Use the following rational numbers to frame an
example of distributive property of multiplication over
addition for rati

1 thought on “Use the following rational numbers to frame an<br />example of distributive property of multiplication over<br />addition for rati”

1. SOLUTION

   TO DETERMINE

   Using the following rational numbers to frame an example of distributive property of multiplication over addition for rational numbers

   [tex] \displaystyle \sf{ \frac{1}{4} \: \: , \: \: \frac{2}{3} \: \: , \: \: – \frac{4}{7} }[/tex]

   CONCEPT TO BE IMPLEMENTED

   For three rational numbers a , b , c distributive property states that

   [tex] \sf{a \times (b + c) = (a \times b) + (a \times c )\: }[/tex]

   EVALUATION

   We wish to prove

   [tex]\displaystyle \sf{ \frac{1}{4} \times \bigg(- \frac{4}{7} + \frac{2}{3} \bigg) = \bigg( \frac{1}{4} \times – \frac{4}{7} \bigg) + \bigg( \frac{1}{4} \times \frac{2}{3} \bigg) }[/tex]

   LHS

   [tex]\displaystyle \sf{ = \frac{1}{4} \times \bigg(- \frac{4}{7} + \frac{2}{3} \bigg) }[/tex]

   [tex]\displaystyle \sf{ = \frac{1}{4} \times \bigg( \frac{ – 12 + 14}{21} \bigg) }[/tex]

   [tex]\displaystyle \sf{ = \frac{1}{4} \times \frac{ 2}{21} }[/tex]

   [tex]\displaystyle \sf{ = \frac{1}{42} }[/tex]

   RHS

   [tex]\displaystyle \sf{ = \bigg( \frac{1}{4} \times – \frac{4}{7} \bigg) + \bigg( \frac{1}{4} \times \frac{2}{3} \bigg) }[/tex]

   [tex]\displaystyle \sf{ = – \frac{1}{7} + \frac{1}{6} }[/tex]

   [tex]\displaystyle \sf{ = \frac{ – 6 + 7}{42} }[/tex]

   [tex]\displaystyle \sf{ = \frac{ 1}{42} }[/tex]

   Hence LHS = RHS

   Hence proved

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