Let's solve $\frac{1}{2} \times \frac{2}{3}$ step by step! 🎉
**Step 1:** Imagine you have half a chocolate bar 🍫. That's $\frac{1}{2}$.
**Step 2:** Now, we want to take two-thirds of that half. So, we multiply $\frac{1}{2}$ by $\frac{2}{3}$.
**Step 3:** Multiply the top numbers (numerators): 1 × 2 = 2.
**Step 4:** Multiply the bottom numbers (denominators): 2 × 3 = 6.
**Step 5:** So, $\frac{1}{2} \times \frac{2}{3} = \frac{2}{6}$.
**Step 6:** Simplify $\frac{2}{6}$ by dividing top and bottom by 2:
$\frac{2 \div 2}{6 \div 2} = \frac{1}{3}$.
Great! The answer is $\frac{1}{3}$. 🎯
Group 1: Half (1/2):
🍫 🍫
(2 pieces, 1 shaded)
➕
🍫 🍫
(2 pieces, 1 shaded)
Group 2: Two-thirds of the half:
🍫 🍫 🍫
(3 pieces, 2 shaded)
=
🍫 🍫 🍫
(3 pieces, 2 shaded)
Total:
🍫 🍫 🍫
(1 piece shaded out of 3)
🍫 🍫 🍫
(1 piece shaded out of 3)