Solving the Simplification of 5÷√5 and Understanding BODMAS Rules

Mathematics can often present us with challenging problems that require a clear understanding of concepts such as simplification. One such problem is simplifying the expression 5÷√5. This article will guide you through the steps to solve this problem and introduce you to the BODMAS rule, a fundamental principle in evaluating expressions.

Simplifying 5÷√5

The expression 5÷√5 can be simplified systematically:

Step 1: Recognize that the denominator contains an irrational number, √5. To simplify the expression, multiply both the numerator and the denominator by √5.

Step 2: Perform the multiplication:

5/√5 (5√5) / (√5 x √5) (5√5) / 5

Step 3: Simplify the fraction:

(5√5) / 5 √5

Therefore, the simplified form of 5÷√5 is √5.

Verification

To verify this, we can multiply √5 by itself:

√5 x √5 5

This confirms that our simplification is correct.

Understanding BODMAS Rule

The BODMAS rule, or the order of operations, is crucial for solving mathematical expressions accurately. BODMAS stands for:

Brackets

Orders (i.e., exponents and roots)

Division

Multiplication

Addition

Subtraction

According to the BODMAS rule, we evaluate expressions in the following order:

First, we evaluate expressions within any brackets.

Next, we evaluate any exponents or roots.

Then, we perform division and multiplication from left to right.

Finally, we perform addition and subtraction from left to right.

Applying BODMAS to 5 ÷ 5 ÷ 5

Lets consider the problem 5 ÷ 5 ÷ 5. According to BODMAS, we should evaluate from left to right:

Step 1: First, we perform the division 5 ÷ 5, which equals 1.

Step 2: Next, we divide the result by 5, which gives us 1 ÷ 5 0.2.

Therefore, the final answer is 0.2.

It's important to note that without the BODMAS rule, one might incorrectly conclude that the answer is 1, as they might perform the divisions from right to left. However, the BODMAS rule ensures that we get the correct result.

Conclusion

Understanding and applying the BODMAS rule is essential for correctly solving mathematical expressions. Whether you're tackling a simple problem like 5 ÷ 5 ÷ 5 or a more complex expression like 5÷√5, the BODMAS rule will ensure that you get the right answer. By following these steps, you can confidently handle any mathematical challenge.

Key Takeaways

BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction) is the order of operations for evaluating mathematical expressions.

To solve 5÷√5, multiply numerator and denominator by √5 to simplify the expression to √5.

Applying BODMAS to 5 ÷ 5 ÷ 5 results in 0.2.

References

[1] Khan Academy. (2023). Order of Operations.

[2] Purplemath. (2023). Order of Operations.

[3] Math Is Fun. (2023). Order of Operations.