Add the fractions \(\dfrac{3}{8}\) and \(\dfrac{2}{3}\).
\(\dfrac{25}{24}=1\dfrac{1}{24}\)
Step 1: Make the denominators the same.
We need the LCM of 8 and 3.
Multiples of 8: 8, 16, 24, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
So, LCM = \(24\).
Step 2: Convert each fraction to denominator 24.
For \(\dfrac{3}{8}\): multiply top and bottom by \(3\).
\(\dfrac{3}{8} = \dfrac{3\times 3}{8\times 3} = \dfrac{9}{24}\).
For \(\dfrac{2}{3}\): multiply top and bottom by \(8\).
\(\dfrac{2}{3} = \dfrac{2\times 8}{3\times 8} = \dfrac{16}{24}\).
Step 3: Add the fractions.
\(\dfrac{9}{24} + \dfrac{16}{24} = \dfrac{9+16}{24} = \dfrac{25}{24}\).
Step 4: Write as a mixed number.
\(\dfrac{25}{24}\) means 25 divided by 24 = 1 remainder 1.
So, \(\dfrac{25}{24} = 1\dfrac{1}{24}\).