Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $20$ and $1$ .

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

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Reorder the factors of $5 \cdot 4$ .

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

Step 2.6

Multiply $4$ by $5$ .

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

Step 2.7

Multiply $4$ by $5$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $4$ .

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

Step 4.2

Multiply $5$ by $5$ .

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

Step 5

Simplify the expression.

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Step 5.1

Add $16$ and $25$ .

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

Step 5.2

Subtract $21$ from $41$ .

$\frac{20}{20}$

Step 5.3

Divide $20$ by $20$ .

$1$