Question 1(a)
Continue: 456, 567, 678, …
Steps only
Add 111 each time.
789, 900, 1,011, 1,122
Answer
789, 900, 1,011, 1,122
CLASS 5 · MATHS MELA · CHAPTER 1
We the Travellers – I
Read, compare, round and regroup five-digit numbers while solving travel calculations and logical puzzles.
75 worked answersAll 5 exercise sets
What you will learn
- Read and order numbers up to 99,999.
- Round numbers to tens, hundreds and thousands.
- Use place value, division and logical strategies.
75 worked answers · short steps first, explanations when you need them
Patterns, Names and Comparing Numbers
Textbook pages 5–7
Question 1(b)
Continue: 1,050, __, 3,150, 4,200, …
Steps only
Add 1,050 each time.
2,100, 5,250, 6,300, 7,350
Answer
2,100, 5,250, 6,300, 7,350
Question 1(c)
Continue: 5,501, 6,401, 7,301, …
Steps only
Add 900 each time.
8,201, 9,101, 10,001, 10,901
Answer
8,201, 9,101, 10,001, 10,901
Question 1(d)
Continue: 10,100, 10,200, 10,300, …
Steps only
Add 100 each time.
10,400, 10,500, 10,600, 10,700, 10,800, 10,900, 11,000
Answer
10,400, 10,500, 10,600, 10,700, 10,800, 10,900, 11,000
Question 1(e)
Continue: 10,105, 10,125, …
Steps only
Add 20 each time.
10,145, 10,165, 10,185, 10,205, 10,225, 10,245, 10,265, 10,285
Answer
10,145, 10,165, 10,185, 10,205, 10,225, 10,245, 10,265, 10,285
Question 1(f)
Continue: 10,992, 10,993, …
Steps only
Add 1 each time.
10,994, 10,995, 10,996, 10,997, 10,998, 10,999, 11,000, 11,001
Answer
10,994, 10,995, 10,996, 10,997, 10,998, 10,999, 11,000, 11,001
Question 1(g)
Continue: 10,794, 10,796, 10,798, …
Steps only
Add 2 each time.
10,800, 10,802, 10,804, 10,806, 10,808, 10,810, 10,812
Answer
10,800, 10,802, 10,804, 10,806, 10,808, 10,810, 10,812
Question 1(h)
Continue: 73,005, 72,004, …
Steps only
Subtract 1,001 each time.
71,003, 70,002, 69,001, 68,000, 66,999, 65,998, 64,997, 63,996
Answer
71,003, 70,002, 69,001, 68,000, 66,999, 65,998, 64,997, 63,996
Question 1(i)
Continue: 82,350, 83,350, …
Steps only
Add 1,000 each time.
84,350, 85,350, 86,350, 87,350, 88,350, 89,350, 90,350, 91,350
Answer
84,350, 85,350, 86,350, 87,350, 88,350, 89,350, 90,350, 91,350
Question 2
Complete the number and number-name table.
Steps only
7,209: seven thousand two hundred nine; 10,599: ten thousand five hundred ninety-nine; ten thousand seven hundred forty-three: 10,743.
13,579: thirteen thousand five hundred seventy-nine; ten thousand ten: 10,010; fifty-six thousand four hundred ninety-one: 56,491.
45,045: forty-five thousand forty-five; 39,593: thirty-nine thousand five hundred ninety-three; 50,005: fifty thousand five.
26,050: twenty-six thousand fifty; 81,200: eighty-one thousand two hundred; ninety thousand nine: 90,009; twenty-three thousand two hundred thirty: 23,230; thirty-six thousand one: 36,001.
Answer
The completed entries are 7,209; 10,599; 10,743; 13,579; 10,010; 56,491; 45,045; 39,593; 50,005; 26,050; 81,200; 90,009; 23,230; and 36,001 with the names shown.
Question 3
Arrange 40,347; 34,407; 40,473; 34,740; 73,404; 74,430; 47,340; 18,926 increasingly.
Steps only
Compare ten-thousands first, then thousands, hundreds, tens and ones.
Answer
18,926 < 34,407 < 34,740 < 40,347 < 40,473 < 47,340 < 73,404 < 74,430.
Question 4
Is 9,990 greater than 49,014 because 9>4?
Steps only
9,990 has no ten-thousands digit; it is below 10,000.
49,014 is above 40,000.
Answer
No. 9,990 < 49,014. The first 9 is in the thousands place, while 4 is in the ten-thousands place.
Question 4 · number line
Fill the equally spaced labels from 5,000 to 50,000.
Steps only
The interval is 5,000 at every tick.
Answer
5,000, 10,000, 15,000, 20,000, 25,000, 30,000, 35,000, 40,000, 45,000, 50,000.
Question 5(a)
Swap two digits in 1,478 to make a number above 5,500.
Steps only
Swap the 1 and 7.
The result is 7,418.
Answer
One valid answer is 7,418.
Question 5(b)(i)
Swap two digits of 10,593 to get a number between 11,000 and 15,000.
Steps only
Swap 0 and 3.
10,593 becomes 13,590.
Answer
13,590.
Question 5(b)(ii)
Swap two digits of 10,593 to get more than 35,000.
Steps only
Swap 1 and 5.
The result is 50,193.
Answer
50,193.
Question 5(c)(i)
Make 48,247 as small as possible with one swap.
Steps only
Move the smallest available digit 2 to the first place by swapping it with the first 4.
Answer
28,447.
Question 5(c)(ii)
Make 48,247 as large as possible with one swap.
Steps only
Move 8 to the first place by swapping it with the first 4.
Answer
84,247.
Nearest Tens, Hundreds and Thousands
Textbook pages 7–9
Question Rabbit · hundreds
Round 2,346 to its nearest hundred and count jumps.
Steps only
Distances: to 2,300 is 46; to 2,400 is 54.
Answer
2,300 is nearest; it takes 46 jumps.
Question Rabbit · thousands
Round 2,346 to its nearest thousand and count jumps.
Steps only
Distances: to 2,000 is 346; to 3,000 is 654.
Answer
2,000 is nearest; it takes 346 jumps.
Question Table
Round 3,176; 4,017; 5,789; 8,203 to tens, hundreds and thousands.
Steps only
3,176 → 3,180; 3,200; 3,000.
4,017 → 4,020; 4,000; 4,000.
5,789 → 5,790; 5,800; 6,000.
8,203 → 8,200; 8,200; 8,000.
Answer
Rows: (3,180, 3,200, 3,000); (4,020, 4,000, 4,000); (5,790, 5,800, 6,000); (8,200, 8,200, 8,000).
Question Think 1
Which of 7,126; 7,835; 7,030; 6,999 round to the same value by nearest hundred and nearest thousand?
Steps only
7,030 rounds to 7,000 in both ways.
6,999 also rounds to 7,000 in both ways.
Answer
7,030 and 6,999.
Question Think 2(a)
Give two numbers with the same nearest ten.
Steps only
21 and 24 both round to 20.
Answer
Example: 21 and 24.
Question Think 2(b)
Give two numbers with the same nearest hundred.
Steps only
241 and 249 both round to 200.
Answer
Example: 241 and 249.
Question Think 2(c)
Give two numbers with the same nearest thousand.
Steps only
2,210 and 2,440 both round to 2,000.
Answer
Example: 2,210 and 2,440.
Question Think 3(a)
Give numbers with the same nearest ten and hundred.
Steps only
121 and 124 both round to 120 and to 100.
Answer
Example: 121 and 124.
Question Think 3(b)
Give numbers with the same nearest hundred and thousand.
Steps only
2,210 and 2,240 both round to 2,200 and 2,000.
Answer
Example: 2,210 and 2,240.
Question Think 3(c)
Give numbers with the same nearest ten, hundred and thousand.
Steps only
2,211 and 2,214 both round to 2,210; 2,200; 2,000.
Answer
Example: 2,211 and 2,214.
Travelling and Large Numbers
Textbook pages 10–11
Question 1
A cyclist covers 15 km each hour. How far in 4 hours?
Steps only
15×4=60.
Answer
60 km.
Question 2(a)
How many bicycles carry 461 girls and 439 boys at 2 per vehicle?
Steps only
Students=461+439=900.
900÷2=450.
Answer
450 bicycles.
Question 2(b)
How many autorickshaws carry 461 girls and 439 boys at 3 per vehicle?
Steps only
Students=461+439=900.
900÷3=300.
Answer
300 autorickshaws.
Question 2(c)
How many cars carry 461 girls and 439 boys at 4 per vehicle?
Steps only
Students=461+439=900.
900÷4=225.
Answer
225 cars.
Question 2(d)
How many big cars carry 461 girls and 439 boys at 6 per vehicle?
Steps only
Students=461+439=900.
900÷6=150.
Answer
150 big cars.
Question 2(e)
How many tempo travellers carry 461 girls and 439 boys at 10 per vehicle?
Steps only
Students=461+439=900.
900÷10=90.
Answer
90 tempo travellers.
Question 2(f)
How many boats carry 461 girls and 439 boys at 20 per vehicle?
Steps only
Students=461+439=900.
900÷20=45.
Answer
45 boats.
Question 2(g)
How many minibuses carry 461 girls and 439 boys at 25 per vehicle?
Steps only
Students=461+439=900.
900÷25=36.
Answer
36 minibuses.
Question 2(h)
How many aeroplanes carry 461 girls and 439 boys at 180 per vehicle?
Steps only
Students=461+439=900.
900÷180=5.
Answer
5 aeroplanes.
Question Large counts
Give reasonable 4- or 5-digit counts around a textbook, classroom, tree and town.
Steps only
Possible textbook example: about 10,000 words.
Possible classroom example: 4,000 floor tiles or small grid squares; possible tree: thousands of leaves.
Possible town example: population, houses or vehicles.
Answer
Answers depend on observation; state what is counted and how the estimate was made.
Pastime Mathematics
Textbook pages 11–13
Question 1
Take lion, sheep and grass across with a one-item boat.
Steps only
Take sheep across; return alone.
Take lion across; bring sheep back.
Take grass across; return alone.
Take sheep across again.
Answer
All three cross safely in 7 one-way trips.
Question 2
Two piles each contain 7 pebbles; a move removes any positive number from one pile. Last move wins.
Steps only
With equal piles, the player moving second can mirror every first-player move in the other pile.
After each pair of moves the piles are equal again; the mirror player takes the final pebbles.
Answer
Choose to play second and always remove from the other pile exactly what the first player removed.
Question 3(1)
What is common to every subtraction result?
Steps only
For digits a>b, (10a+b)−(10b+a)=9(a−b).
Answer
Every difference is a multiple of 9.
Question 3(2)
Why does repeating the process finish at 9?
Steps only
Every positive result remains a multiple of 9.
The only positive one-digit multiple of 9 is 9.
Answer
The process eventually reaches 9 for any two distinct starting digits.
Question 3(3)
Which digit pairs give one digit immediately?
Steps only
First difference is 9 times the digit difference.
It is one digit only when the digit difference is 1.
Answer
Choose consecutive digits, such as 3 and 4 or 8 and 9.
Question 3(4)
Find digits whose reversed numbers differ by 27.
Steps only
27=9×3, so the digits must differ by 3.
Answer
Examples: 1 and 4, 2 and 5, or 6 and 9.
Question 3(5) · table
Extend the table for digit differences 2,3,5,7.
Steps only
Use pairs (0,2),(0,3),(0,5),(0,7).
20−02=18; 30−03=27; 50−05=45; 70−07=63.
Answer
Rows may be 0,2→18; 0,3→27; 0,5→45; 0,7→63.
Question 3(5) · third subtraction
Which starting pairs reach 9 on the third subtraction?
Steps only
Starting digit difference 3 gives 27→45→9.
Starting digit difference 8 gives 72→45→9.
Answer
Any pair of digits differing by 3 or 8.
Question 3(5) · maximum
Which pairs take the maximum number of subtractions?
Steps only
Difference 2 gives 18→63→27→45→9.
Difference 9 gives 81→63→27→45→9.
Answer
Pairs differing by 2 or 9 take 5 subtractions, the maximum.
Let Us Do and King’s Horses
Textbook pages 13–16
Question 1
Give five numbers strictly between 23,568 and 24,234.
Steps only
Choose any integers above the first and below the second.
Answer
Example: 23,569; 23,700; 23,999; 24,100; 24,233.
Question 2
Give five numbers strictly between 38,125 and 38,600.
Steps only
Choose values from 38,126 through 38,599.
Answer
Example: 38,126; 38,200; 38,350; 38,500; 38,599.
Question 3
Compare 56,987 km and 67,543 km.
Steps only
67 thousand is greater than 56 thousand.
Answer
Sheetal’s car has been driven more.
Question 4
Order ₹90,000; ₹89,999; ₹94,983; ₹49,900; ₹93,743; ₹39,999.
Steps only
Arrange from the smallest ten-thousands digit upward.
Answer
₹39,999 < ₹49,900 < ₹89,999 < ₹90,000 < ₹93,743 < ₹94,983.
Question 5
Order the six town populations from largest to smallest.
Steps only
Compare 66,540;65,232;56,380;53,231;51,336;45,858.
Answer
Town 6, Town 1, Town 3, Town 2, Town 4, Town 5.
Question 6
List numbers between 42,750 and 53,500 ending in 000.
Steps only
These are whole thousands from 43,000 through 53,000.
Answer
43,000; 44,000; 45,000; 46,000; 47,000; 48,000; 49,000; 50,000; 51,000; 52,000; 53,000.
Question 7(b)
Expand 8,062.
Steps only
8,000 + 60 + 2
Answer
8,000 + 60 + 2.
Question 7(c)
Expand 9,980.
Steps only
9,000 + 900 + 80
Answer
9,000 + 900 + 80.
Question 7(d)
Expand 10,304.
Steps only
10,000 + 300 + 4
Answer
10,000 + 300 + 4.
Question 7(e)
Expand 23,004.
Steps only
20,000 + 3,000 + 4
Answer
20,000 + 3,000 + 4.
Question 7(f)
Expand 70,405.
Steps only
70,000 + 400 + 5
Answer
70,000 + 400 + 5.
Question 8(b)
68 = __ tens + 18 ones.
Steps only
68−18=50=5 tens.
Answer
5 tens.
Question 8(c)
607 = 4 hundreds + __ ones.
Steps only
607−400=207.
Answer
207 ones.
Question 8(d)
5,621 = 4 thousand + __ hundreds + 2 tens + __ ones.
Steps only
After 4,000 and 20, 1,601 remains.
1,601=16 hundreds+1 one.
Answer
16 hundreds and 1 one.
Question 8(e)
7,069 = __ thousand + 20 hundreds + __ ones.
Steps only
20 hundreds=2,000. Choose 5 thousands; remainder=69.
Answer
5 thousands and 69 ones.
Question 8(f)
37,608 = __ ten-thousand + 17 thousand + __ hundreds + 8 ones.
Steps only
Choose 2 ten-thousands: 20,000+17,000=37,000.
Remaining 608=6 hundreds+8 ones.
Answer
2 ten-thousands and 6 hundreds.
Question 8(g)
43,001 = 3 ten-thousands + __ thousand + __ hundreds + 1 one.
Steps only
43,001−30,000−1=13,000.
Answer
13 thousands and 0 hundreds.
Question 9(a)
How many ₹10 notes in ₹7,934?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 793.
Answer
793.
Question 9(b)
How many ₹100 notes in ₹7,934?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 79.
Answer
79.
Question 9(c)
How many whole thousands in 7,934?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 7.
Answer
7.
Question 9(d)
How many ₹500 notes in ₹7,934?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 15.
Answer
15.
Question 9(e)
How many ₹10 notes in ₹65,342?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 6534.
Answer
6534.
Question 9(f)
How many ₹100 notes in ₹65,342?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 653.
Answer
653.
Question 9(g)
How many whole thousands in 65,342?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 65.
Answer
65.
Question 9(h)
How many ₹500 notes in ₹65,342?
Steps only
Use whole-number division; ignore any remainder.
The quotient is 130.
Answer
130.
Question King’s horses · mistake
Why are there 19 horses although each of four sides shows 5?
Steps only
Four side-counts total 20 appearances.
The one horse in a corner belongs to two sides and was counted twice.
Answer
There are 19 distinct horses; the caretaker double-counted the corner horse.
Question King’s horses · 18
Arrange 18 horses with 5 counted on each side.
Steps only
The four sides need 20 appearances.
Place horses in two corner cells so those two horses are each counted twice; fill the remaining side positions to total 5 per side.
Answer
Use exactly two occupied corners and 16 other side horses, balanced so every side counts 5.
Question King’s horses · limit
How many more can be stolen after 18 while still showing 5 on every side?
Steps only
At most all four corners can be occupied.
Minimum distinct horses=20−4=16.
Answer
Two more horses can be stolen; 16 is the minimum possible.