Solve 21-(6-13): Order of Operations with Nested Subtraction

Q: Why can't I just work from left to right like 21 - 6 - 13?

The parentheses change the order! $ 21-(6-13) $ means subtract the entire result of (6-13) from 21. Working left to right without parentheses gives a completely different problem.

Q: What happens when I get a negative number inside parentheses?

That's totally normal! When 6 - 13 = -7, you then have $ 21 - (-7) $. Remember: subtracting a negative equals adding the positive, so this becomes 21 + 7 = 28.

Q: How do I remember that subtracting a negative means adding?

Think of it as "opposite of opposite"! The minus sign outside parentheses is like saying "do the opposite" of what's inside. Since -7 is negative, the opposite is +7.

Q: Can I check my answer a different way?

Yes! You can work backwards: if 28 is correct, then $ 28 + (6-13) $ should equal 21. Let's see: $ 28 + (-7) = 21 $ ✓

Q: What if the numbers inside parentheses were switched to 13 - 6?

Great question! Then you'd have $ 21-(13-6) = 21-7 = 14 $. The order inside parentheses matters a lot - it determines whether you get a positive or negative result!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 When opening parentheses, minus multiplied by minus always equals plus

00:08 Therefore when opening the parentheses, in the end we get divided by C

00:13 Let's solve according to the order of operations from left to right

00:21 We'll use long addition

00:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$21-(6-13)=$

2

Step-by-step solution

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

Step 1: Evaluate the inner expression $6 - 13$
Step 2: Substitute the result from Step 1 into $21 - \text{result from Step 1}$

Now, let's work through each step:

Step 1: Calculate $6 - 13$ . In this calculation, we subtract 13 from 6. The result is $-7$ , because when subtracting a larger number from a smaller one, the result is negative.

Step 2: Substitute $-7$ into the outer expression $21 - (-7)$ . Since subtracting a negative is equivalent to adding the positive opposite, this simplifies to $21 + 7$ .

Now, compute $21 + 7$ , which equals 28.

Therefore, the solution to the problem is $28$ .

3

Final Answer

28

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always solve parentheses first before outer operations
Technique: Calculate 6 - 13 = -7, then 21 - (-7) = 21 + 7
Check: Substitute back: 21 - (-7) = 28 confirms our answer ✓

Common Mistakes

Avoid these frequent errors

Working left to right without considering parentheses
Don't calculate 21 - 6 first = 15 - 13 = 2! This ignores the parentheses and gives the wrong answer. Always solve what's inside parentheses first, even if it creates a negative number.

Practice Quiz

Test your knowledge with interactive questions

$70:(14\times5)=$

FAQ

Everything you need to know about this question

Why can't I just work from left to right like 21 - 6 - 13?

+

The parentheses change the order! $21-(6-13)$ means subtract the entire result of (6-13) from 21. Working left to right without parentheses gives a completely different problem.

What happens when I get a negative number inside parentheses?

+

That's totally normal! When 6 - 13 = -7, you then have $21 - (-7)$ . Remember: subtracting a negative equals adding the positive, so this becomes 21 + 7 = 28.

How do I remember that subtracting a negative means adding?

+

Think of it as "opposite of opposite"! The minus sign outside parentheses is like saying "do the opposite" of what's inside. Since -7 is negative, the opposite is +7.

Can I check my answer a different way?

+

Yes! You can work backwards: if 28 is correct, then $28 + (6-13)$ should equal 21. Let's see: $28 + (-7) = 21$ ✓

What if the numbers inside parentheses were switched to 13 - 6?

+

Great question! Then you'd have $21-(13-6) = 21-7 = 14$ . The order inside parentheses matters a lot - it determines whether you get a positive or negative result!

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Solve 21-(6-13): Order of Operations with Nested Subtraction

Parentheses with Negative Results

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