Solve: 35-(400÷(20/13)-12) Complex Order of Operations

Q: Can I use a calculator for the fraction division?

Yes, but be careful! Make sure to enter it as $ 400 ÷ (20 ÷ 13) $ or convert to $ 400 × 13 ÷ 20 $. Using parentheses correctly is crucial for calculators.

Q: Why is my answer different from the choices?

Double-check your order of operations! The most common error is not following PEMDAS properly. Work step-by-step: parentheses first, then division, then subtraction from left to right.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the math problem step-by-step.

00:14 Remember, dividing is like multiplying by the reciprocal.

00:27 A negative times a positive gives a negative result.

00:32 Move the multiplication to the top, or numerator.

00:36 A negative times a negative equals a positive.

00:45 Break down four hundred into factors of twenty.

00:55 Simplify as much as you can along the way.

01:11 And that's how we find the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$35-(400:\frac{20}{13}-12)=\text{?}$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Evaluate the division $400 : \frac{20}{13}$ .
Step 2: Subtract 12 from the result obtained in Step 1.
Step 3: Subtract the entire result from 35.

Now, let's work through each step:
Step 1: Evaluate the division $400 : \frac{20}{13}$ . Division by a fraction is the same as multiplying by its reciprocal, so we have:
$400 \times \frac{13}{20} = \frac{400 \times 13}{20} = \frac{5200}{20} = 260$

Step 2: Now subtract 12 from 260:
$260 - 12 = 248$

Step 3: Finally, subtract the result from 35:
$35 - 248 = -213$

Thus, the solution to the problem is $-213$ .

3

Final Answer

$-213$

Key Points to Remember

Essential concepts to master this topic

Rule: Follow PEMDAS strictly when fractions are inside parentheses
Technique: $400 ÷ \frac{20}{13} = 400 \times \frac{13}{20} = 260$
Check: Work backwards: $35 - (260 - 12) = 35 - 248 = -213$ ✓

Common Mistakes

Avoid these frequent errors

Solving left to right without following order of operations
Don't solve 35 - 400 first = wrong equation structure! This ignores the parentheses and gives completely wrong results. Always solve inside parentheses first, then work outward following PEMDAS.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why do I multiply by the reciprocal when dividing by a fraction?

+

Division by a fraction is the same as multiplying by its reciprocal! When you see $400 ÷ \frac{20}{13}$ , flip the fraction to get $\frac{13}{20}$ and multiply instead.

What if I forget to work inside the parentheses first?

+

You'll get the wrong answer! The parentheses tell you to solve $(400÷\frac{20}{13}-12)$ completely before subtracting from 35. Always work from the inside out.

How do I handle the negative result?

+

Negative answers are perfectly normal! When you subtract a larger number from a smaller one like $35 - 248$ , you get a negative result. Don't worry - just be careful with your signs.

Can I use a calculator for the fraction division?

+

Yes, but be careful! Make sure to enter it as $400 ÷ (20 ÷ 13)$ or convert to $400 × 13 ÷ 20$ . Using parentheses correctly is crucial for calculators.

Why is my answer different from the choices?

+

Double-check your order of operations! The most common error is not following PEMDAS properly. Work step-by-step: parentheses first, then division, then subtraction from left to right.

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Solve: 35-(400÷(20/13)-12) Complex Order of Operations

Order of Operations with Division by Fractions

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