Calculate 5÷(13² - 12²): Division with Difference of Squares

Q: Why do I calculate the exponents before the division?

The order of operations (PEMDAS) requires you to handle exponents first, especially when they're inside parentheses. Division comes later in the sequence.

Q: Can I use the difference of squares formula here?

Yes! $ 13^2 - 12^2 $ is a difference of squares pattern. You can use $ a^2 - b^2 = (a+b)(a-b) $ to get $ (13+12)(13-12) = 25 \times 1 = 25 $.

Q: How do I write division as a fraction?

Division and fractions are the same thing! $ 5 \div 25 $ equals $ \frac{5}{25} $. Then simplify by dividing both numerator and denominator by their greatest common factor.

Q: Why is the answer 1/5 and not 5?

Because $ 5 \div 25 = \frac{5}{25} = \frac{1}{5} $. When the divisor (25) is larger than the dividend (5), the result is always less than 1.

Q: What if I calculated 13² - 12² incorrectly?

Double-check: $ 13^2 = 169 $ and $ 12^2 = 144 $, so $ 169 - 144 = 25 $. If you get a different result for the parentheses, your final answer will be wrong.

Order of Operations with Algebraic Expressions

Calculate and indicate the answer:

$5:(13^2-12^2)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve the following problem

00:03 Calculate the powers in order to solve the parentheses

00:07 A power is actually the number multiplied by itself according to the exponent

00:11 Let's calculate the powers and then substitute into our exercise

00:21 Always solve parentheses first

00:29 Convert division to fraction

00:33 Break down 25 into factors 5 and 5

00:39 Simplify wherever possible

00:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate and indicate the answer:

$5:(13^2-12^2)$

Step-by-step solution

Previously mentioned in the order of arithmetic operations, exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the terms with exponents inside the parentheses first) :

$5:(13^2-12^2) =5:(169-144) =5:25=\frac{5}{25}$ where in the second step we simplified the expression in parentheses, and in the next step we wrote the division operation as a fraction,

Then we'll perform the division (we'll actually reduce the fraction):

$\frac{\not{5}}{\not{25}}=\frac{1}{5}$ Therefore the correct answer is answer C.

Final Answer

$\frac{1}{5}$

Key Points to Remember

Essential concepts to master this topic

Rule: Calculate exponents first, then parentheses, then division
Technique: Use difference of squares: $13^2 - 12^2 = 169 - 144 = 25$
Check: Substitute back: $5 \div 25 = \frac{1}{5}$ matches our answer ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and dividing first
Don't calculate 5 ÷ 13 first = wrong result of approximately 0.38! This breaks the order of operations since exponents and parentheses must be calculated before division. Always follow PEMDAS: solve exponents inside parentheses first, then perform the division.

Practice Quiz

Test your knowledge with interactive questions

$$ 100+5-100+5 $$

FAQ

Everything you need to know about this question

Why do I calculate the exponents before the division?

The order of operations (PEMDAS) requires you to handle exponents first, especially when they're inside parentheses. Division comes later in the sequence.

Can I use the difference of squares formula here?

Yes! $13^2 - 12^2$ is a difference of squares pattern. You can use $a^2 - b^2 = (a+b)(a-b)$ to get $(13+12)(13-12) = 25 \times 1 = 25$ .

How do I write division as a fraction?

Division and fractions are the same thing! $5 \div 25$ equals $\frac{5}{25}$ . Then simplify by dividing both numerator and denominator by their greatest common factor.

Why is the answer 1/5 and not 5?

Because $5 \div 25 = \frac{5}{25} = \frac{1}{5}$ . When the divisor (25) is larger than the dividend (5), the result is always less than 1.

What if I calculated 13² - 12² incorrectly?

Double-check: $13^2 = 169$ and $12^2 = 144$ , so $169 - 144 = 25$ . If you get a different result for the parentheses, your final answer will be wrong.

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Calculate 5÷(13² - 12²): Division with Difference of Squares

Order of Operations with Algebraic Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do I calculate the exponents before the division?

Can I use the difference of squares formula here?

How do I write division as a fraction?

Why is the answer 1/5 and not 5?

What if I calculated 13² - 12² incorrectly?

🌟 Unlock Your Math Potential

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