Let's solve step by step! 🎉
**Step 1:** Look at the problem: $\frac{1}{4} \div \left( \frac{1}{8} - \frac{1}{16} \right)$
**Step 2:** First, subtract inside the parentheses: $\frac{1}{8} - \frac{1}{16}$
Let's make a picture with candies 🍬🍬🍬🍬 (imagine 8 candies split into halves)
🍬 🍬 🍬 🍬 (4 candies = 1/2)
Now, $\frac{1}{8}$ is like 1 candy out of 8, and $\frac{1}{16}$ is like half a candy out of 8, so subtracting means:
**Box 1:**
Group 1: $\frac{1}{8}$
🍬
(1 candy)
Add ➖
**Box 2:**
🍬
(1 candy)
Group 2: $\frac{1}{16}$
½ 🍬
(half candy)
=
**Total box:**
½ 🍬
(half candy)
Subtraction Result
½ 🍬
(half candy = $\frac{1}{16}$)
So $\frac{1}{8} - \frac{1}{16} = \frac{1}{16}$
**Step 3:** Now divide $\frac{1}{4}$ by $\frac{1}{16}$
Dividing fractions means multiply by the flipped fraction:
$$\frac{1}{4} \times \frac{16}{1} = \frac{16}{4} = 4$$
Imagine 4 big apples 🍎🍎🍎🍎!
**Box 1:**
½ 🍬
(half candy = $\frac{1}{16}$)
Group 1:
🍎
(1 apple)
Add ➕
**Box 2:**
🍎
(1 apple)
Group 2:
🍎 🍎 🍎
(3 apples)
=
**Total box:**
🍎 🍎 🍎
(3 apples)
Total apples:
🍎 🍎 🍎 🍎
(4 apples)
**Great job!** The answer is $4$! 🎯🍎 🍎 🍎 🍎
(4 apples)