section_path: Arithmetic with fractions/Equivalent fractions
section_name: Equivalent fractions
paragraph_text: Equivalent fractions
  
  Multiplying the numerator and denominator of a fraction by the same (non-zero) number results in a fraction that is equivalent to the original fraction. This is true because for any non-zero number n {\displaystyle n}, the fraction n n {\displaystyle {\tfrac {n}{n}}} equals 1. Therefore, multiplying by n n {\displaystyle {\tfrac {n}{n}}} is the same as multiplying by one, and any number multiplied by one has the same value as the original number. By way of an example, start with the fraction 1 2 {\displaystyle {\tfrac {1}{2}}}. When the numerator and denominator are both multiplied by 2, the result is 2 / 4, which has the same value (0.5) as 1 / 2. To picture this visually, imagine cutting a cake into four pieces; two of the pieces together (2 / 4) make up half the cake (1 / 2).