# How to Cross Multiply to Solve Equations with Fractions?

How to cross multiply and solve algebraic equations including fractions? Examples and questions with their detailed solutions are presented.

It can be used to solve equations. Example 2: Solve the equation \( \dfrac{x}{3} = \dfrac{10}{6} \). 1 - Cross multiply the denominator of one with the numerator of the other obtain the equation. \( 6 \times x = 3 \times 10 \) 2 - Divide both sides by the coefficient of \( x \) which is 6 \( \dfrac{6 \times x}{6} = \dfrac{3 \times 10}{6} \) 3 - Simplify to find x. \( x = 5 \) It can be used to verify if two fractions are equivalent. Example 3: Are the fractions \( \dfrac{4}{3} \) and \( \dfrac{12}{9} \) equivalent? 1 - Cross multiply the denominator of one with numerator of the other to obtain two quantities. \( 4 \times 9 = 36\) and \( 3 \times 12 = 36\) 2 - Compare the two quantities. If they are equal, then the fractions are equivalent which is the case in the above example and we can write. \( \dfrac{4}{3} = \dfrac{12}{9} \) The exercises below with solutions and explanations are all about using cross multiplication. Answer the following questions. -
Solve the equations
a) \( \dfrac{x}{6} = \dfrac{3}{2} \) b) \( \dfrac{1}{3x} = \dfrac{2}{24} \) c) \( \dfrac{3}{2} = \dfrac{12}{4x} \) d) \( \dfrac{4}{6} = \dfrac{x}{9} \) e) \( 2 = \dfrac{x}{14} \) f) \( \dfrac{2}{x+2} = \dfrac{1}{7} \) -
Which of the following pairs of fractions are equivalent (equal)?
a) \( \dfrac{5}{6} \) and \( \dfrac{15}{18} \) b) \( \dfrac{5}{3} \) and \( \dfrac{20}{13} \) c) \( \dfrac{25}{35} \) and \( \dfrac{5}{7} \) d) \( \dfrac{23}{7} \) and \( \dfrac{46}{17} \)
solutions and explanations |

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