We the Travellers 2 Class 5 Solutions Question Answer Maths Chapter 4

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Class 5 Maths Chapter 4 We the Travellers 2 Question Answer Solutions

We the Travellers 2 Class 5 Maths Solutions

Class 5 Maths Chapter 4 Solutions

Making Sums Equal (Page 43)

In each of the following, there are two groups of numbers. Look carefully at the numbers in each group and their sums. Interchange pairs of numbers between the two groups to make their sums equal. Try to do this using the least number of moves. You could write each number on a small piece of paper.

Solution:

Swaping 2 ↔ 3 both sums become 20 (1 move)

Solution:

Swaping 5 ↔ 9 both sums become 43 (1 move)

Solution:

Swaping 11 ↔ 13 and 15 ↔ 17 both sums become 72 (2 moves)

Solution:

Swaping 77 ↔ 81 and 78 ↔ 82 both sums become 322 (2 moves)

Let us try one more. (Page 43)

Find the sum of 49 and 89.

Solution:
1 3 8

Let Us Solve

Add the following numbers. Wherever possible, find easier ways to add the pairs of numbers.

1. 15 + 79
Solution:

94
Also 15 + 79 = 15 + (80 – 1)
= 95 – 1
= 94

2. 46 + 99
Solution:

145
46 + 99 = 46 + (100 – 1)
= 146 – 1
= 145

3. 38 + 35
Solution:

73

4. 5 + 89
Solution:

94

5. 76 + 28
Solution:

104

6. 69 + 20
Solution:

89

Relationship Between Addition and Subtraction (Page 44)

Question 1.
Find the relationship between the numbers in the given statements and fill in the blanks appropriately.
(a) If 46 + 21 = 67, then,
67 – 21 = _______.
67 – 46 = _______.
Solution:
If 46 + 21 = 67, then,
67 – 21 = 46
67 – 46 = 21 .

(b) If 198 – 98 = 100, then,
100 + _______ = 198.
198 – _______ = 98.
Solution:
If 198 – 98 = 100, then,
100 + 98 = 198.
198 – 100 = 98.

(c) If 189 + 98 = 287, then,
287 – 98 = _______.
287 – 189 = _______.
Solution:
If 189 + 98 = 287,
then, 287 – 98 = 189.
287 – 189 = 98

(d) If 872 – 672 = 200, then,
200 + _______ = 872.
872 – _______ = 672.
Solution:
If 872 – 672 = 200, then,
200 + 672 = 872.
872 – 200 = 672.

Question 2.
In each of the following, write the subtraction and addition sentences that follow from the given sentence.

Solution:
(a) If 78 + 164 = 242,
then, 242- 78 = 164

(b) If 462 + 839 = 1301,
then, 1301 – 462 = 839

(c) If 921- 137 = 784,
then, 784 + 137 = 921

(d) If 824-234 = 590,
then, 590 + 234 = 824

Let Us Solve

Question 1.
What is the difference between 82 and 37?

Solution:

Check your answer.
Is 37 + 45 = 82? Yes

2. 57 – 11 = _______
Solution:

3. 23 – 19 = _______
Solution:

4. 49 – 21 = _______
Solution:

5. 56 – 18 = _______
Solution:

6. 93 – 35 = _______
Solution:

7. 84 – 23 = _______
Solution:

8. 70 – 43 = _______
Solution:

9. 65 – 47 = _______
Solution:

Sums of Consecutive Numbers (Page 45)

Numbers that follow one another in order without skipping any number are called consecutive numbers. Here are some examples —

Question 1.
In each of the boxes above, state whether the sums are even or odd. Explain why this is happening.
Solution:
(i) Sum of 2 consecutive numbers: Always odd.
Reason: Each pair has one even and one odd number;
even + odd = odd.

(ii) Sum of 3 consecutive numbers: Alternates even/odd.
Reason: odd + even + odd = even, and even + odd + even = odd.

(iii) Sum of 4 consecutive numbers: Always even.
Reason: There are two evens and two odds.
Even + even = even, odd + odd = even, and even + even = even.

Question 2.
What is the difference between two successive sums in each box? Is it the same throughout?
Solution:
(i) Sum of 2 consecutive numbers:
Differences:
5 – 3 = 2, 7 – 5 = 2, 9 – 7 = 2.
The difference is always 2.

(ii) Sum of 3 consecutive numbers:
Differences:
9 – 6 = 3, 12 – 9 = 3, 15 – 12 = 3
The difference is always 3.

(iii) Sum of 4 consecutive numbers:
Differences:
14 – 10 = 4, 18 – 14 = 4, 22 – 18 = 4
The difference is always 4.
So, the difference between successive sums is the same throughout each box.

Question 3.
What will be the difference between two successive sums for
(a) 5 consecutive numbers
(b) 6 consecutive numbers
Solution:
(a) Sum of 5 consecutive numbers:
1 + 2 + 3 + 4 + 5 = 15
2 + 3 + 4 + 5 + 6 = 20
3 + 4 + 5 + 6 + 7 = 25
Difference: 20 – 15 = 5, 25 – 20 = 5.
The difference is 5.

(b) Sum of 6 consecutive numbers:
1 + 2 + 3 + 4 + 5 + 6 = 21
2 + 3 + 4 + 5 + 6 + 7 = 27
3 + 4 + 5 + 6 + 7 + 8 = 33
Difference: 27 – 21 = 6, 33 – 27 = 6.
The difference is 6.

(Page 46)

Notice how the sums of 3, 4, and 5 consecutive numbers are related to the numbers being added. Use your understanding to find the following sums without adding the numbers directly.
(a) 67 + 68 + 69
Solution:
67 + 68 + 69

= 68 + 68 + 68
= 68 × 3
= 204

OR

67 + 68 + 69
= 68 × 3
(When no. of addends is odd.)

(b) 24 + 25 + 26+ 27
Solution:

= 102 (When no. of addends is even pair them up)

(c) 48 + 49 + 50 + 51 + 52
Solution:

= 5 × 50
= 250 (no. of addends is odd)

(d) 237 + 238 + 239 + 240 + 241 + 242
Solution:

= 479 × 3
= 1437

Let Us SoLve (Page 48)

Question 1.
Find the following sums. Try not to write TTh, Th, H, T, and O at the top. Just align the digits properly, at least for the smaller numbers.
(a) 238 + 367
Solution:

(b) 1,234 + 12,345
Solution:

(c) 12 + 123
Solution:

(d) 46,120 + 12,890
Solution:

(e) 878 + 8,789
Solution:

(f) 1,749 + 17,490
Solution:

Question 2.
The great Indian road trip!
Nazrana and her friends planned a road trip across India, starting from Delhi. They first drove to Mumbai, then Goa, then Hyderabad, and finally Puri.
Look at the distances marked on the map and help them find the total distance travelled.

Solution:
Total distance travelled by Nazrana and her friends
= 1600 km + 590 km + 670 km + 1055 km

= 3,915 km

Question 3.
Find 2 numbers among 5,205,6,220,7,095,8,455, and 4,840 whose sum is closest to the following.
(a) 10,000
Solution:
5,205 + 4,840 = 10045 which is closest to 10,000

(b) 15,000
Solution:
8,455 + 6,220 = 14675 which is closest to 15,000

(c) 13,000
Solution:
8,455 + 4,840 = 13295 which is closest to 13,000

(d) 16,000
Solution:
8,455 + 7,095 = 15550 which is closest to 16,000

Let Us Solve (Pages 50-51)

Question 1.
Subtract the following. Try not to write TTh, Th, H, T, and O at the top. Align the digits carefully.
(a) 4,578 – 2,222
Solution:

(b) 15,324 – 11,780
Solution:

(c) 5,423 – 423
Solution:

(d) 123 – 12
Solution:

(e) 77,777 – 777
Solution:

(f) 826 – -752
Solution:

Question 2.
Mary’s train journey to Delhi.
Mary is on a train journey. She starts from Kolkata with ₹ 12,540.
She spends ₹ 3,275 on food and other expenses during her trip to Varanasi.
In Varanasi, her uncle gives her a gift worth ₹ 4,900. She then travels to Delhi, spending ₹ 2,645 on the train ticket. She spends ₹ 1,275 on souvenirs in Delhi.
How much money is Mary left with at the end of the Delhi trip?

Solution:

At the beginning of the journey Mary had = ₹ 12,540
Money Mary spends on food = ₹ 3,275
Money Mary spends on train ticket =₹ 2,645
Money Mary spends on souvenirs = ₹ 1,275
Total money spent = ₹ 3275 + ₹ 2645 + ₹ 1275
= ₹ 7,195

Money left with her
=₹ 12,540 – ₹ 7195 and a gift worth ₹ 4900

= ₹ 5345 + gift worth ₹ 4900

Question 3.
Members of a school council have raised ₹ 70,500. They plan to setup a Maths Lab with some games and models worth ₹ 39,785, buy library books worth ₹ 9,545, and purchase sports equipment worth ₹ 19,548.
(a) Estimate whether the school council has raised enough money to make the purchases. Share your thoughts in the class.
(b) Check your estimate with calculations.
Solution:
Money raised by school council = ₹ 70,500
(a) Money is to be spend on:
Games and Model worth = ₹ 39,785
Library books = ₹ 9,545
Sports equipment = ₹ 19,548
Estimated money spend is less than
= ₹ 40,000 + ₹ 10,000 + ₹ 20,000 = ₹ 70,000
Council has raised enough money to make the purchase.

(b) Exact money spent

= ₹ 68,878

Question 4.
A truck can carry 8,250 kg of goods. A factory loads 3,675 kg of cement and 2,850 kg of steel on it.
(a) What is the total weight loaded onto the truck?
(b) How much more weight can the truck carry before reaching its maximum capacity?
Solution:
(a) Weight a truck can carry = 8,250 kg
Weight of cement loaded on truck = 3,675 kg
Weight of steel loaded on truck = 2,850 kg

Total weight loaded on truck

= 6,525 kg

(b) More weight that can be loaded on truck
= 8,250 kg – 6,525 kg

= 1,725 kg

Quick Sums and Differences (Pages 51-52)

Sukanta likes the numbers 10, 100, 1,000, and 10,000. He wants to figure out what number he should add to a given number such that the sum is 100 or 1,000. Help him fill in the blanks with an appropriate number.
32 + _______ = 100
Sukanta’s friend Piku shows him an interesting way to solve the problems.
Do you think this method will always work?

59 + _______ = 100
Try this method for the number 59.

This method always work.

Now, use this method to solve the following.
877 + _______ = 1,000 and 666 + _______ = 1,000
4,103 + _______ = 10,000 and 5,555 + _______ = 10,000
Solution:

Will this method work if the units digit is 0? What do you think? What other methods can you use to find the missing number to fill in the blanks? Share your thoughts in the class.
(a) 180 + _______ = 1,000
(b) 760 + _______ = 1,000
(c) 400 + _______ = 1,000
Solution:
Yes this method work if the units digit is 0.

Subtracting 9 is like subtracting 10 and adding 1. Subtracting 99 is same as subtracting 100 and adding 1.
Namita likes the number 9. She wants to subtract 9 or 99 from any number. Find a way to quickly subtract 9 or 99 from any number.
(a) 67 – 9 = 67 – 10 + 1 = 57 + 1 = 58
(b) 83 – 9 = 74
(c) 144 – 9 = 135
(d) 187 – 99 = 88
(e) 247 – 99 = 148
(f) 763 – 99 = 664

Now, use the above solutions to find answers to the following problems. Do not calculate again.
Namita wonders if she can get 9 or 99 as the answer to any subtraction problem. Find a way to get the desired answer.
(a) 32 – 23 = 9
(b) 56 – 47 = 9
(c) 877 – 778 = 99
(d) 666 – 567 = 99

Let Us Think and Solve (Page 53)

Question 1.
Nitin likes numbers that read the same when read from left to right or from right to left. Such numbers are called palindrome numbers. The numbers 22, 363, 404, and 8,558 are some examples.
List all palindrome numbers between 100 and 200.
List all palindrome numbers between 900 and 1,200.
List all palindrome numbers between 25,000 and 27,000.
Solution:
Palindrome numbers between 100 and 200 are
101, 111, 121, 131, 141, 151, 161, 171, 181, 191

Palindrome numbers between 900 and 1200 are
909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001, 1111

Palindrome numbers between 25000 and 27000 are
25052, 25152, 25252, 25352, 25452, 25552, 25652, 25752, 25852, 25952,
26062, 26162, 26262, 26362, 26462, 26562, 26662, 26762, 26862, 26962

Question 2
In a 3×3 grid, arrange the numbers 1 to 9 such that each row and each column has numbers in an increasing (inc) order. Each number should be used only once.

Solution:

This time, fill the grid such that each row and column has numbers in decreasing (dec) order.

Solution:

Now, fill the grids below with numbers (1-9) based on the inc (increasing) and dec (decreasing) conditions, as indicated below

Solution:

Even and Odd Numbers (Page 54)

Question 1.
Circle the numbers that are even.
(a) 297
(b) 498
(c) 724
(d) 100
(e) 199
(f) 789
(g) 49
(h) 6,893
(i) 846
(j) 111
(k) 222
(l) 1,023
Solution:

Question 2.
Observe the given arrangement.

Add 2 to 18. What changes or does not change in the arrangement?
Add 2 to 23. What changes or does not change in the arrangement?
Solution:
On adding 2 to 18 the arrangement will still remain paired.
On adding 2 to 23 the arrangement will still have one unpaired circle.

Question 3.
What do you notice about the sums in each of the following cases? Do you think it will be true for all pairs of such numbers? Explain your observations. You may use the paired arrangement to explain your thinking.
(a) 12 and 6 are a pair of even numbers. Choose 5 such pairs of even numbers. Add the numbers in each of the pairs.
(b) 13 and 9 are a pair of odd numbers. Choose 5 such pairs of odd numbers. Add the numbers in each of the pairs.
(c) 7 and 12 are a pair of odd and even numbers. Choose 5 such pairs of odd and even numbers. Add the numbers in each of the pairs.
Solution:
We observe that sum of even number and even number is always even and sum of odd number and even number is always odd number.
(a) 5 pairs of even numbers and their sum
6 and 8
6 + 8 = 14

4 and 10
4 + 10 = 14

16 and 20
16 + 20 = 36

18 and 14
18 + 14 = 32

20 and 18
20 + 18 = 38
We observe that sum of a pair of even numbers is always even.

(b) 5 pairs of odd numbers and their sum
7 and 9
7 + 9 = 16

9 and 13
9 + 13 = 22

15 and 19
15 + 19 = 34

3 and 17
3 + 17 = 20

11 and 27
11 + 27 = 38
We observe that sum of a pair of odd numbers is always even.

(c) 5 pairs of odd and even numbers and their sum
5 and 12
5 + 12 = 17

7 and 24
7 + 24 = 31

9 and 24
9 + 24 = 33

13 and 16
13 + 16 = 29

15 and 6
15 + 6 = 21
We observe that sum of odd and even numbers is always odd.

Let us Think (Pages 54-55)

Question 1.
Jincy opened her piggy bank. She found 8 coins of ₹ 1, 9 coins of ₹ 2 and 5 coins of ₹ 5. She wants to buy stickers worth ₹ 38. What possible combination of coins can she use to pay the exact amount₹
Solution:
Possible combination of coins 1st combination
₹5 × 5 + ₹ 2 × 3 + ₹1 × 7 = 25 + 6 + 7 = ₹ 38

2nd combination
₹5 × 5 + ₹ 2 × 4 + ₹ 1 × 5 = 25 + 8 + 5 = ₹ 38

3rd combination
₹5 × 5 + ₹ 2 × 5 + ₹ 1 × 3 = 25 + 10 + 3 = ₹38

4th combination
₹5 × 5 + ₹ 2 × 6 + ₹ 1 × 1 = 25 + 12 + 1 = ₹38

5th combination
₹5 × 4 + ₹ 2 × 9 = 20 + 18 = ₹ 38 6th combination
₹5 × 4 + ₹ 2 × 8 + ₹ 1 × 2 = 20 + 16 + 2 = ₹ 38

7th combination
₹5 × 4 + ₹ 2 × 7 + ₹ 1 × 4 = 20 + 14 + 4 = ₹38

8th combination
₹5 × 4 + ₹ 2 × 6 + ₹ 1 × 6 = 20 + 12 + 6 = ₹38

9th combination
₹5 × 4 + ₹ 2 × 5 + ₹ 1 × 8 = 20 + 10 + 8 = ₹38

10th combination
₹5 × 3 + ₹ 2 × 9 + ₹ 1 × 5 = 15 + 18 + 5 = ₹38

Question 2.
Raghu is fond of his grandfather’s torch. He starts playing with it. He presses the switch once and the light turns ON. He presses it a second time and the light turns OFF. He presses the switch a third time and the light turns ON. He keeps doing this several times. Will the torch be ON or OFF after the 23rd press? How do you know?
For what number of presses will the torch be ON? For what number of presses of the switch will the torch be OFF?
Solution:
On 23rd press the torch will be ON. Torch is switched on when the switch is pressed for odd number of press and torch is switched off for even number of press the switch is pressed.

Question 3.
Mountain climbing
Priyanka Mohite is the first Indian woman to climb five Himalayan peaks above 8,000 metres. In addition to that, she has also climbed mountain peaks in other parts of the world. Read the table below and answer the questions that follow.

(a) Which is the highest peak she climbed?
(b) What is the difference in height between the highest and lowest peaks she has climbed, as per the table?
(c) What is the difference between heights of Mount Elbrus and Mount Kanchenj unga?
(d) If Priyanka was 20 years old when she summited Mount Everest in 2013, in which year was she born?
Solution:
(a) The highest peak she climbed is Mount Everest.

(b) Difference between highest and lowest peak climbed by Priyanka is

(c) Height of Mount Kanchenj unga – Height of Mount Elbrus =

(d) In 2013 Priyanka was 20 years old. So Priyanka was born in 2013-20

Let Us Do (Page 56)

Question 1.
Add.
(a) 2,009 + 7,388
Solution:

(b) 26,444 + 71,111
Solution:

(c) 777 + 888
Solution:

(d) 1,234 + 1,234
Solution:

(e) 56 + 56,789
Solution:

(f) 777 + 77,777
Solution:

(g) 5,922 + 9,221
Solution:

(h) 4,321 + 8,765
Solution:

(i) 50,050 + 55,000
Solution:

Question 2.
Subtract.
(a) 458 – 226
Solution:

(b) 7,777 – 4,449
Solution:

(c) 65,447 – 47,299
Solution:

(d) 1,234 – 123
Solution:

(e) 12,345 – 1,234
Solution:

(f) 56,789 – 56
Solution:

(g) 87,326- 11,111
Solution:

(h) 878 – 52
Solution:

(i) 749 – 222
Solution:

Question 3.
Ambrish saved ₹ 92,375 over a year to buy cows and goats. He buys a cow for ₹ 26,000 and a goat for ₹ 17,000. He also buys a milking machine for ₹ 19,873. Does he have enough money to buy these? How much more or less does he have than he needs?
Solution:
Money Ambrish has = ₹ 92,375
Money spent on buying cow = ₹ 26,000
Money spent on buying goat = ₹ 17,000
Money spent on milking machine = ₹ 19873

Total money spent by Ambrish =

Total money Ambrish has spent = ₹ 62,873
He has enough money to buy all these
He has more money than he needs.

Ambrish has ₹ 29,502 more than he needs.

Question 4.
A factory produces 54,000 nuts and bolts in a day. An order is placed for 85,300 nuts and bolts. How many more nuts and bolts does the factory need to produce to complete the order?
Solution:
Number of nuts and bolts produced in a day = 54,000
Number of nuts and bolts ordered = 85,300
To complete the order number of nuts and bots needed

Question 5.
Virat Kohli has scored 27,599 runs. He has 6,758 runs less than Sachin Tendulkar. How many runs has Sachin Tendulkar scored?
Solution:
Total runs scored by Virat Kohli = 27599
Virat’s score is less than Sachin’s score by = 6,758
Sachin Tendulkar score = 27599 + 6758

Runs scored by Sachin Tendulkar = 34357