Mathematical puzzles can be both fun and challenging, especially when you need to apply a specific order of operations. The image above presents one such problem:
Problem:
110−10×10+10=?110 – 10 \times 10 + 10 = ?110−10×10+10=?
At first glance, it might look simple, but if we don’t follow the correct order of operations, the result will be incorrect. That’s where PEMDAS (in the U.S.) or BODMAS (used in other countries) comes in.
What is PEMDAS/BODMAS?
PEMDAS stands for:
Parentheses
Exponents (or Orders in BODMAS)
Multiplication
Division
Addition
Subtraction
The rule dictates that multiplication and division take precedence over addition and subtraction. Following this order ensures accuracy in solving equations.
Step-by-Step Solution:
Let’s break down the equation using the correct order of operations:
Given Equation:
110−10×10+10110 – 10 \times 10 + 10110−10×10+10
Identify the Operations: We see subtraction, multiplication, and addition in the equation.
Apply Multiplication First: According to PEMDAS, multiplication takes precedence over both addition and subtraction. So, we first solve:
10×10=10010 \times 10 = 10010×10=100Now, the equation becomes:
110−100+10110 – 100 + 10110−100+10
Perform Addition and Subtraction (Left to Right): Next, we handle the subtraction and addition from left to right:
110−100=10110 – 100 = 10110−100=10And then:
10+10=2010 + 10 = 2010+10=20
So, the final answer is:
20\boxed{20}20
The Importance of Following PEMDAS/BODMAS
Many people might mistakenly solve this problem by working from left to right without considering the order of operations. If someone incorrectly subtracts and adds before multiplying, they might end up with an entirely different result. However, by following PEMDAS/BODMAS, the correct solution is easy to find.
Conclusion
This daily math challenge reminds us how crucial it is to stick to the order of operations. Whether you’re working through a complex algebraic equation or a simple arithmetic problem, applying PEMDAS/BODMAS ensures that your results are accurate every time.
Keep practicing, and these problems will become second nature!
