Questions: Simplify: 1/2 + 2/3 * 5/12.

Solution Steps

First, simplify the multiplication part of the expression:

\[ \frac{2}{3} \cdot \frac{5}{12} = \frac{2 \times 5}{3 \times 12} = \frac{10}{36} \]

Next, simplify the fraction \(\frac{10}{36}\) by finding the greatest common divisor (GCD) of 10 and 36, which is 2:

\[ \frac{10}{36} = \frac{10 \div 2}{36 \div 2} = \frac{5}{18} \]

Now, add \(\frac{1}{2}\) and \(\frac{5}{18}\). To do this, find a common denominator. The least common multiple (LCM) of 2 and 18 is 18. Convert \(\frac{1}{2}\) to a fraction with a denominator of 18:

\[ \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \]

Now add the fractions:

\[ \frac{9}{18} + \frac{5}{18} = \frac{9 + 5}{18} = \frac{14}{18} \]

Simplify \(\frac{14}{18}\) by finding the GCD of 14 and 18, which is 2:

\[ \frac{14}{18} = \frac{14 \div 2}{18 \div 2} = \frac{7}{9} \]

Final Answer