The image you uploaded is a colorful poster that explains the
Mathematical Order of Operations, often remembered by the acronym
GEMDAS. This acronym helps in solving mathematical expressions by specifying the order in which operations should be performed to ensure consistent and correct results.
Explanation of GEMDAS:
1.
G (Grouping Symbols):
- Perform operations inside grouping symbols first, such as parentheses `()`, brackets `[]`, and braces `{}`.
- Example: In the expression \( 2 \times (3 + 4) \), solve \( 3 + 4 \) first because it is inside parentheses.
2.
E (Exponents):
- Solve any exponents (powers or roots) next.
- Example: In the expression \( 2^3 + 5 \), calculate \( 2^3 = 8 \) before adding 5.
3.
M (Multiplication) and
D (Division):
- Perform multiplication and division from left to right.
- These operations have equal precedence, so you do not prioritize one over the other; just work from left to right.
- Example: In the expression \( 6 \div 3 \times 2 \), first divide \( 6 \div 3 = 2 \), then multiply \( 2 \times 2 = 4 \).
4.
A (Addition) and
S (Subtraction):
- Perform addition and subtraction from left to right.
- These operations also have equal precedence, so you work from left to right.
- Example: In the expression \( 10 - 3 + 2 \), first subtract \( 10 - 3 = 7 \), then add \( 7 + 2 = 9 \).
Why is the Order of Operations Important?
- Without a standard order, different people might solve the same expression differently, leading to inconsistent results.
- The order ensures that everyone follows the same rules, making mathematics predictable and reliable.
How to Use GEMDAS:
1. Identify all parts of the expression.
2. Follow the steps in the GEMDAS order:
- Grouping symbols
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
Example Problem:
Solve the expression: \( 3 + 6 \times (5 + 4) \div 3 - 7 \).
#### Step-by-Step Solution:
1.
Grouping Symbols: Solve the expression inside the parentheses first.
\[
5 + 4 = 9
\]
So the expression becomes: \( 3 + 6 \times 9 \div 3 - 7 \).
2.
Exponents: There are no exponents in this expression, so move to the next step.
3.
Multiplication and Division: Perform these operations from left to right.
- First, multiply \( 6 \times 9 = 54 \).
- Then, divide \( 54 \div 3 = 18 \).
So the expression now is: \( 3 + 18 - 7 \).
4.
Addition and Subtraction: Perform these operations from left to right.
- First, add \( 3 + 18 = 21 \).
- Then, subtract \( 21 - 7 = 14 \).
Final Answer:
\[
\boxed{14}
\]
This poster is a helpful tool for students to remember the correct order of operations when solving mathematical expressions.
Parent Tip: Review the logic above to help your child master the concept of order of operations poster printable.
