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Question

Use the distributivity of multiplication of rational numbers over their addition to simplify:

(i) 35×(3524+101)

(ii)54×(85+165)

(iii)27×(716214)

(iv)34×(8940)

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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=24=6

(iii)27×(716214)=27×71627×214=2×77×162×217×4=1×11×81×31×2=1832=1128=118

(iv)34×(8940)=34×8934×401=3×84×93×404×1=1×21×33×101×1=23301=2903=883


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