Algebra Examples

$1 \frac{3}{4} - 2 + (- 4 \frac{3}{4})$

Step 1

Remove parentheses.

$1 \frac{3}{4} - 2 - 4 \frac{3}{4}$

Step 2

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$1 + \frac{3}{4} - 2 - 4 \frac{3}{4}$

Step 2.2

Add $1$ and $\frac{3}{4}$ .

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Step 2.2.1

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

$\frac{4}{4} + \frac{3}{4} - 2 - 4 \frac{3}{4}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} - 2 - 4 \frac{3}{4}$

Step 2.2.3

Add $4$ and $3$ .

$\frac{7}{4} - 2 - 4 \frac{3}{4}$

Step 3

Convert $4 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{7}{4} - 2 - (4 + \frac{3}{4})$

Step 3.2

Add $4$ and $\frac{3}{4}$ .

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Step 3.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7}{4} - 2 - (4 \cdot \frac{4}{4} + \frac{3}{4})$

Step 3.2.2

Combine $4$ and $\frac{4}{4}$ .

$\frac{7}{4} - 2 - (\frac{4 \cdot 4}{4} + \frac{3}{4})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{7}{4} - 2 - \frac{4 \cdot 4 + 3}{4}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $4$ by $4$ .

$\frac{7}{4} - 2 - \frac{16 + 3}{4}$

Step 3.2.4.2

Add $16$ and $3$ .

$\frac{7}{4} - 2 - \frac{19}{4}$

Step 4

Combine the numerators over the common denominator.

$- 2 + \frac{7 - 19}{4}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $19$ from $7$ .

$- 2 + \frac{- 12}{4}$

Step 5.2

Divide $- 12$ by $4$ .

$- 2 - 3$

Step 5.3

Subtract $3$ from $- 2$ .

$- 5$