Solve the Expression: 28÷(210÷15)-(12+42) Order of Operations Challenge

Q: Why do I solve the parentheses first instead of going left to right?

The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer. Parentheses always come first, no matter where they appear in the expression!

Q: What if I get confused about which parentheses to solve first?

When you have multiple sets of parentheses like $ (210÷15) $ and $ (12+42) $, you can solve them in any order since they're independent of each other.

Q: How do I remember the order of operations?

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally"!

Q: Can I use a calculator for this problem?

Yes, but be careful! Make sure to use parentheses correctly in your calculator. Enter it exactly as: $ 28 ÷ (210 ÷ 15) - (12 + 42) $

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Let's write division as a fraction

00:10 Always solve parentheses first

00:15 Division is also multiplication by the reciprocal

00:26 Let's break down 28 into factors 14 and 2

00:33 Let's break down 210 into factors 14 and 15

00:46 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

$28:(210:15)-(12+42)=\text{?}$

2

Step-by-step solution

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

Step 1: Calculate the expression inside the parentheses by performing the division $210:15$ .
Step 2: Add the numbers inside the other parentheses, $12 + 42$ .
Step 3: Use the result from Step 1 to perform the division $28:\text{(result of Step 1)}$ .
Step 4: Subtract the result of Step 2 from the result of Step 3.

Now, let's work through each step:
Step 1: Compute $210 : 15 = 14$ .
Step 2: Compute $12 + 42 = 54$ .
Step 3: Compute the division $28 : 14 = 2$ .
Step 4: Finally, compute the subtraction $2 - 54 = -52$ .

Therefore, the solution to the problem is $-52$ .

3

Final Answer

$-52$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always solve operations inside parentheses first
Technique: Calculate $210 ÷ 15 = 14$ and $12 + 42 = 54$ before other operations
Check: Verify final calculation: $28 ÷ 14 - 54 = 2 - 54 = -52$ ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't solve $28 ÷ 210$ first = $0.133...$ leading to completely wrong answer! This ignores parentheses which must be solved first. Always calculate everything inside parentheses before moving to other operations.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(5+55)= $$

FAQ

Everything you need to know about this question

Why do I solve the parentheses first instead of going left to right?

+

The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer. Parentheses always come first, no matter where they appear in the expression!

What if I get confused about which parentheses to solve first?

+

When you have multiple sets of parentheses like $(210÷15)$ and $(12+42)$ , you can solve them in any order since they're independent of each other.

How do I remember the order of operations?

+

Use PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Many students remember it as "Please Excuse My Dear Aunt Sally"!

Why is my final answer negative?

+

Don't worry! Negative answers are perfectly normal in math. Here we get $2 - 54 = -52$ because we're subtracting a larger number from a smaller one.

Can I use a calculator for this problem?

+

Yes, but be careful! Make sure to use parentheses correctly in your calculator. Enter it exactly as: $28 ÷ (210 ÷ 15) - (12 + 42)$

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Solve the Expression: 28÷(210÷15)-(12+42) Order of Operations Challenge

Order of Operations with Nested Parentheses

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