Solve: 5+5-5²+4² Using Order of Operations

Q: Why can't I just solve from left to right?

The order of operations (BODMAS/PEMDAS) is a mathematical rule that everyone follows. Exponents must be calculated before addition and subtraction, or you'll get the wrong answer!

Q: What does 5² actually mean?

$ 5^2 $ means 5 × 5 = 25. The small 2 (exponent) tells you how many times to multiply the base number by itself.

Q: How do I remember the order of operations?

Use BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Work through each step in order!

Q: What if I get a negative number in the middle?

That's normal! In this problem, we get $ 10 - 25 = -15 $, then add 16 to get 1. Keep going with the calculation even when you see negative numbers.

Order of Operations with Exponents

$5+5-5^2+4^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:02 Break down the exponents

00:08 Always solve multiplication and division before addition and subtraction

00:14 Continue to solve according to the correct order of operations from left to right

00:24 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5+5-5^2+4^2=$

Step-by-step solution

Let's solve the expression $5+5-5^2+4^2$ using the order of operations, also known as BODMAS/BIDMAS (Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction).

Here is the step-by-step breakdown:

1. Identify and calculate powers and roots first:
- Calculate $5^2$ :
$5^2 = 25$
- Calculate $4^2$ :
$4^2 = 16$

2. Rewrite the expression using these calculations:
$5+5-25+16$

3. Perform addition and subtraction from left to right:
- First addition: $5 + 5 = 10$
- Subtract the next number: $10 - 25 = -15$
- Finally add: $-15 + 16 = 1$

The final result of the expression $5+5-5^2+4^2$ is therefore $1$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate exponents before addition and subtraction operations
Technique: Evaluate $5^2 = 25$ and $4^2 = 16$ first
Check: Substitute calculated values: 5+5-25+16 = 1 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without calculating exponents first
Don't solve 5+5-5²+4² by going left to right = getting 51! This ignores the order of operations and treats exponents like regular numbers. Always calculate all exponents first, then work left to right.

Practice Quiz

Test your knowledge with interactive questions

What is the result of the following equation?

$36-4\div2$

FAQ

Everything you need to know about this question

Why can't I just solve from left to right?

The order of operations (BODMAS/PEMDAS) is a mathematical rule that everyone follows. Exponents must be calculated before addition and subtraction, or you'll get the wrong answer!

What does 5² actually mean?

$5^2$ means 5 × 5 = 25. The small 2 (exponent) tells you how many times to multiply the base number by itself.

How do I remember the order of operations?

Use BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Work through each step in order!

What if I get a negative number in the middle?

That's normal! In this problem, we get $10 - 25 = -15$ , then add 16 to get 1. Keep going with the calculation even when you see negative numbers.

Can I use a calculator for this?

Yes, but make sure your calculator follows order of operations! Some basic calculators work left to right and might give wrong answers. Scientific calculators usually handle order of operations correctly.

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