Solving Step-by-Step: Computation in 35 - (82 - 39 ÷ (3 × 2))

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

Mathematics has a specific order of operations (PEMDAS) that must be followed! Working left to right would give you the wrong answer because parentheses and multiplication/division have higher priority than subtraction.

Q: What does the colon (:) mean in 39 ÷ (3 × 2)?

The colon (:) is just another way to write division, like the ÷ symbol. So $ 39 : 6 $ means the same as $ 39 \div 6 = 6.5 $.

Q: How do I convert 6.5 to a mixed number?

$ 6.5 = 6\frac{1}{2} $ because the decimal 0.5 equals the fraction $ \frac{1}{2} $. So $ -40.5 = -40\frac{1}{2} $.

Q: What if I get confused with all the parentheses?

Start from the deepest level and work your way out! Circle or highlight each set of parentheses as you solve them. For nested parentheses, always solve the innermost ones first.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Negative times positive is always negative

00:08 Negative times negative is always positive

00:14 Write division as a fraction

00:21 Factor 39 into 13 and 3

00:28 Simplify what we can

00:39 Use the distribution law and split 35 into 30 plus 5

00:46 Use the distribution law and split 82 into 80 and 2

00:50 Collect terms

01:06 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

$35-(82-39:(3\cdot2))=\text{?}$

2

Step-by-step solution

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

Step 1: Evaluate the expression inside the parentheses, focusing first on multiplication.
Step 2: Perform the division inside the parentheses.
Step 3: Simplify the expression by completing the subtraction inside the parentheses.
Step 4: Subtract the result from 35.

Now, let's work through each step:

Step 1: Evaluate the multiplication inside the parentheses.
The expression is $3 \cdot 2$ , which equals $6$ .

Step 2: Perform the division inside the parentheses.
Substitute the result into $39 : 6$ , which is $39 \div 6 = 6.5$ .

Step 3: Simplify the expression inside the parentheses by performing the subtraction.
The expression becomes $82 - 6.5 = 75.5$ .

Step 4: Subtract the result from 35.
Hence, $35 - 75.5 = -40.5$ .

Therefore, the solution to the problem is $-40.5$ , which corresponds to the first choice given in the possible answers as $-40\frac{1}{2}$ .

3

Final Answer

$-40\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always work from innermost parentheses outward first
Technique: Calculate $3 \times 2 = 6$ , then $39 \div 6 = 6.5$
Check: Final answer $-40.5 = -40\frac{1}{2}$ matches given choices ✓

Common Mistakes

Avoid these frequent errors

Working left to right without following order of operations
Don't solve 35 - 82 = -47 first! This ignores the parentheses and gives a completely wrong result like -53.5. Always solve innermost parentheses first: (3 × 2), then division, then work outward.

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 specific order of operations (PEMDAS) that must be followed! Working left to right would give you the wrong answer because parentheses and multiplication/division have higher priority than subtraction.

What does the colon (:) mean in 39 ÷ (3 × 2)?

+

The colon (:) is just another way to write division, like the ÷ symbol. So $39 : 6$ means the same as $39 \div 6 = 6.5$ .

How do I convert 6.5 to a mixed number?

+

$6.5 = 6\frac{1}{2}$ because the decimal 0.5 equals the fraction $\frac{1}{2}$ . So $-40.5 = -40\frac{1}{2}$ .

What if I get confused with all the parentheses?

+

Start from the deepest level and work your way out! Circle or highlight each set of parentheses as you solve them. For nested parentheses, always solve the innermost ones first.

Why is my answer negative when the problem starts with 35?

+

Even though we start with positive 35, we're subtracting a larger number (75.5) from it. When you subtract a bigger number from a smaller one, the result is always negative: $35 - 75.5 = -40.5$ .

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Commutative, Distributive and Associative Properties questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solving Step-by-Step: Computation in 35 - (82 - 39 ÷ (3 × 2))

Order of Operations with Nested Parentheses

❤️ Continue Your Math Journey!