Operations with Whole Numbers
Key Concepts
Whole numbers are the set of numbers that include zero and all positive integers (0, 1, 2, 3, ...). Operations with whole numbers involve basic arithmetic operations: addition, subtraction, multiplication, and division. Understanding these operations is fundamental for solving mathematical problems.
1. Addition of Whole Numbers
Addition is the process of combining two or more numbers to find their total. The result of addition is called the sum.
Example: Add 15 and 23.
Step 1: Write the numbers in a column format.
Step 2: Add the digits in the units place: 5 + 3 = 8.
Step 3: Add the digits in the tens place: 1 + 2 = 3.
Step 4: Combine the results: 3 tens and 8 units = 38.
So, 15 + 23 = 38.
2. Subtraction of Whole Numbers
Subtraction is the process of taking away one number from another to find the difference. The result of subtraction is called the difference.
Example: Subtract 45 from 72.
Step 1: Write the numbers in a column format with the larger number on top.
Step 2: Subtract the digits in the units place: 2 - 5. Since 2 is less than 5, borrow 1 from the tens place (7 becomes 6), and add 10 to the units place (2 becomes 12).
Step 3: Subtract the digits in the units place: 12 - 5 = 7.
Step 4: Subtract the digits in the tens place: 6 - 4 = 2.
Step 5: Combine the results: 2 tens and 7 units = 27.
So, 72 - 45 = 27.
3. Multiplication of Whole Numbers
Multiplication is the process of adding a number to itself a certain number of times. The result of multiplication is called the product.
Example: Multiply 12 by 5.
Step 1: Write the numbers in a column format.
Step 2: Multiply the units digit of the second number (5) by each digit of the first number (12).
Step 3: 5 * 2 = 10 (write 0, carry 1).
Step 4: 5 * 1 = 5 + 1 (carry) = 6.
Step 5: Combine the results: 6 tens and 0 units = 60.
So, 12 * 5 = 60.
4. Division of Whole Numbers
Division is the process of splitting a number into equal parts. The result of division is called the quotient.
Example: Divide 72 by 6.
Step 1: Write the division in the form of a division bracket.
Step 2: Determine how many times the divisor (6) can go into the first digit of the dividend (7). It goes 1 time.
Step 3: Multiply 1 * 6 = 6, and subtract from 7 to get the remainder 1.
Step 4: Bring down the next digit (2) to make it 12.
Step 5: Determine how many times 6 can go into 12. It goes 2 times.
Step 6: Multiply 2 * 6 = 12, and subtract from 12 to get the remainder 0.
Step 7: Combine the results: 1 ten and 2 units = 12.
So, 72 รท 6 = 12.
Practical Application
Understanding operations with whole numbers is essential for everyday tasks such as budgeting, cooking, and measuring distances. By mastering these operations, you can solve real-world problems more efficiently.
Summary
Operations with whole numbers involve addition, subtraction, multiplication, and division. Each operation has its own set of rules and steps to follow, which are essential for accurate calculations. Practicing these operations will enhance your mathematical skills and problem-solving abilities.