Solve Decimal Expression: 10.75 - (7.20 - 2.7) Using Order of Operations

Q: Why can't I just work from left to right like reading?

Mathematics has a special order called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Parentheses always come first, no matter where they appear in the expression!

Q: Do I need to line up the decimal points when subtracting?

Yes, always! Lining up decimal points ensures you're subtracting the correct place values. Think of it like subtracting money - you wouldn't subtract cents from dollars!

Q: What if the numbers inside parentheses have different decimal places?

Add zeros to make them the same length! For example, $ 7.20 - 2.7 $ becomes $ 7.20 - 2.70 $. This makes subtraction much easier and prevents mistakes.

Q: What's the difference between 2.7 and 2.70?

They're exactly the same value! The extra zero doesn't change the number, but it helps you align decimal points correctly when doing calculations.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's begin solving the problem step by step.

00:13 Remember, when you multiply a negative by a negative, you get a positive.

00:18 Now, let's apply this rule to our example.

00:27 We'll follow the order of operations from left to right.

00:33 Next, use long subtraction to substitute values in our problem.

00:57 Then, we'll use long addition to continue solving.

01:11 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$10.75-(7.20-2.7)=$

2

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Simplify the expression inside the parentheses: $7.20 - 2.7$ .
Step 2: Subtract the result from 10.75.

Let's work through these steps:

Step 1: Simplify $7.20 - 2.7$ .
Align the decimal points:
$\qquad 7.20$
$- \quad \underline{2.70}$
$\qquad 4.50$

Step 2: Now subtract the result from 10.75:
Align the decimal points:
$\qquad 10.75$
$- \quad \underline{4.50}$
$\qquad 6.25$

Therefore, the solution to the problem is $6.25$ .

3

Final Answer

6.25

Key Points to Remember

Essential concepts to master this topic

Rule: Always solve parentheses first, then work outside operations
Technique: Align decimal points: 7.20 - 2.70 = 4.50
Check: Verify by working backwards: 6.25 + 4.50 = 10.75 ✓

Common Mistakes

Avoid these frequent errors

Working left to right without respecting parentheses
Don't calculate 10.75 - 7.20 first = 3.55, then subtract 2.7 = wrong answer! This ignores the parentheses which change the order completely. Always solve what's inside parentheses before doing outside operations.

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 reading?

+

Mathematics has a special order called PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Parentheses always come first, no matter where they appear in the expression!

Do I need to line up the decimal points when subtracting?

+

Yes, always! Lining up decimal points ensures you're subtracting the correct place values. Think of it like subtracting money - you wouldn't subtract cents from dollars!

What if the numbers inside parentheses have different decimal places?

+

Add zeros to make them the same length! For example, $7.20 - 2.7$ becomes $7.20 - 2.70$ . This makes subtraction much easier and prevents mistakes.

How do I know if I did the parentheses correctly?

+

Work backwards! Take your final answer and add it to what was in parentheses. If you get the original first number, you're correct. Like: $6.25 + 4.50 = 10.75$ ✓

What's the difference between 2.7 and 2.70?

+

They're exactly the same value! The extra zero doesn't change the number, but it helps you align decimal points correctly when doing calculations.

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Solve Decimal Expression: 10.75 - (7.20 - 2.7) Using Order of Operations

Order of Operations with Decimal Subtraction

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