What fraction is equal to 2/3?

Steps to Solve

1. Understand the concept of equivalent fractions

   Equivalent fractions are different fractions that represent the same part of a whole. To find an equivalent fraction, you can multiply or divide both the numerator (top number) and the denominator (bottom number) by the same nonzero integer.

2. Multiply the numerator and denominator by the same number

   To find fractions equivalent to $\frac{2}{3}$, we can multiply both the numerator and the denominator by the same number. For example, to find one equivalent fraction, multiply both the numerator and denominator by 2:

   $$\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$$

3. Other equivalent fractions

   We can find more equivalent fractions by multiplying the numerator and denominator by other integers. For example:

   $$\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$$ $$\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$$ $$\frac{2 \times 5}{3 \times 5} = \frac{10}{15}$$

4. Confirmation step

   To confirm that the given fractions are equivalent to $\frac{2}{3}$, you can simplify each fraction back to its simplest form:

   • $\frac{4}{6} \div 2/2 = \frac{2}{3}$
   • $\frac{6}{9} \div 3/3 = \frac{2}{3}$
   • $\frac{8}{12} \div 4/4 = \frac{2}{3}$
   • $\frac{10}{15} \div 5/5 = \frac{2}{3}$