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Question

Simplify : 324÷( 3-14 ) +( 25÷115)


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Solution

Step 1 : Convert the mixed fractions into improper fractions

324 =(3×4)+24 =12+24 =144

115 =(1×5)+15 = 5+15 = 65

324÷( 3-14 ) +( 25÷115) =144÷( 3-14 )+( 25÷65)

Step 2 : Simplifying the first bracket

( 3-14 ) ,3 we can write it as 31

3-14 = 31 -14

Step 3: The bottom numbers are different, To make it same take the L.C.M of 1 and 4

L.C.M of 1and 4 is 4

Step 4: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

31=3×41×4 =124

14=1×14×1 =14

Step 5: Subtract the numerators and put the answer over the denominator

124-14 =114

Step 6 : Simplifying the second bracket

( 25÷115) =( 25÷65)

Step 7: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

25×56 =2×55×6 =1030

324÷( 3-14 ) +( 25÷115) =144÷114+1030

Step 8 : First do division

144÷114

Step 9: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

144×411=14×44×11 =5644

144÷114+1030 =5644+1030

Step 10: The bottom numbers are different, To make it same take the L.C.M of 44 and 30

L.C.M of 44and 30 is 660

Step 11: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

5644=56×1544×15 =840660

1030=10×2230×22 =220660

Step 12:Add the numerators and put the answer over the denominator

840660+220660 =1060660

Step13: Simplify the fraction

Divide numerator 1060 by the denominator 660

1060660=1400660

Here ,400660=400÷20660÷20=2033

1400660 =12033

Hence, 324÷( 3-14 ) +( 25÷115) =12033


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