Find the Exact Value 4/5+5/4-1 1/20

$\frac{4}{5} + \frac{5}{4} - 1 \frac{1}{20}$

Convert $1 \frac{1}{20}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{4}{5} + \frac{5}{4} - (1 + \frac{1}{20})$

Add $1$ and $\frac{1}{20}$ .

Write $1$ as a fraction with a common denominator.

$\frac{4}{5} + \frac{5}{4} - (\frac{20}{20} + \frac{1}{20})$

Combine the numerators over the common denominator.

$\frac{4}{5} + \frac{5}{4} - \frac{20 + 1}{20}$

Add $20$ and $1$ .

$\frac{4}{5} + \frac{5}{4} - \frac{21}{20}$

Find the common denominator.

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$\frac{4}{5} \cdot \frac{4}{4} + \frac{5}{4} - \frac{21}{20}$

Multiply $\frac{4}{5}$ by $\frac{4}{4}$ .

$\frac{4 \cdot 4}{5 \cdot 4} + \frac{5}{4} - \frac{21}{20}$

Multiply $\frac{5}{4}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 4}{5 \cdot 4} + \frac{5}{4} \cdot \frac{5}{5} - \frac{21}{20}$

Multiply $\frac{5}{4}$ by $\frac{5}{5}$ .

$\frac{4 \cdot 4}{5 \cdot 4} + \frac{5 \cdot 5}{4 \cdot 5} - \frac{21}{20}$

Reorder the factors of $5 \cdot 4$ .

$\frac{4 \cdot 4}{4 \cdot 5} + \frac{5 \cdot 5}{4 \cdot 5} - \frac{21}{20}$

Multiply $4$ by $5$ .

$\frac{4 \cdot 4}{20} + \frac{5 \cdot 5}{4 \cdot 5} - \frac{21}{20}$

Multiply $4$ by $5$ .

$\frac{4 \cdot 4}{20} + \frac{5 \cdot 5}{20} - \frac{21}{20}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 5 \cdot 5 - 21}{20}$

Simplify each term.

Multiply $4$ by $4$ .

$\frac{16 + 5 \cdot 5 - 21}{20}$

Multiply $5$ by $5$ .

$\frac{16 + 25 - 21}{20}$

Simplify the expression.

Add $16$ and $25$ .

$\frac{41 - 21}{20}$

Subtract $21$ from $41$ .

$\frac{20}{20}$

Divide $20$ by $20$ .

$1$