tell if each pair  of fractions is equivalent 2/5 and 8/20

To determine if the fractions \( \frac{2}{5} \) and \( \frac{8}{20} \) are equivalent, you can either simplify \( \frac{8}{20} \) or cross-multiply the fractions and compare the products.

### Method 1: Simplifying the Fraction
Simplify \( \frac{8}{20} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:

\[
\frac{8 \div 4}{20 \div 4} = \frac{2}{5}
\]

Since \( \frac{8}{20} \) simplifies to \( \frac{2}{5} \), the fractions \( \frac{2}{5} \) and \( \frac{8}{20} \) are equivalent.

### Method 2: Cross-Multiplication
Cross-multiply the fractions to see if the products are equal:

\[
2 \times 20 = 40
\]

\[
5 \times 8 = 40
\]

Since both products are equal (40 = 40), the fractions \( \frac{2}{5} \) and \( \frac{8}{20} \) are equivalent.

Would you like further details or explanations?

### Related Questions:
1. How do you simplify fractions?
2. What is the cross-multiplication method for comparing fractions?
3. Can you explain why cross-multiplication works to compare fractions?
4. How do you find the GCD of two numbers?
5. What are other methods to check if fractions are equivalent?
6. How do you convert improper fractions to mixed numbers?
7. How do you add equivalent fractions?
8. How do you find a common denominator for fractions?

**Tip:** When working with fractions, simplifying them first can make comparisons and calculations much easier!

Learn how to determine if fractions 2/5 and 8/20 are equivalent with detailed step-by-step methods including simplification and cross-multiplication. This problem covers key concepts in fractions and equivalence. Suitable for students in Grades 4-6.

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