Question Unit · India Gate
Choose m or cm for the India Gate measurement 42.
Steps only
42 metres (m).
Answer
42 metres (m).
CLASS 5 · MATHS MELA · CHAPTER 5
Far and Near
Choose suitable length units, convert millimetres through kilometres, and solve measurement problems using all four operations.
87 worked answersAll 6 exercise sets
What you will learn
- Relate millimetres, centimetres, metres and kilometres.
- Compare, add, subtract, multiply and divide lengths.
- Measure or estimate distances with an appropriate method.
87 worked answers · short steps first, explanations when you need them
Choosing, Matching and Comparing Units
Textbook pages 57–58
Question Unit · handkerchief
Choose m or cm for the handkerchief measurement 40.
Steps only
40 centimetres (cm).
Answer
40 centimetres (cm).
Question Unit · well
Choose m or cm for the well measurement 50.
Steps only
50 metres (m).
Answer
50 metres (m).
Question Unit · mobile phone
Choose m or cm for the mobile phone measurement 13.
Steps only
13 centimetres (cm).
Answer
13 centimetres (cm).
Question Unit · elephant’s trunk
Choose m or cm for the elephant’s trunk measurement 2.
Steps only
2 metres (m).
Answer
2 metres (m).
Question Unit · shirt buttons
Choose m or cm for the shirt buttons measurement 5.
Steps only
Question Number line
Complete the double number line for 100, 200, 400, 500 and 700 cm.
Steps only
100 cm=1 m, so divide centimetres by 100.
Answer
100, 200, 400, 500, 700 cm correspond to 1, 2, 4, 5, 7 m.
Question Match 1
Match 204 cm with an equal mixed-unit length.
Steps only
Convert metres to centimetres: 204 cm=2 m 4 cm.
Answer
204 cm = 2 m 4 cm.
Question Match 2
Match 540 cm with an equal mixed-unit length.
Steps only
Convert metres to centimetres: 540 cm=5 m 40 cm.
Answer
540 cm = 5 m 40 cm.
Question Match 3
Match 750 cm with an equal mixed-unit length.
Steps only
Convert metres to centimetres: 750 cm=6 m 150 cm.
Answer
750 cm = 6 m 150 cm.
Question Match 4
Match 240 cm with an equal mixed-unit length.
Steps only
Convert metres to centimetres: 240 cm=2 m 40 cm.
Answer
240 cm = 2 m 40 cm.
Question Match 5
Match 404 cm with an equal mixed-unit length.
Steps only
Convert metres to centimetres: 404 cm=2 m 204 cm.
Answer
404 cm = 2 m 204 cm.
Question 1(a)
Compare 456 cm and 5 m.
Steps only
Convert both sides to centimetres.
Answer
456 cm < 5 m.
Question 1(b)
Compare 55 cm+200 cm and 200 cm+54 cm.
Steps only
Convert both sides to centimetres.
Answer
55 cm+200 cm > 200 cm+54 cm.
Question 1(c)
Compare 6 m 5 cm and 6 m 50 cm.
Steps only
Convert both sides to centimetres.
Answer
6 m 5 cm < 6 m 50 cm.
Question 1(d)
Compare 2 m 150 cm and 3 m 50 cm.
Steps only
Convert both sides to centimetres.
Answer
2 m 150 cm = 3 m 50 cm.
Question 1(e)
Compare 238 cm and 138 cm+1 m.
Steps only
Convert both sides to centimetres.
Answer
238 cm = 138 cm+1 m.
Question Statues (a)
Find the difference between the 182 m Statue of Unity and the 93 m Statue of Liberty.
Steps only
182−93=89.
Answer
89 m.
Question Statues (b)
Which two listed statues have the least height difference?
Steps only
91 m and 93 m differ by 2 m.
Answer
The Motherland Calls and the Statue of Liberty; difference 2 m.
Question Statues (c)
Which two listed statues have the largest height difference?
Steps only
Largest=182 m; smallest=38 m.
182−38=144.
Answer
Statue of Unity and Christ the Redeemer; difference 144 m.
Question Statues (d)
Which statue becomes as high as the 182 m Statue of Unity when doubled?
Steps only
182÷2=91.
Answer
The Motherland Calls, 91 m.
Kilometres and Long Distances
Textbook pages 59–61
Question Local distances
Measure at least three locations using a known step length.
Steps only
Walk a measured 100 m and count steps.
Estimated distance=(location steps÷100 m steps)×100 m.
Answer
Answers depend on the student’s locations and step length; record the location, step count and calculated distance.
Question Nearest and farthest
Identify the nearest and farthest measured locations from home.
Steps only
Compare the recorded distances.
Answer
The location with the smallest distance is nearest; the one with the largest is farthest.
Question Increasing order
Write the measured local distances in increasing order.
Steps only
Arrange from the smallest number of metres to the largest.
Answer
Student-specific; convert kilometres to metres first if the units differ.
Question At least 1 km
Name a measured location at least 1,000 m away.
Steps only
1,000 m=1 km.
Answer
Any recorded location whose distance is 1,000 m or more is valid.
Question Ropes · 100 m
How many 100 m ropes make 1 km?
Steps only
1 km=1,000 m; 1,000÷100=10.
Answer
10 ropes.
Question Ropes · 10 m
How many 10 m ropes make 1 km?
Steps only
1 km=1,000 m; 1,000÷10=100.
Answer
100 ropes.
Question Ropes · 200 m
How many 200 m ropes make 1 km?
Steps only
1 km=1,000 m; 1,000÷200=5.
Answer
5 ropes.
Question Ropes · 500 m
How many 500 m ropes make 1 km?
Steps only
1 km=1,000 m; 1,000÷500=2.
Answer
2 ropes.
Question Ropes · 250 m
How many 250 m ropes make 1 km?
Steps only
1 km=1,000 m; 1,000÷250=4.
Answer
4 ropes.
Question Race 1
A 3 km race has water stations every 500 m. How many and where?
Steps only
3 km=3,000 m.
3,000÷500=6.
Answer
6 stations: 500, 1,000, 1,500, 2,000, 2,500 and 3,000 m from the start.
Question Race 2
Children stand every 300 m along a 3 km race. How many and where?
Steps only
3,000÷300=10.
Answer
10 children: at 300, 600, 900, 1,200, 1,500, 1,800, 2,100, 2,400, 2,700 and 3,000 m.
Question Race 3
Red and blue flags alternate every 50 m through 3 km. How many of each?
Steps only
3,000÷50=60 flags.
An even total divides equally between two alternating colours.
Answer
30 red and 30 blue flags.
Question Train 1
Find the Dibrugarh–Kanniyakumari route length.
Steps only
Kanniyakumari is marked 4,187 km from Dibrugarh.
Answer
4,187 km.
Question Train 2
Find the distance from Jalpaiguri Road to Vijayawada.
Steps only
2,800−983=1,817.
Answer
1,817 km.
Question Train 3
Find the distance from Visakhapatnam to Vijayawada.
Steps only
2,800−2,450=350.
Answer
350 km.
Question Train 4
Which pair is farther apart: Guwahati–Dimapur or Bhubaneswar–Jalpaiguri Road?
Steps only
Guwahati–Dimapur=556−306=250 km.
Bhubaneswar–Jalpaiguri=2,007−983=1,024 km.
Answer
Bhubaneswar and Jalpaiguri Road, by a gap of 1,024 km.
Question Train 5
Find the distance from Guwahati to Coimbatore.
Steps only
3,675−556=3,119.
Answer
3,119 km.
Millimetres, Measuring and Drawing
Textbook pages 61–62
Question Scale marks
How is one centimetre divided on a metric ruler?
Steps only
There are 10 equal spaces, each 1 mm; there are 9 small interior marks between the two centimetre marks.
Answer
1 cm=10 mm.
Question Design lines
Measure each line in the printed design in cm and mm.
Steps only
Place the zero mark at one endpoint and read the other endpoint to the nearest millimetre.
Answer
Measurements depend on the physical print size; record each as __ cm __ mm.
Question Sprout table
Measure one sprout on each of four days.
Steps only
Keep seed type and measuring method the same.
Record Day 1–Day 4 lengths to the nearest millimetre.
Answer
Answers depend on the experiment; a valid table contains four observed millimetre lengths.
Question Draw 1
Draw a line 5 cm 5 mm long.
Steps only
Convert if helpful: 5 cm 5 mm=55 mm.
Answer
Use the ruler from 0 to 55 mm.
Question Draw 2
Draw a line 3 cm 6 mm long.
Steps only
Convert if helpful: 3 cm 6 mm=36 mm.
Answer
Use the ruler from 0 to 36 mm.
Question Draw 3
Draw a line 8 cm 3 mm long.
Steps only
Convert if helpful: 8 cm 3 mm=83 mm.
Answer
Use the ruler from 0 to 83 mm.
Question Draw 4
Draw a line 36 mm long.
Steps only
Convert if helpful: 36 mm=3 cm 6 mm.
Answer
Use the ruler from 0 to 3 cm 6 mm.
Question Draw 5
Draw a line 67 mm long.
Steps only
Convert if helpful: 67 mm=6 cm 7 mm.
Answer
Use the ruler from 0 to 6 cm 7 mm.
Relationships Between Units
Textbook pages 63–64
Question Line (a)
Complete the centimetre–millimetre number line.
Steps only
Multiply centimetres by 10.
Answer
1, 7, 15, 25, 32, 45, 50 cm correspond to 10, 70, 150, 250, 320, 450, 500 mm.
Question Line (b)
Complete the metre–centimetre number line.
Steps only
Multiply metres by 100.
Answer
1, 4, 10, 12, 14, 17, 21 m correspond to 100, 400, 1,000, 1,200, 1,400, 1,700, 2,100 cm.
Question Line (c)
Complete the kilometre–metre number line.
Steps only
Multiply kilometres by 1,000.
Answer
1, 9, 25, 41, 55, 67, 82 km correspond to 1,000, 9,000, 25,000, 41,000, 55,000, 67,000, 82,000 m.
Question 2(a)
Convert 4 cm 5 mm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
45 mm.
Question 2(b)
Convert 89 mm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
8 cm 9 mm.
Question 2(c)
Convert 234 cm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
2,340 mm.
Question 2(d)
Convert 514 mm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
51 cm 4 mm.
Question 2(e)
Convert 6 m 34 cm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
634 cm.
Question 2(f)
Convert 20 m 12 cm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
2,012 cm.
Question 2(g)
Convert 397 m.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
39,700 cm.
Question 2(h)
Convert 5,792 cm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
57 m 92 cm.
Question 2(i)
Convert 9,108 cm.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
91 m 8 cm.
Question 2(j)
Convert 34 km.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
34,000 m.
Question 2(k)
Convert 6,870 m.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
6 km 870 m.
Question 2(l)
Convert 10,552 m.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
10 km 552 m.
Question 2(m)
Convert 29 km 30 m.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
29,030 m.
Question 2(n)
Convert 32 km 359 m.
Steps only
Use 10 mm=1 cm, 100 cm=1 m or 1,000 m=1 km.
Answer
32,359 m.
Operations on Lengths
Textbook pages 64–67
Question Walking
Add 3 km 450 m and 4 km 650 m.
Steps only
Metres: 450+650=1,100 m=1 km 100 m.
Kilometres: 3+4+1=8.
Answer
8 km 100 m.
Question Cable
A 63 m cable has 16 m 75 cm used. Find what remains.
Steps only
63 m=62 m 100 cm.
62 m 100 cm−16 m 75 cm=46 m 25 cm.
Answer
46 m 25 cm.
Question 1
Add ribbon lengths 3 m 75 cm and 2 m 25 cm.
Steps only
75+25=100 cm=1 m.
3+2+1=6 m.
Answer
6 m.
Question 2
Sanchi is 48 km 700 m from Bhopal; the waterfall is 17 km 900 m from Bhopal. Find the remaining distance.
Steps only
Regroup 48 km 700 m as 47 km 1,700 m.
47 km 1,700 m−17 km 900 m=30 km 800 m.
Answer
30 km 800 m.
Question 3
Add Gondola sections 2 km 300 m and 2 km 650 m.
Steps only
300+650=950 m; 2+2=4 km.
Answer
4 km 950 m.
Question 4(a)
Circle the larger of 11 mm and 1 cm and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
11 mm is larger; difference 1 mm.
Question 4(b)
Circle the larger of 26 mm and 2 cm and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
26 mm is larger; difference 6 mm.
Question 4(c)
Circle the larger of 20 cm and 201 mm and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
201 mm is larger; difference 1 mm.
Question 4(d)
Circle the larger of 1,020 mm and 1 m and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
1,020 mm is larger; difference 20 mm.
Question 4(e)
Circle the larger of 2 m and 245 cm and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
245 cm is larger; difference 45 cm.
Question 4(f)
Circle the larger of 5,678 m and 6 km and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
6 km is larger; difference 322 m.
Question 4(g)
Circle the larger of 6 km 1,480 m and 7 km 479 m and find the difference.
Steps only
Convert both measurements to the same unit.
Answer
6 km 1,480 m is larger; difference 1 m.
Question Shirts
Each shirt needs 1 m 80 cm. Find cloth for 20 shirts.
Steps only
1 m 80 cm=180 cm.
180×20=3,600 cm=36 m.
Answer
36 m.
Question Cloth rate
Five metres of cloth cost ₹100. Complete the length–cost line.
Steps only
₹100÷5=₹20 per metre.
Answer
5, 10, 20, 40, 100 m cost ₹100, ₹200, ₹400, ₹800, ₹2,000 respectively.
Question Embroidery length
One metre of thread covers 50 cm of border. Find thread for 5 m of border.
Steps only
5 m=500 cm.
500÷50=10 groups, so thread=10×1 m.
Answer
10 m of thread.
Question Embroidery cost
Thread costs ₹50 per metre. Find the cost of 10 m.
Steps only
10×₹50=₹500.
Answer
₹500.
Question Road per day
A 12 km 600 m road is completed equally in 6 days. Find one day’s work.
Steps only
12 km 600 m=12,600 m.
12,600÷6=2,100 m=2 km 100 m.
Answer
2 km 100 m per day.
Estimation, Feet and Inches
Textbook pages 68–69
Question Estimate building
Estimate the tallest nearby building’s height.
Steps only
Choose a known reference such as one storey≈3 m.
Multiply by the observed number of storeys.
Answer
Student-specific example: a 4-storey building is about 12 m high.
Question Estimate tree
Estimate the tallest nearby tree’s height.
Steps only
Compare it with a known pole, person or storey height.
Answer
Student-specific; record the reference and estimated height.
Question Estimate depth
Estimate a nearby well or pool depth.
Steps only
Use posted information, a safe measurement supplied by an adult, or a known pool marking.
Answer
Student-specific; do not lean over or enter a well to measure it.
Question Inch
Express one inch using the chapter’s metric approximation.
Steps only
Read the centimetre scale opposite the one-inch mark.
Answer
1 inch≈2 cm 5 mm.
Question Foot
How many inches and about how many centimetres make one foot?
Steps only
A foot contains 12 inches.
Answer
1 foot=12 inches≈30 cm.
Question Height activity
Measure height in feet and inches and find the tallest student.
Steps only
Mark each height against a wall, measure from floor to mark, and record feet and remaining inches.
Answer
Class-specific; the tallest student has the greatest measured height after converting all heights to inches.
Question Operation grid
Fill the 4×4 operation grid so no row, column or 2×2 box repeats +, −, × or ÷.
Steps only
Treat the four signs like four Sudoku symbols.
A valid completed pattern is rows: ÷ × − + / + − × ÷ / × + ÷ − / − ÷ + ×.
Answer
÷ × − + / + − × ÷ / × + ÷ − / − ÷ + ×.