Solve: (2/3 × 1/4) + (1/6 × 5/2) Fraction Expression

To solve the expression $\frac{2}{3}\times\frac{1}{4}+\frac{1}{6}\times\frac{5}{2}$, we need to follow the order of operations (also known as BODMAS/BIDMAS: Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction). Multiplication and division should be handled from left to right before addition or subtraction.

First, we perform the multiplication:

• $\frac{2}{3} \times \frac{1}{4}$: To multiply fractions, multiply the numerators and multiply the denominators.
  Numerator: $2 \times 1 = 2$
  Denominator: $3 \times 4 = 12$
  Thus, $\frac{2}{3} \times \frac{1}{4} = \frac{2}{12}$.
• Simplify $\frac{2}{12}$: The greatest common divisor (GCD) of 2 and 12 is 2.
  So, divide both the numerator and the denominator by 2:
  $\frac{2\div2}{12\div2} = \frac{1}{6}$.
• $\frac{1}{6} \times \frac{5}{2}$: Again, multiply the numerators and multiply the denominators.
  Numerator: $1 \times 5 = 5$
  Denominator: $6 \times 2 = 12$
  Thus, $\frac{1}{6} \times \frac{5}{2} = \frac{5}{12}$.

Now, we have the expression $\frac{1}{6} + \frac{5}{12}$.

To add these fractions, find a common denominator. The least common multiple of 6 and 12 is 12.

• Convert $\frac{1}{6}$ to have a denominator of 12.
  Multiply the numerator and denominator by 2:
  $\frac{1\times2}{6\times2} = \frac{2}{12}$.
• Now, add $\frac{2}{12} + \frac{5}{12}$.
  Add the numerators and keep the common denominator:
  $\frac{2+5}{12} = \frac{7}{12}$.

Therefore, the answer is $\frac{7}{12}$, which matches the given correct answer.