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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Find the quotient:
(i) 23÷310\dfrac{2}{3} \div \dfrac{3}{10}32÷103
(ii) 711÷58\dfrac{7}{11} \div \dfrac{5}{8}117÷85
(iii) −47÷514-\dfrac{4}{7} \div \dfrac{5}{14}−74÷145
Show that: (12+34)×83=12×83+34×83\left(\dfrac{1}{2} + \dfrac{3}{4}\right) \times \dfrac{8}{3} = \dfrac{1}{2} \times \dfrac{8}{3} + \dfrac{3}{4} \times \dfrac{8}{3}(21+43)×38=21×38+43×38.
Find the rational number xxx such that: 56(x+35)=56x+12\dfrac{5}{6}\left(x + \dfrac{3}{5}\right) = \dfrac{5}{6}x + \dfrac{1}{2}65(x+53)=65x+21.
Try and represent 85\dfrac{8}{5}58 and −74-\dfrac{7}{4}−47 on a number line.
