)/(b×d) and ask the class to copy it
• B. Begin with an everyday story like 'Aaron's tortoise walks 1/4 km in 1 hour — how far in 3 hours?' and let students reason
• C. Hand out a worksheet of 30 multiplication sums
• D. Define multiplier and multiplicand on the board and quiz the class

Q12. 1 kg of sugar costs ₹46. The cost of 2 and 1/2 kg of sugar is

• A. ₹92
• B. ₹46 and 1/2
• C. ₹115
• D. ₹48 and 1/2

Q13. Consider these statements about applying Brahmagupta's formula to a mixed-fraction product such as 1 and 1/2 × 2 and 1/3: I. The mixed fractions must first be converted to improper fractions. II. The formula gives 1 × 2 + 1/2 × 1/3 directly. III. After conversion, 3/2 × 7/3 = 21/6 = 7/2.

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

Q14. Ravi reads '1/2 of 60 minutes' and writes 60 ÷ 1/2 = 120 minutes. The teacher's best correction is to point out that

• A. Division by 1/2 means doubling, so the operation itself is correctly chosen
• B. 'of' here means multiplication, so 1/2 of 60 = 1/2 × 60 = 30 minutes
• C. 1/2 of 60 cannot be calculated without a calculator
• D. The student should first convert 1/2 to a decimal

Q15. Using cancellation before multiplying , the value of 25/9 × 3/10 in lowest form is

• A. 75/90
• B. 1/6
• C. 5/3
• D. 5/6

Q16. A school garden is divided so that each of 9 classes tends 1/3 of an acre. The total area tended by all 9 classes is

• A. 1/27 acre
• B. 9/3 acres
• C. 3 acres
• D. 1/12 acre

Q17. Six identical pieces of rope, each 2 and 1/3 metres long, are tied end-to-end. The total length is

• A. 12 and 1/3 m
• B. 14 m
• C. 8 and 1/3 m
• D. 13 m

Q18. A small rectangular carpet measures 2/3 metre by 3/5 metre. Its area is

• A. 5/8 sq m
• B. 6/15 sq m
• C. 2/5 sq m
• D. 1/15 sq m

Q19. Using Brahmagupta's formula, 2/7 × 14/6 in lowest form equals

• A. 28/42
• B. 2/3
• C. 16/13
• D. 1/3

Q20. Using cancellation before multiplying, 21/32 × 8/7 in lowest form equals

• A. 168/224
• B. 29/39
• C. 3/4
• D. 3/32

Q21. To make 'of means multiply' meaningful to Class 7 learners, the most effective real-world question to begin with is

• A. Find 1/2 of 18 chocolates among 9 children — children physically share and count
• B. Define the word 'of' as a synonym of '×' in the notebook and underline it twice
• C. Calculate 7/13 × 11/17 on the board first
• D. Give a list of 50 'of' problems for home practice

Q22. A dairy sells milk in pouches of 3/4 litre each. The total milk in 12 such pouches is

• A. 9 litres
• B. 12 and 3/4 litres
• C. 36 litres
• D. 3/48 litre

Q23. In the unit-square area model for a/b × c/d , the total number of small parts the square is cut into equals

• A. a × c
• B. a + c
• C. b × d
• D. b + d

Q24. Consider these statements about the product of two proper fractions (each less than 1): I. The product is always less than each of the two factors. II. The product can equal one of the factors. III. The product is always a proper fraction.

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

Q25. Asha computes 18/35 × 25/24 by cancelling 18 and 24 by 6, then 25 and 35 by 5. Ravi multiplies first to get 450/840 and then reduces. Their final answers will be

• A. Different — Asha's path is the only correct one
• B. Different — Ravi's path is the only correct one
• C. The same, because the lowest form of a product is unique
• D. The same only if 18 and 24 have no other common factor

Q26. A school has 1200 students. 3/8 of them go by school bus. The number of students who go by school bus is

• A. 450
• B. 400
• C. 3600
• D. 150

Q27. Meena tells her teacher, 'Multiplication always makes a number bigger, so 5 × 1/2 must be at least 5.' The teacher's best response is to

• A. Agree — multiplication never makes numbers smaller
• B. Use a fresh example, 5 × 1/2 = 5 ÷ 2 = 2 and 1/2, showing the product is half of 5 because the multiplier is less than 1
• C. Tell Meena to skip fraction multiplication and go to addition
• D. Say the rule is correct only for whole-number multipliers and leave it there

Q28. In the unit-square model the shaded smaller rectangle (not the full square) represents

• A. The sum of the two fractions
• B. The product of the two fractions
• C. The larger of the two fractions
• D. The difference of the two fractions

Q29. Attributes the general fraction-multiplication rule a/b × c/d = (a×c)/(b×d) to

• A. Aryabhata's Aryabhatiya, 5th century
• B. Brahmagupta's Brahma-sphuta-siddhanta, 628 CE
• C. Bhaskara II's Lilavati, 12th century
• D. Mahavira's Ganita-sara-sangraha, 9th century

Q30. Consider a wooden frame 1 and 1/2 metre long and 2/3 metre wide. I. Its area, in lowest form, is 1 sq m. II. Brahmagupta's formula requires the mixed length to be written as 3/2 first. III. Cancelling 3 in the numerator with 3 in the denominator before multiplying is valid here.

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