NCERT Class 5 Mathematics Maths Mela Chapter 04 We the Travellers II PDF Download

Chapter 4: We the Travellers - II

Making Sums Equal

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.

Think what will happen to the sums if we interchange 2 and 5? Try interchanging other pairs of numbers and find the one that will make the sums equal.

(a)

(b)

(c)

(d)

Teacher's Note

When you interchange two numbers between groups, both sums change by the same amount. If you move a number \( x \) from one group to another, that group loses \( x \) and gains a different number \( y \), so the difference changes by \( x + y \). To find the pair to swap, look at how much bigger one sum is than the other, then find which pair makes up exactly that difference.

Fuel Arithmetic

Different vehicles need different quantities of fuel. This quantity can vary from 5 to 15 litres in the case of motorbikes, 15 to 50 litres in the case of cars, 150 to 500 litres in the case of lorries and trucks, and 5,000 litres in the case of a train.

Remember - We must save fuel as it is a limited resource. Reducing fuel usage also helps in cutting down pollution. Electric vehicles are now available that help conserve natural fuel and reduce pollution.

1. A lorry has 28 litres of fuel in its tank. An additional 75 litres is filled. What is the total quantity of fuel in the lorry?

The total quantity of fuel in the tank is 28 l + 75 l.

Do you remember how to add two numbers using place value of numbers?

Regroup, 10 Ones = 1 Ten

Let us try one more.

2. Find the sum of 49 and 89.

Let Us Solve

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

1. 15 + 79
2. 46 + 99
3. 38 + 35
4. 5 + 89
5. 76 + 28
6. 69 + 20

Relationship Between Addition and Subtraction

1. Find the relationship between the numbers in the given statements and fill in the blanks appropriately.

1. If 46 + 21 = 67, then,
   67 − 21 = _______.
   67 − 46 = _______.
2. If 198 − 98 = 100, then,
   100 + _______ = 198.
   198 − _______ = 98.
3. If 189 + 98 = 287, then,
   287 − 98 = _______.
   287 − 189 = _______.
4. If 872 − 672 = 200, then,
   200 + _______ = 872.
   872 − _______ = 672.

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

1. If 78 + 164 = 242, then,
   _________________________.
   _________________________.
2. If 462 + 839 = 1301, then,
   _________________________.
   _________________________.
3. If 921 − 137 = 784, then,
   _________________________.
   _________________________.
4. If 824 − 234 = 590, then,
   _________________________.
   _________________________.

More Fuel Arithmetic

A minibus has 18 l of fuel left. After refuelling, the fuel meter indicates 65 l. How much fuel has been filled in the fuel tank of the minibus?

The quantity of fuel filled is 65 l − 18 l.

Regroup, 1 Tens = 10 Ones

Check if 18 + 47 = 65?

Teacher's Note

Addition and subtraction are inverse operations: they undo each other. When you add or subtract large numbers using columns, regrouping (carrying) happens when a column adds up to 10 or more, and borrowing happens when you need to take from the next column. Always check your subtraction by adding: if \( a - b = c \), then \( b + c \) should equal \( a \).

Let Us Solve

1. What is the difference between 82 and 37?

Remember subtraction using place value? Try this.

Check your answer. Is 37 + ____ = 82?

2. 57 − 11 = _________
3. 23 − 19 = _________
4. 49 − 21 = _________
5. 56 − 18 = _________
6. 93 − 35 = _________
7. 84 − 23 = _________
8. 70 − 43 = _________
9. 65 − 47 = _________

Sums of Consecutive Numbers

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

1, 2, 3, 4, 5 29, 30, 31, 32 512, 513 2023, 2024, 2025

Sum of 2 consecutive numbers.

1 + 2 = 3
2 + 3 = 5
3 + 4 = 7
4 + 5 = 9

Sum of 3 consecutive numbers.

1 + 2 + 3 = 6
2 + 3 + 4 = 9
3 + 4 + 5 = 12
4 + 5 + 6 = 15

Sum of 4 consecutive numbers.

1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14
3 + 4 + 5 + 6 = 18
4 + 5 + 6 + 7 = 22

1. In each of the boxes above, state whether the sums are even or odd. Explain why this is happening.
2. What is the difference between two successive sums in each box? Is it the same throughout?
3. What will be the difference between two successive sums for -
   (a) 5 consecutive numbers (b) 6 consecutive numbers

Let us see some more interesting patterns in sums.

1 + 2 + 3 = 6
1 + 2 + 3 + 4 = 10
1 + 2 + 3 + 4 + 5 = 15

2 + 3 + 4 = 9
2 + 3 + 4 + 5 = 14
2 + 3 + 4 + 5 + 6 = 20

3 + 4 + 5 = 12
3 + 4 + 5 + 6 = 18
3 + 4 + 5 + 6 + 7 = 25

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.

1. 67 + 68 + 69
2. 24 + 25 + 26 + 27
3. 48 + 49 + 50 + 51 + 52
4. 237 + 238 + 239 + 240 + 241 + 242

The Longest Land Route - Adding Large Numbers

The longest distance one can travel by road is between Talon (in Russia) and Sagres (in Portugal). It is 15,150 km long.

In 2019, the North-South Corridor was the longest land route within India, starting from Srinagar in Jammu and Kashmir and ending at Kanniyakumari in Tamil Nadu. Do you know how long it was? Let us find out.

One of the places on the North-South Corridor was 1,855 km from Srinagar and 1,862 km from Kanniyakumari. What was the total length of the North-South Corridor in 2019?

[Figure: Map of India showing the North-South Corridor with distances 1885 km and 1862 km marked, See in your textbook]

Key Points

• When you swap numbers between two groups, the difference in their sums changes by the sum of the two numbers being exchanged.
• Addition and subtraction are inverse operations: if \( a + b = c \), then \( c - a = b \) and \( c - b = a \). Use this to check your answers.
• When adding numbers with regrouping, carry the extra tens to the next column. When subtracting with borrowing, take 10 from the tens place to add to the ones place.
• The sum of consecutive numbers follows a pattern. For example, the sum of 3 consecutive numbers equals 3 times the middle number, and the sum of 4 consecutive numbers equals the sum of the two middle numbers times 2.
• To add large numbers, align them by place value (ones, tens, hundreds, thousands) and add from right to left, regrouping when necessary.

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