The table in your image provides a part-to-part ratio with the numbers:

• First row: 7 : 10
• Second row: 70 : 100

These represent equivalent ratios since 7/10 is equal to 70/100. The task is to find the set of options that match this equivalent ratio pattern.

To check:

• $\frac{7}{10} = \frac{70}{100}$ simplifies to the ratio $7:10$, which is constant in both rows.

Now, checking the provided options for matching equivalent ratios:

1. $13:10$ and $45:42$:

   • $13/10 \neq 45/42$, so this option is incorrect.

2. $14:20$ and $56:80$:

   • $14/20 = 0.7$ and $56/80 = 0.7$, so this option is correct.

3. $20:14$ and $80:56$:

   • $20/14 \neq 80/56$, so this option is incorrect.

4. $10:13$ and $42:45$:

   • $10/13 \neq 42/45$, so this option is incorrect.

Thus, the correct answer is 14:20 and 56:80.

Would you like further details on ratio simplification or equivalent ratios?

Related Questions:

1. How do you simplify a ratio to its simplest form?
2. What are some real-world applications of equivalent ratios?
3. How can cross-multiplication help verify equivalent ratios?
4. Can ratios be used to solve proportion problems in algebra?
5. How do you convert part-to-part ratios to part-to-whole ratios?

Tip: Always reduce ratios to their simplest form to easily compare equivalency between them.