Which fractions are equivalent to \( \frac{8}{10} \) ? Hint: There may be more than one.

Equivalent fractions are different fractions that represent the same value or proportion. To find fractions equivalent to \( \frac{8}{10} \), you can multiply both the numerator (top number) and the denominator (bottom number) by the same non-zero integer. Here are several fractions equivalent to \( \frac{8}{10} \): 1. **Simplified Form:** \[ \frac{8}{10} = \frac{4}{5} \] *By dividing both the numerator and the denominator by 2.* 2. **By Multiplying by 2:** \[ \frac{8 \times 2}{10 \times 2} = \frac{16}{20} \] 3. **By Multiplying by 3:** \[ \frac{8 \times 3}{10 \times 3} = \frac{24}{30} \] 4. **By Multiplying by 4:** \[ \frac{8 \times 4}{10 \times 4} = \frac{32}{40} \] 5. **By Multiplying by 5:** \[ \frac{8 \times 5}{10 \times 5} = \frac{40}{50} \] 6. **By Multiplying by 6:** \[ \frac{8 \times 6}{10 \times 6} = \frac{48}{60} \] 7. **By Multiplying by 7:** \[ \frac{8 \times 7}{10 \times 7} = \frac{56}{70} \] 8. **By Multiplying by 8:** \[ \frac{8 \times 8}{10 \times 8} = \frac{64}{80} \] **General Method:** To generate equivalent fractions to \( \frac{8}{10} \), choose any integer \( n \neq 0 \) and multiply both the numerator and the denominator by \( n \): \[ \frac{8 \times n}{10 \times n} \] For example, if \( n = 9 \): \[ \frac{8 \times 9}{10 \times 9} = \frac{72}{90} \] **Infinite Equivalent Fractions:** There are infinitely many fractions equivalent to \( \frac{8}{10} \), as you can continue multiplying by larger integers to generate new equivalent fractions each time. **Key Point:** All equivalent fractions to \( \frac{8}{10} \) share the same ratio between the numerator and the denominator, meaning they simplify to the same value when reduced to their simplest form (in this case, \( \frac{4}{5} \)).