What is MDAS (Multiplication, Division, Addition, Subtraction)?

MDAS refers to the order of operations in mathematics, dictating the sequence in which calculations should be performed in an expression.

Understanding MDAS

MDAS is an acronym that helps remember the correct order for solving mathematical problems. It stands for:

• Multiplication
• Division
• Addition
• Subtraction

This order dictates that multiplication and division operations are performed before addition and subtraction operations.

Order of Operations Explained

The fundamental principle of MDAS is to ensure consistency in solving mathematical expressions. Without a set order, the same expression could lead to multiple different answers, which is unacceptable in mathematics.

Detailed Breakdown:

1. Multiplication and Division:
   • These operations are performed from left to right as they appear in the expression.
   • This means that if division appears before multiplication from left to right, then division is done first.
2. Addition and Subtraction:
   • Once all multiplications and divisions are completed, addition and subtraction operations are done from left to right.
   • Like multiplication and division, this means that if subtraction appears before addition from left to right, then subtraction is done first.

Practical Insights and Examples:

• Example 1: 10 + 2 x 3

  1. Multiplication first: 2 x 3 = 6
  2. Addition next: 10 + 6 = 16
  3. Correct Answer: 16

• Example 2: 10 x 2 / 5 + 1

  1. Multiplication first: 10 x 2 = 20. The expression is rewritten as 20 / 5 + 1
  2. Division next: 20 / 5 = 4. The expression is rewritten as 4 + 1.
  3. Addition next: 4 + 1 = 5.
  4. Correct Answer: 5

• Example 3: 20 - 10 / 2 + 5

  1. Division first: 10 / 2 = 5. The expression is rewritten as 20 - 5 + 5.
  2. Subtraction next: 20 - 5 = 15. The expression is rewritten as 15 + 5
  3. Addition next: 15 + 5 = 20
  4. Correct Answer: 20

• Reference: According to MDAS, simplify all multiplication or division before adding or subtracting. Reading the expression from left to right, start by multiplying 10×2. Since 10×2=20, rewrite the expression using 20. The two operations remaining in the expression are addition and division.

Why is MDAS Important?

The importance of MDAS lies in:

• Consistency: It ensures that mathematical expressions are evaluated consistently, preventing ambiguities.
• Accuracy: Following MDAS provides the correct numerical answer every time.
• Foundation: MDAS is a fundamental concept in basic arithmetic and is essential for all higher-level mathematics.

Conclusion

MDAS, which stands for Multiplication, Division, Addition, Subtraction, is a vital mathematical principle used to ensure calculations are done in the correct sequence. Performing these operations in the MDAS order, from left to right, ensures consistency and accuracy in all mathematical problem solving.