Class 5 — Mathematics
Large Numbers and Operations
Class 5
- ✓By the end of this lesson students will be able to read and write large numbers up to crores using the Indian Place Value System.
- ✓By the end of this lesson students will be able to identify the place value and face value of digits in large numbers.
- ✓By the end of this lesson students will be able to perform basic arithmetic operations (addition, subtraction, multiplication, division) with large numbers.
- ✓By the end of this lesson students will be able to understand and apply the BODMAS rule to simplify numerical expressions.
Key concepts
In the Indian Place Value System, we group digits into periods: Ones, Thousands, Lakhs, and Crores. Starting from the right, the first period is 'Ones' (ones, tens, hundreds). The second period is 'Thousands' (thousands, ten thousands). The third period is 'Lakhs' (lakhs, ten lakhs). The fourth period is 'Crores' (crores, ten crores). Commas are used to separate these periods. The first comma comes after the hundreds place (3 digits from the right), and then after every two digits.
The Face Value of a digit is the digit itself, regardless of its position in the number. For example, in the number 7,45,210, the face value of 4 is 4. The Place Value of a digit is its face value multiplied by the value of its position in the number. For example, in 7,45,210, the digit 4 is in the ten thousands place, so its place value is 4 × 10,000 = 40,000.
Performing addition, subtraction, multiplication, and division on large numbers follows the same rules as for smaller numbers. It is important to align the digits correctly according to their place values and to be careful with carrying over in addition/multiplication and borrowing in subtraction. Division involves repeated subtraction and finding quotients and remainders.
When we have an expression with multiple operations, we must follow a specific order to get the correct answer. This order is given by the BODMAS rule:\nB - Brackets (first solve operations inside brackets)\nO - Of (perform 'of' operations, which usually means multiplication)\nD - Division (perform division from left to right)\nM - Multiplication (perform multiplication from left to right)\nA - Addition (perform addition from left to right)\nS - Subtraction (perform subtraction from left to right)\nRemember that Division and Multiplication have equal priority, and Addition and Subtraction have equal priority. When they appear together, solve them from left to right.
Key facts to remember
- 1The Indian Place Value System uses periods: Ones, Thousands, Lakhs, Crores.
- 2Commas are placed after the hundreds digit, then after every two digits (e.g., 1,23,45,678).
- 31 lakh = 100 thousands.
- 41 crore = 100 lakhs.
- 5The Face Value of a digit is the digit itself.
- 6The Place Value of a digit depends on its position in the number.
- 7BODMAS stands for Brackets, Of, Division, Multiplication, Addition, Subtraction.
- 8Division and Multiplication have equal priority; Addition and Subtraction have equal priority. Solve from left to right for operations of equal priority.
Worked examples
Example 1
Write the number name for 8,07,65,432. Also, write the place value of the digit 7 in this number.
Answer
Number Name: Eight crore seven lakh sixty-five thousand four hundred thirty-two.\nPlace Value of 7: 7,00,000.
Always place commas correctly to easily read large numbers.
Example 2
A library has 3,45,678 Hindi books and 2,89,123 English books. How many books are there in total in the library?
Answer
There are 6,34,801 books in total in the library.
Always align digits carefully before performing addition or subtraction to avoid errors.
Example 3
Simplify: 40 + 12 × 5 - 36 ÷ 4
Answer
91
Strictly follow the BODMAS order. If you change the order, you will get a different and incorrect answer.
Common mistakes
- ✗Confusing the Indian Place Value System with the International Place Value System (e.g., placing commas incorrectly).
- ✗Incorrectly carrying over digits in addition/multiplication or borrowing in subtraction with large numbers.
- ✗Not following the BODMAS rule, leading to incorrect results in expressions with multiple operations.
- ✗Making errors in basic arithmetic facts (addition, subtraction, multiplication tables) during calculations with large numbers.
- ✗Performing addition/subtraction before multiplication/division when no brackets are present.
Exam tips
- ★Practice reading and writing large numbers regularly to become familiar with the Indian Place Value System and comma placement.
- ★Always show all steps clearly when performing operations or simplifying expressions. This helps in identifying errors and earns partial marks.
- ★Double-check your calculations, especially carrying and borrowing, to ensure accuracy in operations with large numbers.
- ★Memorise the BODMAS rule and practice applying it to various expressions to ensure you follow the correct order of operations.
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