Solve for x: 5 1/4 + x = 7 2/5

Let the unknown number be $x$.

$$5 \frac{1}{4} + x = 7 \frac{2}{5}$$

$$5 \frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}$$ $$7 \frac{2}{5} = \frac{(7 \times 5) + 2}{5} = \frac{35 + 2}{5} = \frac{37}{5}$$

$$\frac{21}{4} + x = \frac{37}{5}$$

To find $x$, subtract $\frac{21}{4}$ from $\frac{37}{5}$:

$$x = \frac{37}{5} - \frac{21}{4}$$

The least common multiple of 5 and 4 is 20.
Convert both fractions to have a denominator of 20:

$$\frac{37}{5} = \frac{37 \times 4}{5 \times 4} = \frac{148}{20}$$ $$\frac{21}{4} = \frac{21 \times 5}{4 \times 5} = \frac{105}{20}$$

$$x = \frac{148}{20} - \frac{105}{20}$$ $$x = \frac{148 - 105}{20}$$ $$x = \frac{43}{20}$$

Divide 43 by 20:

$$43 \div 20 = 2 \text{ with a remainder of } 3$$

So, $x = 2 \frac{3}{20}$.

The number that should be added is $2 \frac{3}{20}$.