Simplify the following using the distributive property: 79(67−34)\dfrac{7}{9}\left(\dfrac{6}{7} - \dfrac{3}{4}\right)97(76−43).
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Given, 79(67−34)\dfrac{7}{9}\left(\dfrac{6}{7} - \dfrac{3}{4}\right)97(76−43)
Using the distributive property : a(b - c) = ab - ac
⇒79(67−34)⇒79×67−79×34⇒13×21−73×14⇒23−712⇒812−712[L.C.M. of 3 and 12 is 12]⇒112.\Rightarrow \dfrac{7}{9}\left(\dfrac{6}{7} - \dfrac{3}{4}\right) \\[1em] \Rightarrow \dfrac{7}{9} \times \dfrac{6}{7} - \dfrac{7}{9} \times \dfrac{3}{4} \\[1em] \Rightarrow \dfrac{1}{3} \times \dfrac{2}{1} - \dfrac{7}{3} \times \dfrac{1}{4} \\[1em] \Rightarrow \dfrac{2}{3} - \dfrac{7}{12} \\[1em] \Rightarrow \dfrac{8}{12} - \dfrac{7}{12} \quad \text{[L.C.M. of 3 and 12 is 12]} \\[1em] \Rightarrow \dfrac{1}{12}.⇒97(76−43)⇒97×76−97×43⇒31×12−37×41⇒32−127⇒128−127[L.C.M. of 3 and 12 is 12]⇒121.
Hence, 79(67−34)=112\dfrac{7}{9}\left(\dfrac{6}{7} - \dfrac{3}{4}\right) = \dfrac{1}{12}97(76−43)=121.
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