Class 5 Mathematics · Chapter 1

1. We the Travellers — I

Solutions to all Let Us Do, Let Us Think and Pastime Mathematics questions. CBSE / NCERT Class 5 Maths Mela.

Reading and Writing Large Numbers

1What numbers do we get when we keep adding a thousand to 1,000?

1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000, 8,000, 9,000.

When we add a thousand to 9,000, we get 10,000 (ten thousand).

2Complete the table of numbers using tokens.

Number	TTh	Th	H	T	O	Number Name
10,033	1	0	0	3	3	Ten thousand thirty-three
10,458	1	0	4	5	8	Ten thousand four hundred fifty-eight
11,214	1	1	2	1	4	Eleven thousand two hundred fourteen
13,520	1	3	5	2	0	Thirteen thousand five hundred twenty
20,000	2	0	0	0	0	Twenty thousand
45,867	4	5	8	6	7	Forty-five thousand eight hundred sixty-seven

Let Us Do

1Fill in the blanks by continuing the pattern in each of the following sequences.

(a) 456 → 567 → 678 → 789 → 900 → 1,011 → 1,122

Pattern: add 111 each time.

(b) 1,050 → 2,100 → 3,150 → 4,200 → 5,250 → 6,300 → 7,350

Pattern: add 1,050 each time.

Pattern: add 900 each time.

(d) 10,100 → 10,200 → 10,300 → 10,400 → 10,500 → 10,600 → 10,700 → 10,800 → 10,900 → 11,000

Pattern: add 100 each time.

(e) 10,105 → 10,125 → 10,145 → 10,165 → 10,185 → 10,205 → 10,225 → 10,245 → 10,265 → 10,285

Pattern: add 20 each time.

(f) 10,992 → 10,993 → 10,994 → 10,995 → 10,996 → 10,997 → 10,998 → 10,999 → 11,000 → 11,001

Pattern: add 1 each time.

(g) 10,794 → 10,796 → 10,798 → 10,800 → 10,802 → 10,804 → 10,806 → 10,808 → 10,810 → 10,812

Pattern: add 2 each time.

(h) 73,005 → 72,004 → 71,003 → 70,002 → 69,001 → 68,000 → 66,999 → 65,998 → 64,997 → 63,996

Pattern: subtract 1,001 each time.

(i) 82,350 → 83,350 → 84,350 → 85,350 → 86,350 → 87,350 → 88,350 → 89,350 → 90,350 → 91,350

Pattern: add 1,000 each time.

2Fill in the blanks appropriately. Use commas as required.

Number	Number Name
8,045	Eight thousand forty-five
7,209	Seven thousand two hundred nine
10,599	Ten thousand five hundred ninety-nine
10,743	Ten thousand seven hundred forty-three
20,869	Twenty thousand eight hundred sixty-nine
13,579	Thirteen thousand five hundred seventy-nine
10,010	Ten thousand ten
56,491	Fifty-six thousand four hundred ninety-one
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
90,009	Ninety thousand nine
23,230	Twenty-three thousand two hundred thirty
36,001	Thirty-six thousand one

3Arrange the numbers below in increasing order.

18,926 < 34,407 < 34,740 < 40,347 < 40,473 < 47,340 < 73,404 < 74,430

4A student said 9,990 is greater than 49,014 because 9 is greater than 4. Is the student correct? Why or why not?

No, the student is not correct.

9,990 is a 4-digit number. 49,014 is a 5-digit number.

49,014 has 4 ten thousands, but 9,990 has no ten thousand.

So, 49,014 > 9,990.

On the number line, 9,990 lies just before 10,000. 49,014 lies just before 50,000.

5Digit swap

(a) Interchange any two digits in 1,478 to make a number larger than 5,500.

Interchange 1 and 7: 7,418. Or interchange 1 and 8: 8,471.

(b) Interchange two digits of 10,593 to make a number —

i) Between 11,000 and 15,000: interchange 0 and 3 → 13,590

ii) More than 35,000: interchange 1 and 5 → 50,193 (or 1 and 9 → 90,513)

i) As small as possible: interchange 4 and 2 → 28,447

ii) As big as possible: interchange 4 and 8 → 84,247

Nearest Tens, Hundreds and Thousands

1The rabbit is at 2,346. Its food is kept at its neighbouring hundreds and thousands. Fill in the blanks.

2,300 is the nearest hundred of 2,346. It will need 46 jumps to reach 2,300.

2,000 is the nearest thousand of 2,346. It will need 346 jumps to reach 2,000.

2Fill in the boxes appropriately.

Number	Nearest Tens	Nearest Hundreds	Nearest Thousands
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

Let Us Think

1Vijay rounded off a number to the nearest hundred. Suma rounded off the same number to the nearest thousand. Both got the same result. Circle the numbers they might have used: 7,126, 7,835, 7,030, 6,999

Circle 7,030 and 6,999.

7,030 → nearest hundred 7,000 and nearest thousand 7,000.

6,999 → nearest hundred 7,000 and nearest thousand 7,000.

7,126 (7,100 and 7,000) and 7,835 (7,800 and 8,000) give different results.

2Think and write two numbers that have the same — (a) Nearest ten (b) Nearest hundred (c) Nearest thousand.

(a) 38 and 42 — both have nearest ten 40.

(b) 360 and 430 — both have nearest hundred 400.

Many other answers are possible.

3Think and write the numbers that have the same — (a) Nearest ten and nearest hundred (b) Nearest hundred and nearest thousand (c) Nearest ten, hundred and thousand.

(a) 1,198 → nearest ten 1,200 and nearest hundred 1,200.

(b) 4,970 → nearest hundred 5,000 and nearest thousand 5,000.

Many other answers are possible.

Travelling, Now and Then — Let Us Do

1A cyclist can cover 15 km in one hour. How much distance will she cover in 4 hours, if she maintains the same speed?

Distance in 1 hour = 15 km

Distance in 4 hours = 15 × 4 = 60 km

She will cover 60 km in 4 hours.

2A school has 461 girls and 439 boys. How many vehicles are needed for all of them to go on a trip using the following modes of travel?

Total students = 461 + 439 = 900

Mode of travel	People in one vehicle	Vehicles needed
(a) Bicycle	2	900 ÷ 2 = 450
(b) Autorickshaw	3	900 ÷ 3 = 300
(c) Car	4	900 ÷ 4 = 225
(d) Big car	6	900 ÷ 6 = 150
(e) Tempo traveller	10	900 ÷ 10 = 90
(f) Boat	20	900 ÷ 20 = 45
(g) Minibus	25	900 ÷ 25 = 36
(h) Aeroplane	180	900 ÷ 180 = 5

Finding Large Numbers Around Us

1Find something in the textbook whose count is a 4-digit number.

The total number of words in one chapter of the textbook is a 4-digit number.

For example, a chapter of 16 pages with about 150 words on each page has about 2,400 words.

2Fill in for your school: (a) classrooms (b) students in my class (c) books in the classroom.

Answers depend on your school. Count and write. Example: (a) Our school has 18 classrooms. (b) There are 42 students in my class. (c) Our classroom has 336 books in total.

3Find something in the classroom whose count is a (i) 4-digit number (ii) 5-digit number.

(i) 4-digit: the total number of pages in all the books in our bags.

(ii) 5-digit: the total number of words in all the textbooks of the class.

4List some quantities whose count is a 4-digit or a 5-digit number in the context of (i) a tree (ii) your village/town/city.

(i) A tree: the number of leaves on a big tree; the number of mangoes on a mango tree in a season.

(ii) A village or town: the number of people living there; the number of houses; the number of vehicles.

Pastime Mathematics

1River crossing puzzle: How can the boatman take the lion, sheep and grass across the river safely in the minimum number of trips?

Trip 1: Take the sheep across. (Lion and grass are safe together.)

Trip 2: Come back alone.

Trip 3: Take the lion across.

Trip 4: Bring the sheep back.

Trip 5: Take the grass across. (Leave it with the lion.)

Trip 6: Come back alone.

Trip 7: Take the sheep across.

All three reach the other side safely in 7 trips.

In Trip 3, he can take the grass instead of the lion. The rest of the steps stay the same.

2Pile of pebbles: There are two piles of 7 pebbles each. The player who picks the last pebble wins. How do you play so that you win?

Let your friend play first.

After each of your turns, keep both piles equal.

If your friend takes some pebbles from one pile, take the same number from the other pile.

In the end, your friend empties one pile and you pick the last pebble. So you win.

3Mira’s puzzle — Answer the questions.

(1) Observe the differences you get in each step. Do you notice anything in common?

The differences are 36, 27, 45 and 9. All of them are in the multiplication table of 9.

The sum of the digits of each difference is 9.

(2) Try the puzzle using any other pair of digits.

Take 2 and 5: 52 − 25 = 27, 72 − 27 = 45, 54 − 45 = 9.

All differences are multiples of 9. We get 9 in the end.

(3) What digits can you choose so that you get a 1-digit number in the first step itself?

Choose two digits that differ by 1 (consecutive digits).

Examples: 4 and 5 (54 − 45 = 9), 2 and 3 (32 − 23 = 9), 7 and 8 (87 − 78 = 9).

(4) Find different digits such that the difference between the numbers is 27.

Choose digits that differ by 3: 1 and 4 (41 − 14 = 27), 2 and 5, 3 and 6, 4 and 7, 5 and 8, 6 and 9.

(5) Extend Mira’s table so that the differences in digits are 2, 3, 5 and 7.

Digits	Difference in digits	Difference in numbers
1, 3	3 − 1 = 2	31 − 13 = 18
1, 4	4 − 1 = 3	41 − 14 = 27
1, 6	6 − 1 = 5	61 − 16 = 45
1, 8	8 − 1 = 7	81 − 18 = 63

What do the differences between the digits indicate? The difference in numbers is 9 times the difference in digits. For example, 9 × 4 = 36.

Numbers that give a 1-digit number in the third subtraction: digits that differ by 3 or 8. For example, 14, 25, 36, 47, 58, 69 and 19 (and their reverse numbers). For 41: 27 → 45 → 9.

Maximum number of subtractions: digits that differ by 2, such as 1 and 3, 2 and 4, 3 and 5, 4 and 6, 5 and 7, 6 and 8, 7 and 9. They take 5 subtractions: 18 → 63 → 27 → 45 → 9.

Let Us Do

1Write 5 numbers between the numbers 23,568 and 24,234.

23,600, 23,700, 23,800, 23,900 and 24,000

2Write 5 numbers that are more than 38,125 but less than 38,600.

38,200, 38,300, 38,400, 38,500 and 38,550

3Ravi’s car has been driven for 56,987 km. Sheetal’s car has been driven 67,543 km. Whose car has been driven more?

67,543 > 56,987. So, Sheetal’s car has been driven more.

4Arrange the prices of electric bikes in ascending (increasing) order.

₹39,999, ₹49,900, ₹89,999, ₹90,000, ₹93,743, ₹94,983

5Arrange the population of the towns in descending (decreasing) order.

Town 6 (66,540), Town 1 (65,232), Town 3 (56,380), Town 2 (53,231), Town 4 (51,336), Town 5 (45,858)

6Find numbers between 42,750 and 53,500 such that the ones, tens, and hundreds digits are all 0.

43,000, 44,000, 45,000, 46,000, 47,000, 48,000, 49,000, 50,000, 51,000, 52,000 and 53,000

7Write the following numbers in the expanded form.

(a) 783 = 700 + 80 + 3

(b) 8,062 = 8,000 + 60 + 2

(d) 10,304 = 10,000 + 300 + 4

(e) 23,004 = 20,000 + 3,000 + 4

(f) 70,405 = 70,000 + 400 + 5

8Fill in the blanks with the correct answer.

(a) 983 = 90 Tens + 83 Ones

(b) 68 = 5 Tens + 18 Ones

(d) 5,621 = 4 Thousand + 16 Hundreds + 2 Tens + 1 Ones

(e) 7,069 = 5 Thousand + 20 Hundreds + 69 Ones

(f) 37,608 = 2 Ten Thousand + 17 Thousand + 6 Hundreds + 8 Ones

(g) 43,001 = 3 Ten Thousand + 13 Thousand + 0 Hundreds + 1 Ones

9Fill in the blanks with the correct answers.

(a) Notes of ₹10 in ₹7,934 = 793

(b) Notes of ₹100 in ₹7,934 = 79

(d) ₹500 notes in ₹7,934 = 15 (7 thousands = 14 notes of ₹500, and 934 has one more ₹500.)

(e) Notes of ₹10 in ₹65,342 = 6,534

(f) Notes of ₹100 in ₹65,342 = 653

(g) Thousands in 65,342 = 65

(h) ₹500 notes in ₹65,342 = 130 (65 thousands = 130 notes of ₹500. 342 is less than 500.)

King’s Horses

1Were there really 20 horses in the stable? What was the mistake in the caretaker’s explanation?

No. There were only 19 horses.

The horse in the corner was counted twice. It was counted on two sides.

So, 5 × 4 = 20 is wrong. Horses in the corners belong to two sides.

2Arrange 18 horses in the stable with 5 on each side.

Put 1 horse in two opposite corners. Put 2 horses in each of the other 8 side places (non-corner). Keep the other two corners empty.

Each side = 1 + 2 + 2 + 0 = 5. Total = 1 + 1 + (8 × 2) = 18.

3How many more horses can the thief steal before the king notices something is wrong?

Put more horses in the corners, because a corner horse is counted on two sides.

Keep 3 horses in two opposite corners and 2 horses in the other two corners. Keep all other places empty.

Each side = 3 + 2 = 5. Total = 3 + 3 + 2 + 2 = 10 horses.

So, from 18 horses, the thief can steal 8 more horses before the king notices.

2. Fractions →