Mathematical Operations: Understanding Order of Operations with Real-World Applications

When solving mathematical expressions, the correct order of operations is crucial for obtaining accurate results. One such expression is 64 ÷ 4 - 2 ÷ 2 × 4 × 4. Understanding how to solve this expression using the order of operations is essential for students and professionals alike. In this article, we will break down the expression step by step and see its practical applications in the biological world, particularly in the function of DNA.

Order of Operations: PEMDAS/BODMAS

First, let's discuss the order of operations. In mathematics, we follow a specific sequence to solve expressions correctly. In the United States, it's commonly referred to as PEMDAS, while in the UK and other countries, it's often known as BODMAS. Here’s what each letter stands for:

P/B - Parentheses/Brackets E/O - Exponents/Orders M/D - Multiplication/Division (from left to right) A/S - Addition/Subtraction (from left to right)

Applying the PEMDAS/BODMAS rules to the expression 64 ÷ 4 - 2 ÷ 2 × 4 × 4, we can follow these steps:

Brackets first: 4 × 4 16 Next, division and multiplication from left to right: 64 ÷ 4 16 2 ÷ 2 1 Substitute back into the expression: 16 - 1 × 16 Multiplication: 1 × 16 16 Finally, perform the subtraction: 16 - 16 0

Therefore, the value of the expression is 0.

Real-World Application: Gene Function in DNA

The function of DNA is highly complex but fascinating. One of its primary functions within cells is to code for proteins, and this function is dictated by the precise order in which the nucleotide bases occur in segments of DNA known as genes. While DNA and its segments are organic molecules, the information conveyed by their nucleotide sequences is of significant commercial and scientific value.

Understanding the order of operations can be applied in various fields, including biology, where the sequencing of nucleotides forms the basis of genetic research. In this context, the order in which bases are arranged (A, T, C, G) determines the function of genes, much like the order of operations determines the result of a mathematical expression.

Additional Examples and Proofs

Let's look at a few more examples to reinforce our understanding of the order of operations:

Example 1:

64 ÷ 4 - 2 ÷ 2 × 4 × 4 16 - 1 × 16 16 - 16 0

Example 2:

64 / 4 - 2 / 2 44 16 - 1 16 16 - 16 0

Example 3:

PREMISES:

y64÷4–2÷2×4×4

CALCULATIONS:

y64/4-2/24×4

y16-14×4

y16-116

y16-16

y0

PROOF:

The inverse of the equation y64/4-2/24×4 returns:

y2/24×464/4

014×464/4

01616

1616

PROOF: 1616

C.H.

Therefore, the proof confirms that y0.

Conclusion: Understanding the order of operations is not only crucial in mathematics but also in the biological world, particularly in the function of DNA. By applying the rules of PEMDAS/BODMAS, we can solve complex mathematical and biological expressions accurately.

Related Keywords:

Order of Operations PEMDAS BODMAS Gene Function DNA