(a) Write the following as a single fraction in its simplest form: \( \frac{2}{3} + \frac{5}{7} \) (b) Solve the following equation in k: \( 4k - 7 = 41 \) - Junior Cycle Mathematics - Question 10 - 2022

To combine ( \frac{2}{3} ) and ( \frac{5}{7} ), we first find a common denominator. The least common multiple of 3 and 7 is 21.

Convert each fraction:

( \frac{2}{3} = \frac{2 \cdot 7}{3 \cdot 7} = \frac{14}{21} )

( \frac{5}{7} = \frac{5 \cdot 3}{7 \cdot 3} = \frac{15}{21} )

Now, add the two fractions:

( \frac{14}{21} + \frac{15}{21} = \frac{14 + 15}{21} = \frac{29}{21} )

Thus, the single fraction in its simplest form is ( \frac{29}{21} ).