Solve 100.6 - (75.7 + 13.2): Decimal Subtraction with Parentheses

Q: Why can't I just subtract from left to right?

The parentheses tell you to do the addition first! Order of operations (PEMDAS) says parentheses come before subtraction. Ignoring this rule leads to completely wrong answers.

Q: What if I forget to align the decimal points?

Always line up the decimal points vertically when adding or subtracting decimals. Think of it like stacking coins - ones under ones, tenths under tenths!

Q: How do I know which operation to do first?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. In this problem, the parentheses tell you to add $ 75.7 + 13.2 $ first.

Q: Can I check my answer a different way?

Yes! Work backwards: if $ 11.7 $ is correct, then $ 11.7 + 88.9 $ should equal $ 100.6 $. Try it!

Q: What if my decimal addition doesn't look right?

Double-check by estimating: $ 75.7 + 13.2 $ is about $ 76 + 13 = 89 $, so $ 88.9 $ makes sense!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 When opening parentheses, minus times plus always equals minus

00:11 Let's use this formula in our exercise

00:15 Let's solve according to the order of operations from left to right

00:24 Let's use long subtraction and substitute in our exercise

00:48 Let's use long subtraction

01:02 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

$100.6-(75.7+13.2)=$

2

Step-by-step solution

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

Step 1: Evaluate the expression inside the parentheses: $75.7 + 13.2$ .
Step 2: Perform the subtraction: $100.6 -$ (result from step 1).

Let's perform each step:

Step 1: Calculate the sum inside the parentheses:

$75.7 + 13.2 = 88.9$ .

Step 2: Subtract the result from 100.6:

$100.6 - 88.9 = 11.7$ .

Therefore, the solution to the problem is $11.7$ .

3

Final Answer

11.7

Key Points to Remember

Essential concepts to master this topic

Order Rule: Always evaluate expressions inside parentheses first
Technique: Calculate $75.7 + 13.2 = 88.9$ before subtracting
Check: Substitute back: $100.6 - 88.9 = 11.7$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting from left to right without following order of operations
Don't calculate 100.6 - 75.7 = 24.9 first and then subtract 13.2! This ignores the parentheses and gives you 11.7 instead of the correct answer. Always evaluate what's inside parentheses before doing the outer subtraction.

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 subtract from left to right?

+

The parentheses tell you to do the addition first! Order of operations (PEMDAS) says parentheses come before subtraction. Ignoring this rule leads to completely wrong answers.

What if I forget to align the decimal points?

+

Always line up the decimal points vertically when adding or subtracting decimals. Think of it like stacking coins - ones under ones, tenths under tenths!

How do I know which operation to do first?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. In this problem, the parentheses tell you to add $75.7 + 13.2$ first.

Can I check my answer a different way?

+

Yes! Work backwards: if $11.7$ is correct, then $11.7 + 88.9$ should equal $100.6$ . Try it!

What if my decimal addition doesn't look right?

+

Double-check by estimating: $75.7 + 13.2$ is about $76 + 13 = 89$ , so $88.9$ makes sense!

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Solve 100.6 - (75.7 + 13.2): Decimal Subtraction with Parentheses

Order of Operations with Decimal Arithmetic

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