Solve: (7² - √36÷6)/(3+3) × (5+2) | Order of Operations Challenge

Q: Why do I solve the parentheses (5+2) before the fraction?

Parentheses always come first in PEMDAS! Even though the fraction looks complicated, you must solve $ (5+2) = 7 $ and $ (3+3) = 6 $ before doing any other operations.

Q: How do I handle the division symbol (:) in the square root?

The symbol (:) means division, just like ÷. So $ \sqrt{36}:6 = 6÷6 = 1 $. This division happens in the numerator before subtracting from $ 7^2 $.

Q: Do I multiply or divide the fraction first?

Think of the fraction bar as grouping symbols! Solve the entire fraction $ \frac{48}{6} = 8 $ first, then multiply by 7. The fraction acts like one number in the multiplication.

Order of Operations with Complex Fractions

Check the correct answer:

$\frac{7^2-\sqrt{36}:6}{3+3}\cdot(5+2)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 Let's solve this problem together.

00:16 First, break it down and calculate the power.

00:22 Now, find the square root of thirty-six.

00:32 Remember, always calculate what's inside parentheses first.

00:37 A number divided by itself is always one.

00:45 Next, let's work out the quotient.

00:50 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Check the correct answer:

$\frac{7^2-\sqrt{36}:6}{3+3}\cdot(5+2)=$

Step-by-step solution

Before solving the exercise, let's start by simplifying the power and the root:

$7^2=7\times7=49$

$\sqrt{36}=\sqrt{6^2}=6$

Now, we arrange the exercise accordingly:

$\frac{49-6:6}{3+3}\times(5+2)=$

According to the rules of the order of operations, parentheses are solved first:

$\frac{49-6:6}{3+3}\times(7)=$

Now we focus on the fraction, we start with the division exercise in the numerator, then we add and subtract as appropriate:

$\frac{49-1}{3+3}\times(7)=\frac{48}{6}\times(7)=$

We solve the exercise from left to right, first the division exercise and finally we multiply:

$8\times7=56$

Final Answer

$56$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction from left to right
Technique: Simplify numerator and denominator separately: $7^2 = 49$ , $\sqrt{36} = 6$
Check: Verify each step: $\frac{48}{6} \times 7 = 8 \times 7 = 56$ ✓

Common Mistakes

Avoid these frequent errors

Solving operations in wrong order
Don't solve from left to right ignoring order of operations = $7^2 - 6 ÷ 6 ÷ 3 + 3 \times 5 + 2 = 89$ ! This ignores parentheses and proper grouping. Always follow PEMDAS strictly: solve parentheses first, then exponents and roots, then handle the fraction as a unit.

Practice Quiz

Test your knowledge with interactive questions

$20\div(4+1)-3=$

FAQ

Everything you need to know about this question

Why do I solve the parentheses (5+2) before the fraction?

Parentheses always come first in PEMDAS! Even though the fraction looks complicated, you must solve $(5+2) = 7$ and $(3+3) = 6$ before doing any other operations.

How do I handle the division symbol (:) in the square root?

The symbol (:) means division, just like ÷. So $\sqrt{36}:6 = 6÷6 = 1$ . This division happens in the numerator before subtracting from $7^2$ .

Do I multiply or divide the fraction first?

Think of the fraction bar as grouping symbols! Solve the entire fraction $\frac{48}{6} = 8$ first, then multiply by 7. The fraction acts like one number in the multiplication.

What if I get a different answer when checking?

Go back and check each step carefully! Common errors include: forgetting $7^2 = 49$ , calculating $\sqrt{36}$ wrong, or mixing up the order of operations. Write each step clearly to catch mistakes.

Why is the answer 56 and not 50?

The key difference is in the order of operations! If you solve incorrectly, you might get $7 \times 7 + 1 = 50$ . But following PEMDAS correctly gives $\frac{49-1}{6} \times 7 = 8 \times 7 = 56$ .

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Solve: (7² - √36÷6)/(3+3) × (5+2) | Order of Operations Challenge

Order of Operations with Complex Fractions

❤️ 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 solve the parentheses (5+2) before the fraction?

How do I handle the division symbol (:) in the square root?

Do I multiply or divide the fraction first?

What if I get a different answer when checking?

Why is the answer 56 and not 50?

🌟 Unlock Your Math Potential

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