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Evaluate the expression.\newline12+14×25\frac{1}{2} + \frac{1}{4} \times \frac{2}{5}\newlineWrite your answer as a fraction or as a whole or mixed number.\newline______

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Q. Evaluate the expression.\newline12+14×25\frac{1}{2} + \frac{1}{4} \times \frac{2}{5}\newlineWrite your answer as a fraction or as a whole or mixed number.\newline______
  1. Perform Multiplication: First, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). There are no parentheses or exponents in this expression, so we start with multiplication.\newlineWe need to multiply 14\frac{1}{4} by 25\frac{2}{5}.
  2. Simplify Result: To multiply fractions, we multiply the numerators together and the denominators together.\newline14×25=1×24×5=220\frac{1}{4} \times \frac{2}{5} = \frac{1\times2}{4\times5} = \frac{2}{20}
  3. Add Fractions: Now we simplify the fraction 220\frac{2}{20} by dividing both the numerator and the denominator by their greatest common divisor, which is 22. \newline220=(2/2)(20/2)=110\frac{2}{20} = \frac{(2/2)}{(20/2)} = \frac{1}{10}
  4. Convert to Common Denominator: Next, we add the simplified fraction to the other fraction in the expression. 12+110\frac{1}{2} + \frac{1}{10}
  5. Add Fractions: To add fractions, they must have a common denominator. The least common denominator (LCD) for 22 and 1010 is 1010. We convert 12\frac{1}{2} to a fraction with a denominator of 1010 by multiplying both the numerator and the denominator by 55. 12=(1×5)(2×5)=510\frac{1}{2} = \frac{(1\times5)}{(2\times5)} = \frac{5}{10}
  6. Simplify Result: Now we can add the two fractions with the common denominator.\newline510+110=(5+1)10=610\frac{5}{10} + \frac{1}{10} = \frac{(5+1)}{10} = \frac{6}{10}
  7. Simplify Result: Now we can add the two fractions with the common denominator.\newline510+110=(5+1)10=610\frac{5}{10} + \frac{1}{10} = \frac{(5+1)}{10} = \frac{6}{10}We simplify the fraction 610\frac{6}{10} by dividing both the numerator and the denominator by their greatest common divisor, which is 22.\newline610=(6/2)(10/2)=35\frac{6}{10} = \frac{(6/2)}{(10/2)} = \frac{3}{5}