Solve 300÷(20×8)-(13+200): Order of Operations Challenge

Q: Why do I solve the parentheses first even though division comes before subtraction?

PEMDAS order matters! Parentheses always come first. You must calculate $20 \times 8 = 160$ and $13 + 200 = 213$ before doing any other operations.

Q: How do I convert 1.875 to a mixed number?

Since 0.875 = $\frac{7}{8}$, we have 1.875 = $1\frac{7}{8}$. But our final answer is negative: $-211\frac{1}{8}$ because 1.875 - 213 = -211.125 = $-211\frac{1}{8}$.

Q: Can I use a calculator for this problem?

Absolutely! Calculators help avoid arithmetic errors, but you still need to follow PEMDAS order. Enter parentheses carefully: 300÷(20×8)-(13+200).

Q: Why is my answer positive when the correct answer is negative?

Check your subtraction! Many students calculate $213 - 1.875$ instead of $1.875 - 213$. The order matters in subtraction: smaller minus larger gives negative.

Q: What does the colon (:) mean in this problem?

The colon (:) means division, just like ÷. So $300:(20\cdot8)$ is the same as $300 \div (20 \times 8)$.

Q: How do I check if -211⅛ is really correct?

Work backwards! Calculate $300 \div 160 = 1.875$ and $13 + 200 = 213$, then $1.875 - 213 = -211.125 = -211\frac{1}{8}$ ✓

Order of Operations with Mixed Decimal Fractions

$300:(20\cdot8)-(13+200)=\text{?}$

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Understand the problem

$300:(20\cdot8)-(13+200)=\text{?}$

Step-by-step solution

To solve the problem $300:(20\cdot8)-(13+200)$ , follow these steps:

Step 1: Evaluate the multiplication $20 \cdot 8$ .
$20 \cdot 8 = 160$
Step 2: Perform the division $300:160$ .
$300 \div 160 = 1.875$
Step 3: Calculate the addition inside the parentheses $13 + 200$ .
$13 + 200 = 213$
Step 4: Subtract the result of the addition from the division.
$1.875 - 213 = -211.125$
Step 5: Convert the decimal to a fraction, if necessary.
Since $-211.125$ is equivalent to $-211\frac{1}{8}$ .

Therefore, the solution to the problem is $-211\frac{1}{8}$ , which corresponds to choice 3.

Final Answer

$-211\frac{1}{8}$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always solve parentheses first, then multiplication/division, then addition/subtraction
Division Technique: Convert 300 ÷ 160 = 1.875 or 1⅞
Check Calculation: Verify 1.875 - 213 = -211.125 = -211⅛ ✓

Common Mistakes

Avoid these frequent errors

Solving operations from left to right instead of following PEMDAS
Don't solve 300 ÷ 20 first = 15, then 15 × 8 = 120! This ignores parentheses and gives the wrong base calculation. Always solve parentheses (20 × 8 = 160) before division, then 300 ÷ 160.

Practice Quiz

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first even though division comes before subtraction?

PEMDAS order matters! Parentheses always come first. You must calculate $20 \times 8 = 160$ and $13 + 200 = 213$ before doing any other operations.

How do I convert 1.875 to a mixed number?

Since 0.875 = $\frac{7}{8}$ , we have 1.875 = $1\frac{7}{8}$ . But our final answer is negative: $-211\frac{1}{8}$ because 1.875 - 213 = -211.125 = $-211\frac{1}{8}$ .

Can I use a calculator for this problem?

Absolutely! Calculators help avoid arithmetic errors, but you still need to follow PEMDAS order. Enter parentheses carefully: 300÷(20×8)-(13+200).

Why is my answer positive when the correct answer is negative?

Check your subtraction! Many students calculate $213 - 1.875$ instead of $1.875 - 213$ . The order matters in subtraction: smaller minus larger gives negative.

What does the colon (:) mean in this problem?

The colon (:) means division, just like ÷. So $300:(20\cdot8)$ is the same as $300 \div (20 \times 8)$ .

How do I check if -211⅛ is really correct?

Work backwards! Calculate $300 \div 160 = 1.875$ and $13 + 200 = 213$ , then $1.875 - 213 = -211.125 = -211\frac{1}{8}$ ✓

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