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(1)/(3)×(2)/(5)+(4)/(5)×(1)/(5)-(1)/(2)×(3)/(5)

13×25+45×15−12×35\frac{1}{3} \times \frac{2}{5}+\frac{4}{5} \times \frac{1}{5}-\frac{1}{2} \times \frac{3}{5}

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Q. 13×25+45×15−12×35\frac{1}{3} \times \frac{2}{5}+\frac{4}{5} \times \frac{1}{5}-\frac{1}{2} \times \frac{3}{5}
  1. Calculate Fraction Products: Calculate the value of (13)×(25)(\frac{1}{3})\times(\frac{2}{5}). To find the product of two fractions, multiply the numerators together and the denominators together. (13)×(25)=(1×23×5)=215(\frac{1}{3})\times(\frac{2}{5}) = (\frac{1\times2}{3\times5}) = \frac{2}{15}
  2. Add and Subtract Fractions: Calculate the value of (45)×(15)(\frac{4}{5})\times(\frac{1}{5}). Similarly, multiply the numerators and the denominators. (45)×(15)=(4×15×5)=425(\frac{4}{5})\times(\frac{1}{5}) = (\frac{4\times1}{5\times5}) = \frac{4}{25}
  3. Add and Subtract Fractions: Calculate the value of (45)×(15)(\frac{4}{5})\times(\frac{1}{5}). Similarly, multiply the numerators and the denominators. (45)×(15)=(4×15×5)=425(\frac{4}{5})\times(\frac{1}{5}) = (\frac{4\times1}{5\times5}) = \frac{4}{25} Calculate the value of (12)×(35)(\frac{1}{2})\times(\frac{3}{5}). Again, multiply the numerators and the denominators. (12)×(35)=(1×32×5)=310(\frac{1}{2})\times(\frac{3}{5}) = (\frac{1\times3}{2\times5}) = \frac{3}{10}
  4. Add and Subtract Fractions: Calculate the value of (45)×(15)(\frac{4}{5})\times(\frac{1}{5}). Similarly, multiply the numerators and the denominators. (45)×(15)=(4×15×5)=425(\frac{4}{5})\times(\frac{1}{5}) = (\frac{4\times1}{5\times5}) = \frac{4}{25} Calculate the value of (12)×(35)(\frac{1}{2})\times(\frac{3}{5}). Again, multiply the numerators and the denominators. (12)×(35)=(1×32×5)=310(\frac{1}{2})\times(\frac{3}{5}) = (\frac{1\times3}{2\times5}) = \frac{3}{10} Add the results from Step 11 and Step 22, then subtract the result from Step 33. Add 215\frac{2}{15} and 425\frac{4}{25}, then subtract 310\frac{3}{10}. To add or subtract fractions, they must have a common denominator. The least common denominator (LCD) for 1515, 2525, and 1010 is 150150. Convert each fraction to an equivalent fraction with a denominator of 150150. 215=(2×1015×10)=20150\frac{2}{15} = (\frac{2\times10}{15\times10}) = \frac{20}{150} 425=(4×625×6)=24150\frac{4}{25} = (\frac{4\times6}{25\times6}) = \frac{24}{150} 310=(3×1510×15)=45150\frac{3}{10} = (\frac{3\times15}{10\times15}) = \frac{45}{150} Now perform the addition and subtraction: (45)×(15)=(4×15×5)=425(\frac{4}{5})\times(\frac{1}{5}) = (\frac{4\times1}{5\times5}) = \frac{4}{25}00

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