https://file.aiquickdraw.com/mathbot/file/1728481763613fkanz58f.jpg

It seems like the image contains several fractions that are compared using the symbol "e" (which is likely shorthand for equivalence or equality) to check if the fractions are equal.

Let's check the equivalency of each fraction pair step by step:

1. **First pair**: \( \frac{5}{8} \) and \( \frac{8}{12} \)
   - Cross-multiply to check equivalence:  
     \( 5 \times 12 = 60 \) and \( 8 \times 8 = 64 \)  
     Since 60 ≠ 64, these two fractions are **not equivalent**.

2. **Second pair**: \( \frac{7}{15} \) and \( \frac{4}{10} \)
   - Cross-multiply:  
     \( 7 \times 10 = 70 \) and \( 15 \times 4 = 60 \)  
     Since 70 ≠ 60, these two fractions are **not equivalent**.

3. **Third pair**: \( \frac{13}{20} \) and \( \frac{10}{30} \)
   - Cross-multiply:  
     \( 13 \times 30 = 390 \) and \( 20 \times 10 = 200 \)  
     Since 390 ≠ 200, these two fractions are **not equivalent**.

4. **Fourth pair**: \( \frac{21}{36} \) and \( \frac{5}{8} \)
   - Cross-multiply:  
     \( 21 \times 8 = 168 \) and \( 36 \times 5 = 180 \)  
     Since 168 ≠ 180, these two fractions are **not equivalent**.

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None of the pairs of fractions are equivalent based on the cross-multiplication method.

Would you like further explanation on how equivalence between fractions is checked, or would you like to explore more about operations with fractions?

Here are some related questions:
1. What is the general method for simplifying fractions?
2. How do you convert fractions into decimals?
3. Can two fractions be equivalent if their numerators and denominators are not the same?
4. How can you find the least common denominator between fractions?
5. What is the process for comparing fractions with different denominators?

**Tip**: To check if two fractions are equivalent, you can either simplify both fractions or cross-multiply and see if the results are equal.

Determine if the following pairs of fractions are equivalent: 5/8 and 8/12, 7/15 and 4/10, 13/20 and 10/30, 21/36 and 5/8.

This lesson focuses on comparing pairs of fractions using cross-multiplication to determine if they are equivalent. The fractions include 5/8 and 8/12, 7/15 and 4/10, 13/20 and 10/30, and 21/36 and 5/8. A step-by-step explanation is provided to help students in grades 6-8 understand the process of fraction comparison.

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