section_path: Arithmetic with fractions/Division
section_name: Division
paragraph_text: Division
  
  To divide a fraction by a whole number, you may either divide the numerator by the number, if it goes evenly into the numerator, or multiply the denominator by the number. For example, 10 3 ÷ 5 {\displaystyle {\tfrac {10}{3}}\div 5} equals 2 3 {\displaystyle {\tfrac {2}{3}}} and also equals 10 3 ⋅ 5 = 10 15 {\displaystyle {\tfrac {10}{3\cdot 5}}={\tfrac {10}{15}}}, which reduces to 2 3 {\displaystyle {\tfrac {2}{3}}}. To divide a number by a fraction, multiply that number by the reciprocal of that fraction. Thus, 1 2 ÷ 3 4 = 1 2 × 4 3 = 1 ⋅ 4 2 ⋅ 3 = 2 3 {\displaystyle {\tfrac {1}{2}}\div {\tfrac {3}{4}}={\tfrac {1}{2}}\times {\tfrac {4}{3}}={\tfrac {1\cdot 4}{2\cdot 3}}={\tfrac {2}{3}}}.