Equivalent Fractions:

To understand equivalent fractions, we first need to define what they are. Equivalent fractions are different fractions that represent the same value or proportion of a whole. ### Known Conditions: 1. **Definition**: Two fractions \( \frac{a}{b} \) and \( \frac{c}{d} \) are equivalent if \( a \times d = b \times c \). 2. **Examples**: Common examples include \( \frac{1}{2} \) and \( \frac{2}{4} \), or \( \frac{3}{6} \) and \( \frac{1}{2} \). ### Steps to Find Equivalent Fractions: 1. **Multiply or Divide**: You can create equivalent fractions by multiplying or dividing both the numerator and the denominator of a fraction by the same non-zero number. For example, to find equivalent fractions for \( \frac{1}{2} \): - Multiply both the numerator and denominator by 2: \[ \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \] - Multiply both by 3: \[ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] 2. **Simplifying Fractions**: You can also simplify fractions to find their equivalent forms. For example, \( \frac{4}{8} \) can be simplified by dividing both the numerator and denominator by 4: \[ \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \] ### Conclusion: To summarize, equivalent fractions can be found by multiplying or dividing the numerator and denominator by the same number, or by simplifying a fraction. If you have a specific fraction in mind and would like to find its equivalent fractions, please provide it, and I can help you with that!