In mathematics, the basic operations serve as the foundation for almost all calculations. These operations include addition, subtraction, multiplication, and division. Understanding and mastering these basic operations are crucial for solving a wide variety of mathematical problems, from simple arithmetic to advanced algebra.
1.1 Addition
Addition is the process of combining two or more numbers to find their total or sum. The symbol used for addition is the plus sign (+).
For example:
- $ 3 + 2 = 5 $
Properties of Addition
- Commutative Property: The order of the numbers doesn’t affect the sum.
- Example: $ 4 + 3 = 3 + 4 = 7 $
- Associative Property: When adding three or more numbers, the way the numbers are grouped doesn’t affect the sum.
- Example: $ (1 + 2) + 3 = 1 + (2 + 3) = 6 $
- Identity Property: Adding 0 to a number doesn’t change its value.
- Example: $ 7 + 0 = 7 $
Examples 1-25: Working with Addition
Example 1: $ 5 + 8 $
Solution: $ 5 + 8 = 13 $
Example 2: $ 15 + 6 + 9 $
Solution: $ 15 + 6 + 9 = 30 $
Example 3: Add $ 23 + 57 $
Solution: $ 23 + 57 = 80 $
Example 4: Find the sum of $ 12 + 33 + 45 $
Solution: $ 12 + 33 + 45 = 90 $
Example 5: $ 10 + 90 $
Solution: $ 10 + 90 = 100 $
Example 6: What is the total of $ 42 + 39 $?
Solution: $ 42 + 39 = 81 $
Example 7: $ 99 + 1 $
Solution: $ 99 + 1 = 100 $
Example 8: $ 8 + 7 + 4 $
Solution: $ 8 + 7 + 4 = 19 $
Example 9: Find the sum of $ 100 + 50 $
Solution: $ 100 + 50 = 150 $
Example 10: Add $ 75 + 25 $
Solution: $ 75 + 25 = 100 $
Example 11: $ 12 + 38 $
Solution: $ 12 + 38 = 50 $
Example 12: $ 22 + 53 + 15 $
Solution: $ 22 + 53 + 15 = 90 $
Example 13: $ 9 + 4 + 6 $
Solution: $ 9 + 4 + 6 = 19 $
Example 14: $ 35 + 45 $
Solution: $ 35 + 45 = 80 $
Example 15: Add $ 60 + 30 + 10 $
Solution: $ 60 + 30 + 10 = 100 $
Example 16: $ 90 + 10 $
Solution: $ 90 + 10 = 100 $
Example 17: $ 25 + 25 $
Solution: $ 25 + 25 = 50 $
Example 18: $ 19 + 21 $
Solution: $ 19 + 21 = 40 $
Example 19: $ 78 + 22 $
Solution: $ 78 + 22 = 100 $
Example 20: Find the total of $ 7 + 14 + 29 $
Solution: $ 7 + 14 + 29 = 50 $
Example 21: $ 60 + 40 $
Solution: $ 60 + 40 = 100 $
Example 22: Add $ 50 + 70 $
Solution: $ 50 + 70 = 120 $
Example 23: $ 33 + 27 $
Solution: $ 33 + 27 = 60 $
Example 24: $ 21 + 79 $
Solution: $ 21 + 79 = 100 $
Example 25: $ 46 + 54 $
Solution: $ 46 + 54 = 100 $
1.2 Subtraction
Subtraction is the process of finding the difference between two numbers. The symbol used for subtraction is the minus sign (−).
For example:
- $ 9 – 4 = 5 $
Properties of Subtraction
- Non-Commutative: The order of the numbers affects the difference.
- Example: $ 10 – 3 \neq 3 – 10 $
- Identity Property: Subtracting 0 from a number doesn’t change its value.
- Example: $ 15 – 0 = 15 $
Examples 26-50: Working with Subtraction
Example 26: Subtract $ 9 – 3 $
Solution: $ 9 – 3 = 6 $
Example 27: $ 20 – 8 $
Solution: $ 20 – 8 = 12 $
Example 28: $ 50 – 25 $
Solution: $ 50 – 25 = 25 $
Example 29: $ 100 – 45 $
Solution: $ 100 – 45 = 55 $
Example 30: Find the difference of $ 72 – 30 $
Solution: $ 72 – 30 = 42 $
Example 31: $ 90 – 25 $
Solution: $ 90 – 25 = 65 $
Example 32: $ 88 – 44 $
Solution: $ 88 – 44 = 44 $
Example 33: $ 100 – 70 $
Solution: $ 100 – 70 = 30 $
Example 34: $ 75 – 50 $
Solution: $ 75 – 50 = 25 $
Example 35: $ 15 – 9 $
Solution: $ 15 – 9 = 6 $
Example 36: $ 84 – 24 $
Solution: $ 84 – 24 = 60 $
Example 37: $ 22 – 12 $
Solution: $ 22 – 12 = 10 $
Example 38: $ 100 – 55 $
Solution: $ 100 – 55 = 45 $
Example 39: $ 19 – 8 $
Solution: $ 19 – 8 = 11 $
Example 40: $ 67 – 34 $
Solution: $ 67 – 34 = 33 $
Example 41: $ 53 – 30 $
Solution: $ 53 – 30 = 23 $
Example 42: $ 47 – 12 $
Solution: $ 47 – 12 = 35 $
Example 43: $ 65 – 40 $
Solution: $ 65 – 40 = 25 $
Example 44: $ 58 – 19 $
Solution: $ 58 – 19 = 39 $
Example 45: $ 100 – 60 $
Solution: $ 100 – 60 = 40 $
Example 46: $ 38 – 14 $
Solution: $ 38 – 14 = 24 $
Example 47: $ 77 – 53 $
Solution: $ 77 – 53 = 24 $
Example 48: $ 95 – 45 $
Solution: $ 95 – 45 = 50 $
Example 49: $ 33 – 12 $
Solution: $ 33 – 12 = 21 $
Example 50: Subtract $ 46 – 23 $
Solution: $ 46 – 23 = 23 $
1.3 Multiplication
Multiplication is the process of adding a number to itself a specified number of times. The symbol used for multiplication is either the multiplication sign (×) or sometimes a dot (·).
For example:
- $ 6 \times 4 = 24 $
Properties of Multiplication
- Commutative Property: The order of numbers doesn’t affect the product.
- Example: $ 3 \times 4 = 4 \times 3 = 12 $
- Associative Property: When multiplying three or more numbers, the grouping of numbers doesn’t affect the product.
- Example: $ (2 \times 3) \times 4 = 2 \times (3 \times 4) = 24 $
- Identity Property: Multiplying any number by 1 gives the same number.
- Example: $ 9 \times 1 = 9 $
- Distributive Property: The sum of two numbers multiplied by a third number is the same as multiplying each of the numbers by the third number and then adding the results.
- Example: $ 2 \times (3 + 4) = (2 \times 3) + (2 \times 4) = 6 + 8 = 14 $
Examples 51-75: Working with Multiplication
Example 51: Multiply $ 7 \times 8 $
Solution: $ 7 \times 8 = 56 $
Example 52: $ 9 \times 6 $
Solution: $ 9 \times 6 = 54 $
Example 53: $ 15 \times 2 $
Solution: $ 15 \times 2 = 30 $
Example 54: $ 12 \times 3 $
Solution: $ 12 \times 3 = 36 $
Example 55: $ 5 \times 4 $
Solution: $ 5 \times 4 = 20 $
Example 56: $ 25 \times 3 $
Solution: $ 25 \times 3 = 75 $
Example 57: $ 14 \times 5 $
Solution: $ 14 \times 5 = 70 $
Example 58: $ 20 \times 10 $
Solution: $ 20 \times 10 = 200 $
Example 59: $ 7 \times 11 $
Solution: $ 7 \times 11 = 77 $
Example 60: Multiply $ 13 \times 6 $
Solution: $ 13 \times 6 = 78 $
1.4 Division
Division is the process of determining how many times one number is contained in another. The symbol for division is either the division sign (÷) or a slash (/).
For example:
- $ 12 \div 4 = 3 $
Properties of Division
- Non-Commutative: The order of numbers matters in division.
- Example: $ 15 \div 3 \neq 3 \div 15 $
- Identity Property: Dividing any number by 1 leaves the number unchanged.
- Example: $ 20 \div 1 = 20 $
- Division by Zero: Dividing any number by 0 is undefined.
- Example: $ 12 \div 0 $ is undefined.
Examples 76-100: Working with Division
Example 76: $ 45 \div 5 $
Solution: $ 45 \div 5 = 9 $
Example 77: $ 64 \div 8 $
Solution: $ 64 \div 8 = 8 $
Example 78: $ 81 \div 9 $
Solution: $ 81 \div 9 = 9 $
Example 79: $ 100 \div 25 $
Solution: $ 100 \div 25 = 4 $
Example 80: $ 54 \div 6 $
Solution: $ 54 \div 6 = 9 $
Example 81: $ 72 \div 8 $
Solution: $ 72 \div 8 = 9 $
Example 82: $ 18 \div 3 $
Solution: $ 18 \div 3 = 6 $
Example 83: $ 40 \div 5 $
Solution: $ 40 \div 5 = 8 $
Example 84: $ 90 \div 10 $
Solution: $ 90 \div 10 = 9 $
Example 85: $ 55 \div 5 $
Solution: $ 55 \div 5 = 11 $
Example 86: $ 36 \div 4 $
Solution: $ 36 \div 4 = 9 $
Example 87: $ 48 \div 8 $
Solution: $ 48 \div 8 = 6 $
Example 88: $ 30 \div 6 $
Solution: $ 30 \div 6 = 5 $
Example 89: $ 77 \div 7 $
Solution: $ 77 \div 7 = 11 $
Example 90: $ 90 \div 15 $
Solution: $ 90 \div 15 = 6 $
Example 91: $ 84 \div 12 $
Solution: $ 84 \div 12 = 7 $
Example 92: $ 50 \div 5 $
Solution: $ 50 \div 5 = 10 $
Example 93: $ 99 \div 9 $
Solution: $ 99 \div 9 = 11 $
Example 94: $ 56 \div 7 $
Solution: $ 56 \div 7 = 8 $
Example 95: $ 63 \div 9 $
Solution: $ 63 \div 9 = 7 $
Example 96: $ 78 \div 6 $
Solution: $ 78 \div 6 = 13 $
Example 97: $ 25 \div 5 $
Solution: $ 25 \div 5 = 5 $
Example 98: $ 88 \div 8 $
Solution: $ 88 \div 8 = 11 $
Example 99: $ 36 \div 9 $
Solution: $ 36 \div 9 = 4 $
Example 100: $ 27 \div 3 $
Solution: $ 27 \div 3 = 9 $
