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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