What is the Order of Operations in Math Grade 8?

The order of operations in math, specifically for grade 8, is a set of rules that dictates the sequence in which mathematical operations should be performed to get the correct answer. This is commonly remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (same level), and Addition and Subtraction (same level).

Understanding PEMDAS

PEMDAS is the key to solving multi-step mathematical problems. Here's a breakdown of each component:

Parentheses

• Operations inside parentheses are always done first. This includes brackets and other grouping symbols.
  • Example: In the expression 2 * (3 + 4), you would add 3 and 4 first because they're inside the parentheses, resulting in 2 * 7 = 14.

Exponents

• Exponents are evaluated next. Exponents indicate repeated multiplication of a base number.
  • Example: In the expression 5 + 2^3, you would evaluate 2^3 = 2 * 2 * 2 = 8 before moving on to addition, giving 5 + 8 = 13.

Multiplication and Division

• Multiplication and division are done from left to right as they appear in the expression. These operations have equal precedence.
  • Example: In the expression 12 / 3 * 2, you would perform the division first 12 / 3 = 4, and then the multiplication 4 * 2 = 8.
  • Example: In the expression 10 * 2 / 5, you would perform the multiplication first 10 * 2 = 20, and then the division 20 / 5 = 4.

Addition and Subtraction

• Addition and subtraction are done from left to right as they appear in the expression. Similar to multiplication and division, these have equal precedence.
  • Example: In the expression 10 - 4 + 2, you would perform subtraction first 10 - 4 = 6 and then the addition 6 + 2 = 8.
  • Example: In the expression 5 + 3 - 2, you would perform the addition first 5 + 3 = 8 and then the subtraction 8 - 2 = 6.

Why is PEMDAS Important?

Using PEMDAS consistently ensures that everyone arrives at the same answer when evaluating mathematical expressions. Without a standard order of operations, mathematical calculations would be ambiguous and could lead to different results.

Example Problem

Let's solve a sample expression using PEMDAS: 10 + 2 * (6 - 3)^2 / 3

1. Parentheses: Evaluate (6 - 3) = 3. The expression becomes 10 + 2 * 3^2 / 3.
2. Exponents: Evaluate 3^2 = 9. The expression becomes 10 + 2 * 9 / 3.
3. Multiplication and Division: Work from left to right:
   • 2 * 9 = 18. Expression becomes 10 + 18 / 3.
   • 18 / 3 = 6. Expression becomes 10 + 6.
4. Addition: 10 + 6 = 16.

Therefore, 10 + 2 * (6 - 3)^2 / 3 = 16.

Summary

Order	Operation
1	Parentheses
2	Exponents
3	Multiplication/Division
4	Addition/Subtraction

Following PEMDAS consistently is crucial for success in math and is a fundamental concept for Grade 8 mathematics.