Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $4$ and $3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $4$ .

$- \frac{7}{4} - \frac{12 + 3}{4}$

Step 2.2.4.2

Add $12$ and $3$ .

$- \frac{7}{4} - \frac{15}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 7 - 15}{4}$

Step 4

Subtract $15$ from $- 7$ .

$\frac{- 22}{4}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $- 22$ and $4$ .

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Step 5.1.1

Factor $2$ out of $- 22$ .

$\frac{2 (- 11)}{4}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot - 11}{2 \cdot 2}$

Step 5.1.2.2

Cancel the common factor.

$\frac{2 \cdot - 11}{2 \cdot 2}$

Step 5.1.2.3

Rewrite the expression.

$\frac{- 11}{2}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{11}{2}$