https://file.aiquickdraw.com/mathbot/file/1727732228127kvvf0o0n.jpg

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.

Display the missing equivalent part-to-part ratios in this two-column table.

Learn how to find the missing equivalent part-to-part ratios in a two-column table with given ratios. This problem involves ratio and proportion concepts and is suitable for students in Grades 6-8. Understand how to use cross-multiplication to verify equivalent ratios.

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