Question

Use the following rational numbers to frame an
example of distributive property of multiplication over
addition for rational numbers
(11/4) (213) and (-4/7)​

Answer 1

SOLUTION

TO DETERMINE

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

$\displaystyle \sf{ \frac{1}{4} \: \: , \: \: \frac{2}{3} \: \: , \: \: - \frac{4}{7} }$

CONCEPT TO BE IMPLEMENTED

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

$\sf{a \times (b + c) = (a \times b) + (a \times c )\: }$

EVALUATION

We wish to prove

$\displaystyle \sf{ \frac{1}{4} \times \bigg(- \frac{4}{7} + \frac{2}{3} \bigg) = \bigg( \frac{1}{4} \times - \frac{4}{7} \bigg) + \bigg( \frac{1}{4} \times \frac{2}{3} \bigg) }$

LHS

$\displaystyle \sf{ = \frac{1}{4} \times \bigg(- \frac{4}{7} + \frac{2}{3} \bigg) }$

$\displaystyle \sf{ = \frac{1}{4} \times \bigg( \frac{ - 12 + 14}{21} \bigg) }$

$\displaystyle \sf{ = \frac{1}{4} \times \frac{ 2}{21} }$

$\displaystyle \sf{ = \frac{1}{42} }$

RHS

$\displaystyle \sf{ = \bigg( \frac{1}{4} \times - \frac{4}{7} \bigg) + \bigg( \frac{1}{4} \times \frac{2}{3} \bigg) }$

$\displaystyle \sf{ = - \frac{1}{7} + \frac{1}{6} }$

$\displaystyle \sf{ = \frac{ - 6 + 7}{42} }$

$\displaystyle \sf{ = \frac{ 1}{42} }$

Hence LHS = RHS

Hence proved

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