1. **Stating the problem:** We need to find which pairs of ratios are equivalent in each question. 2. **Formula and rule:** Two ratios $a:b$ and $c:d$ are equivalent if their cross products are equal, i.e., $a \times d = b \times c$. 3. **Step-by-step for question 1:** - Ratios: 2:8, 2:6, 4:8, 4:16, 1:4, 1:2 - Check pairs: - 2:8 and 4:16: $2 \times 16 = 32$, $8 \times 4 = 32$ so equivalent. - 2:8 and 1:4: $2 \times 4 = 8$, $8 \times 1 = 8$ so equivalent. - 4:8 and 1:2: $4 \times 2 = 8$, $8 \times 1 = 8$ so equivalent. 4. **General method:** For each pair, multiply the first term of one ratio by the second term of the other and compare with the product of the second term of the first ratio and the first term of the second ratio. 5. **Example for question 2:** - Ratios: 2:12, 1:8, 4:22, 1:6, 1:4, 4:24 - Check 2:12 and 1:6: $2 \times 6 = 12$, $12 \times 1 = 12$ equivalent. - Check 2:12 and 4:24: $2 \times 24 = 48$, $12 \times 4 = 48$ equivalent. 6. **Summary:** To find equivalent ratios, simplify each ratio to its lowest terms or use cross multiplication to check equality. This method applies to all questions similarly.