Question

# Use the distributivity of multiplication of rational numbers over their addition to simplify: (i) 35×(3524+101) (ii)−54×(85+165) (iii)27×(716−214) (iv)34×(89−40)

Solution

## (i) 35×(3524+101)=35×3524+35×101=3×355×24+3×105×1=1×71×8+3×21×1=78+6=78+481=7+488=558 (ii)−54×(85+165)=−54×85+−54×165=−5×84×5+−5×164×5=−1×21×1+−1×41×1=−2−4=−6 (iii)27×(716−214)=27×716−27×214=2×77×16−2×217×4=1×11×8−1×31×2=18−32=1−128=−118 (iv)34×(89−40)=34×89−34×401=3×84×9−3×404×1=1×21×3−3×101×1=23−301=2−903=−883MathematicsRD SharmaStandard VIII

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