Solve Complex Division: 112÷(0.5÷0.25)² Step-by-Step

Q: Why do I divide 0.5 by 0.25 instead of the other way around?

The colon : means division, so $ 0.5:0.25 $ reads as "0.5 divided by 0.25". Think of it like a fraction: $ \frac{0.5}{0.25} $.

Q: How do I divide by a decimal like 0.25?

Dividing by 0.25 is the same as multiplying by 4 because $ 0.25 = \frac{1}{4} $. So $ 0.5 \div 0.25 = 0.5 \times 4 = 2 $.

Q: What if I calculated the parentheses wrong?

If you got anything other than 2 for $ (0.5:0.25) $, double-check your division! Remember: 0.5 ÷ 0.25 = 2, then $ 2^2 = 4 $, finally $ 112 ÷ 4 = 28 $.

Q: Why don't I square 112 as well?

The exponent only applies to what's in parentheses! The expression is $ 112 ÷ (0.5:0.25)^2 $, not $ (112 ÷ 0.5:0.25)^2 $.

Q: Can I use a calculator for decimal division?

Yes! But understanding that 0.25 = 1/4 helps you work faster. $ 0.5 ÷ 0.25 $ becomes $ 0.5 \times 4 $, which is easier to calculate mentally.

Order of Operations with Nested Division

$112:(0.5:0.25)^2=$

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Understand the problem

$112:(0.5:0.25)^2=$

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Simplify $0.5 : 0.25$ .
Step 2: Square the result of step 1.
Step 3: Divide 112 by the result of step 2.

Let's perform each step:
Step 1: Calculate $0.5 : 0.25$ .
To find this, divide 0.5 by 0.25. Since dividing by a fraction is the same as multiplying by its reciprocal,
we have: $0.5 \div 0.25 = 0.5 \times 4 = 2$ .
Step 2: Now, square this result:
$(2)^2 = 4$ .
Step 3: Finally, divide 112 by this square:
$\frac{112}{4} = 28$ .

Thus, the solution to the problem is $28$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Solve innermost operations first, then apply exponents before division
Technique: Convert 0.5 ÷ 0.25 to 0.5 × 4 = 2
Check: Verify 112 ÷ 4 = 28 by calculating 28 × 4 = 112 ✓

Common Mistakes

Avoid these frequent errors

Squaring each number separately instead of the division result
Don't calculate $(0.5)^2 : (0.25)^2$ = wrong answer! This changes the order of operations and gives 0.25 : 0.0625 = 4, then 112 ÷ 4 = 28 by coincidence, but method is wrong. Always solve parentheses completely first, then square the entire result.

Practice Quiz

Test your knowledge with interactive questions

$$ 100-(30-21)= $$

FAQ

Everything you need to know about this question

Why do I divide 0.5 by 0.25 instead of the other way around?

The colon : means division, so $0.5:0.25$ reads as "0.5 divided by 0.25". Think of it like a fraction: $\frac{0.5}{0.25}$ .

How do I divide by a decimal like 0.25?

Dividing by 0.25 is the same as multiplying by 4 because $0.25 = \frac{1}{4}$ . So $0.5 \div 0.25 = 0.5 \times 4 = 2$ .

What if I calculated the parentheses wrong?

If you got anything other than 2 for $(0.5:0.25)$ , double-check your division! Remember: 0.5 ÷ 0.25 = 2, then $2^2 = 4$ , finally $112 ÷ 4 = 28$ .

Why don't I square 112 as well?

The exponent only applies to what's in parentheses! The expression is $112 ÷ (0.5:0.25)^2$ , not $(112 ÷ 0.5:0.25)^2$ .

Can I use a calculator for decimal division?

Yes! But understanding that 0.25 = 1/4 helps you work faster. $0.5 ÷ 0.25$ becomes $0.5 \times 4$ , which is easier to calculate mentally.

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