Solve 84 ÷ (4.8 × 3.5): Order of Operations with Decimals

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

The parentheses tell you exactly what to do first! Order of operations (PEMDAS) requires you to handle parentheses before division. Ignoring them changes the entire problem.

Q: How do I multiply 4.8 × 3.5 without a calculator?

Break it down: $ 4.8 \times 3.5 = 48 \times 35 ÷ 100 $. Calculate $ 48 \times 35 = 1680 $, then move the decimal two places left to get 16.8.

Q: What if I get a decimal answer instead of 5?

Check your parentheses work! If $ 4.8 \times 3.5 \neq 16.8 $, you'll get the wrong final answer. Always double-check your decimal multiplication first.

Q: Can I convert decimals to fractions to make it easier?

Absolutely! $ 4.8 = \frac{24}{5} $ and $ 3.5 = \frac{7}{2} $. Then $ \frac{24}{5} \times \frac{7}{2} = \frac{168}{10} = 16.8 $. Use whichever method feels more comfortable!

Q: How do I know 84 ÷ 16.8 equals exactly 5?

Think of it as $ \frac{84}{16.8} = \frac{840}{168} $. Since $ 168 \times 5 = 840 $, the answer is exactly 5 with no remainder.

Division with Parenthetical Decimal Products

$84:(4.8\times3.5)=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$84:(4.8\times3.5)=$

Step-by-step solution

To solve this problem, follow these steps:

Step 1: First, compute the product of $4.8$ and $3.5$ . We calculate:

$4.8 \times 3.5 = 16.8$

Step 2: Next, divide $84$ by the product calculated in Step 1:

$84 \div 16.8 = 5$

Therefore, the solution to the problem is $5$ .

Final Answer

$5$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Always calculate operations inside parentheses first
Technique: Multiply decimals first: $4.8 \times 3.5 = 16.8$
Check: Verify final division: $5 \times 16.8 = 84$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring parentheses and dividing left to right
Don't calculate 84 ÷ 4.8 = 17.5 first and then multiply by 3.5 = 61.25! This violates order of operations and gives the wrong answer. Always solve what's inside parentheses first before doing any other operations.

Practice Quiz

Test your knowledge with interactive questions

$60:(10\times2)=$

FAQ

Everything you need to know about this question

Why can't I just divide from left to right?

The parentheses tell you exactly what to do first! Order of operations (PEMDAS) requires you to handle parentheses before division. Ignoring them changes the entire problem.

How do I multiply 4.8 × 3.5 without a calculator?

Break it down: $4.8 \times 3.5 = 48 \times 35 ÷ 100$ . Calculate $48 \times 35 = 1680$ , then move the decimal two places left to get 16.8.

What if I get a decimal answer instead of 5?

Check your parentheses work! If $4.8 \times 3.5 \neq 16.8$ , you'll get the wrong final answer. Always double-check your decimal multiplication first.

Can I convert decimals to fractions to make it easier?

Absolutely! $4.8 = \frac{24}{5}$ and $3.5 = \frac{7}{2}$ . Then $\frac{24}{5} \times \frac{7}{2} = \frac{168}{10} = 16.8$ . Use whichever method feels more comfortable!

How do I know 84 ÷ 16.8 equals exactly 5?

Think of it as $\frac{84}{16.8} = \frac{840}{168}$ . Since $168 \times 5 = 840$ , the answer is exactly 5 with no remainder.

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