Which Expression Is Equal To 72

Which Expression is Equal to 72? A Deep Dive into Mathematical Expressions

Finding an expression equal to 72 might seem simple at first glance. After all, 72 + 0 = 72, right? While true, this exercise offers a fantastic opportunity to explore the diverse world of mathematical expressions, delving into various operations and the creative ways we can manipulate numbers to arrive at a specific result. This article will explore numerous expressions equal to 72, categorized for clarity and demonstrating a range of mathematical concepts.

Understanding Mathematical Expressions

Before diving into the expressions themselves, let's briefly define what a mathematical expression is. It's a combination of numbers, variables, and operators (like +, -, *, /) that represents a mathematical value or a relationship between values. An expression differs from an equation in that an equation includes an equals sign (=), while an expression doesn't need one; it simply represents a value.

This article will primarily focus on numerical expressions, meaning expressions containing only numbers and operators. We will explore a variety of approaches to arrive at 72, showcasing the flexibility and creativity within mathematics.

Simple Arithmetic Expressions Equal to 72

We'll start with the most straightforward methods, using basic arithmetic operations:

Addition and Subtraction

• 72 + 0 = 72: This is the most obvious solution.
• 73 - 1 = 72: A simple subtraction.
• 70 + 2 = 72: Another straightforward addition.
• 80 - 8 = 72: Subtracting a larger number to reach 72.
• 60 + 12 = 72: Using multiples of 10 for easier calculations.
• 100 - 28 = 72: A more complex subtraction requiring mental arithmetic or a calculator.
• 50 + 22 = 72: Combining numbers to reach the target.
• 36 + 36 = 72: Using a repeated number for elegance.
• 10 + 62 = 72 A simple addition with varied numbers

These examples illustrate the simplest ways to achieve 72 using addition and subtraction. They demonstrate the fundamental operations and how various number combinations can yield the same result.

Multiplication and Division

Multiplication and division offer more complex avenues to reach 72:

• 8 * 9 = 72: A classic multiplication fact.
• 72 * 1 = 72: Multiplying by the multiplicative identity.
• 144 / 2 = 72: Dividing a larger number by 2.
• 36 * 2 = 72: Using a smaller multiplier to reach 72.
• 24 * 3 = 72: Demonstrates different factor pairs.
• 18 * 4 = 72: Further illustrates the concept of multiplication factors.
• 6 * 12 = 72: Shows a different combination of factors.
• 720 / 10 = 72: Utilizing division with larger numbers.

These expressions showcase the versatility of multiplication and division in achieving our target number.

Combining Operations

Things get more interesting when we combine addition, subtraction, multiplication, and division within a single expression:

• (10 * 7) + 2 = 72: Combining multiplication and addition.
• (12 * 6) = 72: simple multiplication reaching 72
• (9 * 8) = 72: Another simple multiplication with a different factor pair.
• (18 * 4) = 72: Illustrating alternative factor pairs.
• (36 * 2) = 72: Showing different factors reaching 72.
• (24 * 3) = 72: Another set of factors reaching the target value.
• 144/2 = 72: Simple division resulting in 72.
• (100 - 28) = 72: Subtraction to reach the target value.
• (1000 - 928) = 72: A more challenging subtraction example.
• (200 - 128) = 72: An easier subtraction example.

These demonstrate the power of combining different operations.

Expressions with Exponents and Roots

Moving beyond basic arithmetic, we can incorporate exponents and roots to create more sophisticated expressions:

• 6² + 6² - 36 = 72: Using squares and subtraction.
• √36 * 12 = 72: Combining square roots and multiplication.
• 12 * 6 = 72: another simple multiplication expression.
• 18 * 4 = 72: another multiplication expression showing different factors.
• 24 * 3 = 72: Using different multipliers to reach 72.
• 9 * 8 = 72: Basic multiplication with a different factor pair.
• 36 * 2 = 72: Another simple multiplication.

These examples introduce exponents and roots, adding another layer of complexity to the expressions.

Expressions with Parentheses and Order of Operations

Parentheses are crucial for controlling the order of operations. The order of operations (PEMDAS/BODMAS) dictates the sequence in which calculations are performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

• (10 + 6) * 6 = 96: Shows a false solution to highlight the importance of order of operations. The correct order results in 96 rather than 72.
• (5 + 7) * 6 = 72: Illustrating correct order of operations with parentheses. This expression correctly uses parentheses to get 72.
• (12 - 4) * 9 = 72: More complex expression showcasing correct usage of parentheses.
• *((24/3)9) = 72: Combining parenthesis with division and multiplication.

Correctly using parentheses is critical in obtaining the desired outcome.

Advanced Expressions (Including Factorials and Other Functions)

For a more advanced exploration, we can introduce factorials (!), which represents the product of all positive integers up to a given number, or even more complex mathematical functions:

• 72! / 71! = 72: Using factorials. Note that factorial calculations for large numbers rapidly become very large.
• (72)^1 = 72: Illustrating exponentiation with an exponent of 1.

These expressions show the possibilities within more advanced mathematical concepts.

Conclusion: The Creativity of Mathematical Expressions

This exploration demonstrates the vast number of ways to express the number 72 using mathematical expressions. From simple additions to complex combinations of operations, exponents, and even factorials, the possibilities are nearly limitless. This exercise highlights the fundamental principles of mathematics and the creativity inherent in finding different solutions to a seemingly straightforward problem. The key takeaway is that while a single answer might exist, the path to reaching that answer is often diverse and fascinating, offering a unique perspective into the beauty and complexity of mathematics. Remember to always follow the order of operations (PEMDAS/BODMAS) to ensure accurate calculations when combining multiple operations within an expression. The ability to construct and manipulate these expressions is a vital skill in various fields, from basic arithmetic to advanced calculus and computer programming.