How-Tos / Math

How to Cross Multiply

Posted by
How to do Cross Multiplication

Last updated on October 13th, 2020

Cross-multiplication requires you to multiply the numerator of the first fraction with the denominator of the second fraction and the numerator of the second fraction with the denominator of the first fraction. Cross-Multiplication is also useful when you’re trying to solve a ratio. Here is how you can do cross multiplication.

How to Cross Multiply Fractions without Variable

The given fractions are \mathbf{\frac{4}{6} = \frac{2}{3}}

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.

    \mathbf{4 * 3 = 12}

  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.

    \mathbf{2 * 6 = 12}
  3. Set the two products equal to each other. 

    \\\textbf{4 * 3 = 2 * 6} \\\mathbf{12 \ \ \ \ \ = \ \ \12}

How to Cross Multiply Fractions with Single Variable

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.

    2.          For Example, The equation is \boldsymbol{\mathbf{}\frac{5}{x} = \frac{10}{25}}.

             Now, multiply 5 * 25 = 125

  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.

    3. Now, multiply x * 10 = 10x

  3. Set the two products equal to each other.

    4. Just set 125 equal to 10x.
    125 = 10x

  4. Solve the variable.

    5. \\ \mathbf{125 = 10x } \\ \\ \mathbf{\\ \frac{125}{5} = \frac{10}{5} } \\ \\ \mathbf{\\ \25 = 2x}

    \mathbf{\frac{25}{2} = 12.5 = x} 

How to Cross Multiply Fractions with Two of the Same Variable

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.

    For Example, The equation is \mathbf{\frac{2x + 5}{3} = \frac{x + 7}{6}}

    Now, Multiply \\ \mathbf{(2x + 5\ *\ 6 = \mathbf{6(2x + 5)}} = \mathbf{12x + 30}

  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.

    Now, Multiply \\ \mathbf{(x + 7)\ *\ 3 = \mathbf{3(x + 7)}} = \mathbf{3x + 21}

  3. Set the two products equal to each other and combine the like terms.

    \\\mathbf{12x + 30 = 3x + 21} \\ \\\mathbf{12x - 3x = 21 - 30} \\ \\\mathbf{\mathbf{}9x = -9}

  4. Solve the equation.

    \\\mathbf{9x = 9} \\ \\\mathbf{x} = -\mathbf{\frac{9}{9}} \\ \\\mathbf{x = -1}

    We can check the equation by plugging in -1.

    \\ \mathbf{\frac{2(-1) + 5}{3} = \frac{-1 + 7}{6}} \\ \\ \mathbf{\ \ \ \ \ \frac{3}{3} = \frac{6}{6}} \\ \\ \mathbf{\ \ \ \ \ \ 1 = 1}