Important Formulas: We the Travellers—II | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Fuel Arithmetic

Vehicles need fuel in litres (L):

• Motorbike: 5–15 L

• Car: 15–50 L

• Lorry/Truck: 150–500 L

• Train: ~5,000 L

Addition Rule:

• To find total fuel, add the existing fuel and new fuel added.

• Use place value addition: Ones, Tens, Hundreds, Thousands.

Example 1:

• A car has 25 L of fuel.

• It is refuelled with 18 L more.

• Total fuel = 25 + 18 = 43 L

Example 2:

• A lorry has 320 L of fuel.

• It is refuelled with 175 L more.

• Total fuel = 320 + 175 = 495 L

Subtraction Rule:

• To find fuel filled, subtract initial fuel from total fuel after refuelling.

• Always regroup (borrow) when the top digit is smaller.

Example 1:

• A motorbike had 7 L.

• After refuelling, it has 12 L.

• Fuel filled = 12 – 7 = 5 L

Example 2:

• A train had 3,450 L.

• After refuelling, it has 4,200 L.

• Fuel filled = 4,200 – 3,450 = 750 L

Relationship Between Addition and Subtraction

Addition and subtraction are inverse operations.

If A + B = C, then:

• C – A = B

• C – B = A

If A – B = C, then:

• C + B = A

• A – C = B

Sums of Consecutive Numbers

Consecutive Numbers: Numbers following each other in order (e.g., 11, 12, 13, 14).

• Rules:

  • Sum of 2 consecutive numbers → Always odd.

  • Sum of 3 consecutive numbers → Multiple of 3 (odd/even depends on middle number).

  • Sum of 4 consecutive numbers → Always even.

• Patterns:

  • For odd number of terms → Sum = Middle Number × Number of Terms.

  • For even number of terms → Sum = (First Number + Last Number) × (Number of Terms ÷ 2).

• Difference Between Successive Sums = Number of terms.

Adding Large Numbers

Steps:

1. Align digits properly: Ones under Ones, Tens under Tens, etc.

2. Add from right to left, regroup when needed.

Example:

• 21,880 + 38,900 = 60,780

Step 1: Ones Place Value

0 + 0 = 0

Put the 0 in Ones place

Step 2: Tens Place Value
8 + 0 = 8
Put the 8 in Tens place

Step 3: Hundreds Place Value
8 + 9 = 17
Put the 7 in Hundreds place
Carry the 1 to Thousands place

Step 4: Thousands Place Value
1 + 1 + 8 = 10
Put the 0 in Thousands place
Carry the 1 to Ten Thousands place

Step 5: Ten Thousands Place Value

1 + 2 + 3 = 6

Put the 6 in Ten Thousands place

Subtracting Large Numbers

Steps:

1. Align digits.

2. Subtract from right to left.

3. If the top digit is smaller, regroup from the next place value.

Example:

• 2,700 – 1,083 = 1,617

Step 1: 3 is greater than 0 so you must regroup:
Take 1 from 7, so 7 becomes 6.
Add 10 to 0, so 0 becomes 10.

Step 2: Take 1 from 10, so 10 becomes 9.
Add 10 to 0, so 0 becomes 10.

Step 3: 10 minus 3 is 7

Step 4: 9 minus 8 is 1

Step 5: 6 minus 0 is 6

Step 6: 2 minus 1 is 1

Quick Mental Addition and Subtraction

Sukanta’s Challenge

To find missing number in: Number + ? = Target → Subtract.

• Example: 100 – 32 = 68

Piku’s Method

• To reach 100:

  1. Add to nearest multiple of 10.

  2. Add the rest.

• Example: 32 + 68 = 100 (via 32 + 67 = 99, then +1).

Namita’s Trick

• To subtract 9: Subtract 10, then add 1.

• To subtract 99: Subtract 100, then add 1.

• To subtract 999: Subtract 1000, then add 1.