Solve the Nested Division: 15÷(15÷½) Step-by-Step Solution

Q: Why do I solve the parentheses first?

Order of operations (PEMDAS) requires you to work inside parentheses first! The expression $ 15:(15:\frac{1}{2}) $ means the inner division must be completed before the outer division.

Q: How do I divide by a fraction like ½?

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $ \frac{1}{2} $ is 2, so $ 15 \div \frac{1}{2} = 15 \times 2 = 30 $.

Q: What's the difference between : and ÷ symbols?

Both : and ÷ mean division - they're just different notation styles. Some countries prefer the colon (:) while others use the division symbol (÷). They work exactly the same way!

Q: How can I check if ½ is correct?

Substitute back step by step: First, $ 15 \div \frac{1}{2} = 30 $. Then, $ 15 \div 30 = \frac{1}{2} $. Your answer matches!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Division is also multiplication by the reciprocal

00:07 Therefore when opening the parentheses, it will end up multiplied by C

00:11 We will use this formula in our exercise

00:16 A number divided by itself is always equal to 1

00:21 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

$15:(15:\frac{1}{2})=$

2

Step-by-step solution

To solve this problem, we must first evaluate the nested division expression $15:(15:\frac{1}{2})$ .

Let's start by handling the innermost division $15:\frac{1}{2}$ . Division by a fraction is equivalent to multiplication by its reciprocal. Therefore:

The reciprocal of $\frac{1}{2}$ is $2$ .
Hence, $15:\frac{1}{2} = 15 \times 2 = 30$ .

Now, we use the result of this inner division, $30$ , as the divisor for the outer expression $15:30$ .

Perform the division $15:30$ , which simplifies to $\frac{15}{30}$ .
Simplify the fraction $\frac{15}{30}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 15.
This gives us $\frac{15 \div 15}{30 \div 15} = \frac{1}{2}$ .

Therefore, the solution to the problem is $\frac{1}{2}$ .

3

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Order of Operations: Work from innermost parentheses outward first
Technique: Division by $\frac{1}{2}$ equals multiplication by 2
Check: $15 \div (15 \div \frac{1}{2}) = 15 \div 30 = \frac{1}{2}$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring order of operations and solving left to right
Don't solve 15÷15÷½ from left to right = 1÷½ = 2! This ignores parentheses and gives the wrong answer. Always solve the innermost parentheses first: (15÷½) = 30, then 15÷30 = ½.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I solve the parentheses first?

+

Order of operations (PEMDAS) requires you to work inside parentheses first! The expression $15:(15:\frac{1}{2})$ means the inner division must be completed before the outer division.

How do I divide by a fraction like ½?

+

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $\frac{1}{2}$ is 2, so $15 \div \frac{1}{2} = 15 \times 2 = 30$ .

What's the difference between : and ÷ symbols?

+

Both : and ÷ mean division - they're just different notation styles. Some countries prefer the colon (:) while others use the division symbol (÷). They work exactly the same way!

Why is my answer a fraction when I started with whole numbers?

+

Division doesn't always give whole number answers! When you divide $15 \div 30$ , you get $\frac{15}{30} = \frac{1}{2}$ . Always simplify your final fraction.

How can I check if ½ is correct?

+

Substitute back step by step: First, $15 \div \frac{1}{2} = 30$ . Then, $15 \div 30 = \frac{1}{2}$ . Your answer matches!

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Solve the Nested Division: 15÷(15÷½) Step-by-Step Solution

Nested Division with Fraction Reciprocals

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