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Using distributivity, find (i) {(7)/(5)×((-3)/(12))}+{(7)/(5)×(5)/(12)}

99. Using distributivity, find\newline(i) {75×(−312)}+{75×512} \left\{\frac{7}{5} \times\left(\frac{-3}{12}\right)\right\}+\left\{\frac{7}{5} \times \frac{5}{12}\right\}

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Q. 99. Using distributivity, find\newline(i) {75×(−312)}+{75×512} \left\{\frac{7}{5} \times\left(\frac{-3}{12}\right)\right\}+\left\{\frac{7}{5} \times \frac{5}{12}\right\}
  1. Apply Distributive Property: First, apply the distributive property to combine the terms with a common factor of (75)(\frac{7}{5}).(75)×(−312)+(75)×(512)=(75)×((−312)+(512))(\frac{7}{5})\times(-\frac{3}{12}) + (\frac{7}{5})\times(\frac{5}{12}) = (\frac{7}{5})\times((-\frac{3}{12}) + (\frac{5}{12}))
  2. Add Fractions: Now, add the fractions inside the parentheses.\newline(−312)+(512)=(212)(-\frac{3}{12}) + (\frac{5}{12}) = (\frac{2}{12})
  3. Simplify Fraction: Simplify the fraction (212)(\frac{2}{12}) to its lowest terms.\newline(212)=(16)(\frac{2}{12}) = (\frac{1}{6})
  4. Multiply by Common Factor: Multiply the simplified fraction by the common factor (75)(\frac{7}{5}).(75)×(16)=(7×15×6)(\frac{7}{5})\times(\frac{1}{6}) = (\frac{7\times1}{5\times6})
  5. Perform Final Multiplication: Perform the multiplication to get the final answer.\newline(7×1)/(5×6)=7/30(7\times1)/(5\times6) = 7/30

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