Section A: Simple Cut-and-Divide Questions
Q1.
A rope is 50 meters long. A piece of length x meters is cut from it. The remaining length is then divided into two equal parts. Which expression represents the length of each part?
(a) (50 − x) × 2
(b) 50/2 − x
(c) (50 − x)/2
(d) 50 − (x/2)
Q2.
A wire is 80 meters long. After cutting a piece of length y meters, the remaining wire is divided into 4 equal parts. Which expression shows the length of each part?
(a) (80 − y) × 4
(b) (80 − y)/4
(c) 80/(4 − y)
(d) 80 − y/4
Q3.
A ribbon is 120 cm long. A portion of p cm is cut off. The rest is divided equally among 3 students. What is the length each student gets?
(a) (120 + p)/3
(b) 120/3 − p
(c) (120 − p)/3
(d) 120 − p/3
Q4.
A wooden plank is L meters long. A carpenter trims t meters from it. The remaining piece is then divided into two equal halves. Which expression represents each half?
(a) (L − t)/2
(b) L/2 − t
(c) 2(L − t)
(d) L − t/2
Q5.
A pipe is 60 meters long. After removing k meters from it, the rest is cut into 5 equal sections. What is the length of each section?
(a) (60 − k)/5
(b) (60 − k) × 5
(c) 60 − k/5
(d) 60/(k − 5)
Q6.
A cloth roll is 40 meters long. A tailor cuts m meters from it. The remaining cloth is divided into 8 equal parts. Which expression gives each part’s length?
(a) (40 − m)/8
(b) (40 − m) × 8
(c) 40/8 − m
(d) 40 − m/8
Q7.
A metal rod is 25 meters long. After cutting off a meters, the remaining rod is divided equally into 2 pieces. Which expression shows their length?
(a) (25 − a)/2
(b) 25 − a/2
(c) (25 − a) × 2
(d) 25/(2 − a)
Q8.
A ribbon of length 100 cm is cut by removing r cm. The leftover ribbon is shared equally by 4 friends. What is each friend’s share?
(a) (100 − r)/4
(b) 100 − r/4
(c) (100 + r)/4
(d) r/(100 − 4)
Q9.
A bamboo stick is B meters long. A portion of h meters is removed. The rest is divided into 3 equal pieces. Which expression shows the length of each piece?
(a) (B − h)/3
(b) B/3 − h
(c) 3(B − h)
(d) B − h/3
Q10.
A hose is 90 meters long. d meters are cut from it. The remaining hose is split equally into 6 smaller hoses. What is the length of each?
(a) (90 − d)/6
(b) (90 − d) × 6
(c) 90 − d/6
(d) 6/(90 − d)
Section B: Slightly Different Expression Questions
Q11.
A rope is x meters long. Another piece of rope that is 15 meters longer is joined to it. What is the total length?
(a) x + 15
(b) x − 15
(c) 15 − x
(d) 2x + 15
Q12.
A stick is 45 meters long. It is cut into two pieces such that one piece is k meters and the other is the rest. What is the length of the second piece?
(a) 45 − k
(b) k − 45
(c) 45/k
(d) 45 + k
Q13.
A pipe is t meters long. It is extended by adding another pipe of half its length. What is the new total length?
(a) t + t/2
(b) t/2 − t
(c) (t − 2)/2
(d) 2t + t
Q14.
A ribbon is 60 cm long. You fold it into 3 equal parts. What is the expression for each part?
(a) 60 × 3
(b) 60 − 3
(c) 60/3
(d) (60 + 3)
Q15.
A wire of length y meters is cut into 5 equal pieces. What is the length of each piece?
(a) y − 5
(b) y/5
(c) 5/y
(d) y × 5
Q16.
A board is 100 meters long. You remove m meters and then shorten the remaining piece by 10 meters. What is its final length?
(a) 100 − m − 10
(b) 100 − (m − 10)
(c) 100/m − 10
(d) m + 10 − 100
Q17.
A rope is 200 meters long. It is cut into two parts. One part is x meters. The second part is then cut into half. What is the length of the smaller piece?
(a) (200 − x)/2
(b) x/2 − 200
(c) 2(200 − x)
(d) 200/(2 − x)
Q18.
A pole is h meters tall. It is extended by adding two sections of length 3 meters each. What is the total height?
(a) h + 6
(b) h − 6
(c) 6 − h
(d) h × 6
Q19.
A rope is r meters long. You fold it in half and then cut off p meters from the folded length. What is the final length (unfolded)?
(a) r − 2p
(b) r/2 − p
(c) (r − p)/2
(d) 2r − p
Q20.
A strip of metal is L meters long. You cut off one-third of its length. What is the remaining length?
(a) L − L/3
(b) L/3 − L
(c) 3L − L
(d) L/(L − 3)
Section C: Complex Expression Questions
Q21.
A rope is 100 meters long. A piece of length x meters is cut from it. From the remaining rope, half is again cut and joined to another rope of length 50 meters. Which expression gives the total length of the joined rope?
(a) (100 − x)/2 + 50
(b) (100 − x) + 50
(c) 100 − x + 50
(d) (100 − x)/2 − 50
Q22.
A wire is y meters long. You cut one-fourth of it and then double the remaining length. What is the expression for the doubled remaining wire?
(a) 2(y − y/4)
(b) y − y/2
(c) (y − y/4)/2
(d) 2y − y/4
Q23.
A ribbon is 120 cm long. A piece of length a cm is cut and 1/3 of the remainder is given to a friend. What is the expression for the length given to the friend?
(a) (120 − a)/3
(b) 120 − a/3
(c) 1/3(120 − a)
(d) Both (a) and (c)
Q24.
A metal rod is 80 meters long. 10 meters are cut off, and then the remaining rod is divided into n equal parts. Which expression represents the length of each part?
(a) (80 − 10)/n
(b) 80/(n − 10)
(c) (80 − n)/10
(d) (80 − 10) × n
Q25.
A cable of length L meters has x meters cut from it. The remaining part is folded in half, and then 5 meters are removed. What is the expression for the final length?
(a) (L − x)/2 − 5
(b) L − x − 5
(c) (L − x − 5)/2
(d) 2(L − x) − 5
Q26.
A rope is 200 meters long. You cut a piece of length p, then cut half of the remaining rope, and add a new rope of length q. Which expression represents the final rope length?
(a) (200 − p)/2 + q
(b) 200 − p/2 + q
(c) (200 − p − q)/2
(d) 200 − (p/2 + q)
Q27.
A wooden plank is 60 meters long. One-third of it is painted, then 10 meters of the painted section is cut off. What is the length of the remaining painted section?
(a) (60/3) − 10
(b) 60 − (60/3 + 10)
(c) 10 − 60/3
(d) 60/3 + 10
Q28.
A rope is 150 meters long. A piece of length x is cut, and the remaining is divided into 3 equal parts. One part is then doubled by joining another rope of the same length. What is the expression for the new doubled part?
(a) 2((150 − x)/3)
(b) (150 − x)/3 + 2
(c) ((150 − x)/3) + ((150 − x)/3)
(d) Both (a) and (c)
Q29.
A ribbon is R meters long. 1/4 of it is cut off, and the remaining is divided into 5 equal pieces. Then one piece is further cut by 2 meters. What is the expression for that final piece?
(a) (R − R/4)/5 − 2
(b) (R − R/4 − 2)/5
(c) (R/4)/5 − 2
(d) (R − 2)/5 − R/4
Q30.
A cable of 300 meters is cut into 3 pieces in the ratio 2:3:4. The largest piece is then shortened by 20 meters. What is the expression for its final length?
(a) (4/9)×300 − 20
(b) (4/3)×300 − 20
(c) 300 − 20
(d) (4/9)×300 + 20
| Q# | Answer | Explanation |
|---|---|---|
| 1 | c | Remaining rope = 50 − x, divided into 2 → (50 − x)/2 |
| 2 | b | Remaining = 80 − y, divided into 4 → (80 − y)/4 |
| 3 | c | Remaining = 120 − p, divided among 3 → (120 − p)/3 |
| 4 | a | Remaining = L − t, divided into 2 halves → (L − t)/2 |
| 5 | a | Remaining = 60 − k, divided into 5 → (60 − k)/5 |
| 6 | a | Remaining = 40 − m, divided into 8 → (40 − m)/8 |
| 7 | a | Remaining = 25 − a, divided into 2 → (25 − a)/2 |
| 8 | a | Remaining = 100 − r, divided among 4 → (100 − r)/4 |
| 9 | a | Remaining = B − h, divided into 3 → (B − h)/3 |
| 10 | a | Remaining = 90 − d, divided into 6 → (90 − d)/6 |
| 11 | a | Total length = x + 15 |
| 12 | a | Second piece = 45 − k |
| 13 | a | Total length = t + t/2 |
| 14 | c | Folded length = 60/3 |
| 15 | b | Each piece = y/5 |
| 16 | a | Final length = 100 − m − 10 |
| 17 | a | Remaining = 200 − x, half = (200 − x)/2 |
| 18 | a | Total height = h + 6 |
| 19 | a | Folded → r/2, remove p → r − 2p |
| 20 | a | Remaining = L − L/3 |
| 21 | a | Half of remaining = (100 − x)/2, add 50 → (100 − x)/2 + 50 |
| 22 | a | Cut 1/4 → remaining = 3y/4, doubled → 2*(y − y/4) |
| 23 | d | Both (120 − a)/3 and 1/3(120 − a) are equivalent |
| 24 | a | Remaining = 80 − 10, divided into n → (80 − 10)/n |
| 25 | a | Fold in half → (L − x)/2, remove 5 → (L − x)/2 − 5 |
| 26 | a | Remaining = 200 − p, half = (200 − p)/2, add q → (200 − p)/2 + q |
| 27 | a | Painted = 60/3 = 20, cut 10 → 20 − 10 = (60/3) − 10 |
| 28 | d | Part = (150 − x)/3, doubled → 2*((150 − x)/3) = ((150 − x)/3) + ((150 − x)/3) |
| 29 | a | Remaining after 1/4 cut = 3R/4, divide by 5 → (R − R/4)/5, cut 2 → (R − R/4)/5 − 2 |
| 30 | a | Largest = 4/9 × 300, subtract 20 → (4/9) × 300 − 20 |
