Question

each card, decide if the fraction of lights that are on is equivalent to \\(\frac{1}{4}\\).

Explanation:

Step1: Count total and on lights

Total bulbs: \( 3 \times 4 = 12 \)? Wait, no, the bottom card: rows? Let's see the bottom card: 3 rows, 4 columns? Wait, no, the bottom card has 3 rows, each with 4 bulbs? Wait, no, the first card (Yes section) has 4 rows, 2 columns: 8 bulbs, 2 on. The bottom card: let's count. Rows: 3, columns: 4? Wait, no, the bottom card's bulbs: first row: 4 (2 off, 2 on? Wait, no, the bottom card: each row has 4 bulbs. Let's count total bulbs: 3 rows × 4 columns = 12. On bulbs: how many? Each row has 1 on? Wait, first row: 2 off, 1 on, 1 off? No, looking at the bottom card: each row has 4 bulbs, with 1 yellow (on) per row? Wait, 3 rows, 1 on per row: 3 on. Wait, no, let's re-express.

Wait, the problem is to decide if the fraction of on lights is \( \frac{1}{4} \). Let's take the bottom card (the one to classify). Total bulbs: let's count. The bottom card: 3 rows, 4 columns: \( 3 \times 4 = 12 \) bulbs. On bulbs: how many? Looking at the image, each row has 1 yellow (on) bulb? Wait, first row: 2 blue (off), 1 yellow (on), 1 blue (off)? No, maybe 3 on? Wait, no, let's check the first card (Yes section): 8 bulbs, 2 on: \( \frac{2}{8} = \frac{1}{4} \), so that's why it's in Yes. Now the bottom card: total bulbs: let's count. Let's see the bottom card: 3 rows, 4 columns: 12 bulbs. On bulbs: 3 (each row has 1 on). So fraction is \( \frac{3}{12} = \frac{1}{4} \)? Wait, no, wait: 3 on, 12 total: \( \frac{3}{12} = \frac{1}{4} \)? Wait, no, \( \frac{3}{12} = \frac{1}{4} \)? Yes, \( 3 \div 12 = \frac{1}{4} \). Wait, but wait, maybe I miscounted. Wait, the bottom card: let's count again. Rows: 3, columns: 4. So 12 bulbs. On bulbs: 3 (each row has 1 on). So \( \frac{3}{12} = \frac{1}{4} \). Wait, but the first card (Yes) has 8 bulbs, 2 on: \( \frac{2}{8} = \frac{1}{4} \), which is correct. Now the bottom card: 12 total, 3 on: \( \frac{3}{12} = \frac{1}{4} \), so it should go to Yes? Wait, no, wait: maybe I made a mistake. Wait, the bottom card: let's count the on bulbs. Looking at the image, the bottom card has 3 yellow (on) bulbs. Total bulbs: 3 rows × 4 columns = 12. So \( \frac{3}{12} = \frac{1}{4} \), so the fraction is equivalent to \( \frac{1}{4} \), so it should be in Yes? Wait, but maybe I miscounted. Wait, no, let's check again.

Wait, the first card (Yes section) has 8 bulbs (4 rows, 2 columns: 4×2=8), 2 on: \( \frac{2}{8} = \frac{1}{4} \), correct. The bottom card: 3 rows, 4 columns: 12 bulbs. On bulbs: 3. \( \frac{3}{12} = \frac{1}{4} \), so fraction is \( \frac{1}{4} \), so it should be in Yes? Wait, but maybe the bottom card has 12 bulbs, 3 on: \( \frac{3}{12} = \frac{1}{4} \), so yes. Wait, but maybe I made a mistake. Wait, let's re-express:

For a fraction to be \( \frac{1}{4} \), on / total = \( \frac{1}{4} \), so total = 4 × on.

First card (Yes): on=2, total=8 (4×2), so 8=4×2: yes.

Bottom card: on=3, total=12 (4×3), so 12=4×3: yes. Wait, but maybe the bottom card's on is 3? Wait, looking at the image, the bottom card has 3 rows, each with 1 on bulb (yellow), so 3 on. Total 12. So \( \frac{3}{12} = \frac{1}{4} \), so it should go to Yes. Wait, but maybe I miscounted the bottom card. Wait, maybe the bottom card has 12 bulbs, 3 on: \( \frac{3}{12} = \frac{1}{4} \), so yes.

Wait, but let's confirm:

Case 1: First card (Yes section): 8 bulbs, 2 on. \( \frac{2}{8} = \frac{1}{4} \): correct.

Case 2: Bottom card: 12 bulbs, 3 on. \( \frac{3}{12} = \frac{1}{4} \): correct. So it should be in Yes.

Step2: Compare fraction

Fraction of on lights: \( \frac{3}{12} = \frac{1}{4} \), so equivalent. Thus, the bottom card should be placed in the "Yes" section.

Answer:

The bottom card (the one in the blue frame) should be placed in the "Yes" section (the left box labeled "Yes").