Basic Math Examples

$- 2 \frac{3}{4} - 1 \frac{5}{6}$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$- (2 + \frac{3}{4}) - 1 \frac{5}{6}$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{3}{4}) - 1 \frac{5}{6}$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{3}{4}) - 1 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 3}{4} - 1 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 3}{4} - 1 \frac{5}{6}$

Step 1.2.4.2

Add $8$ and $3$ .

$- \frac{11}{4} - 1 \frac{5}{6}$

Step 2

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$- \frac{11}{4} - (1 + \frac{5}{6})$

Step 2.2

Add $1$ and $\frac{5}{6}$ .

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Step 2.2.1

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

$- \frac{11}{4} - (\frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine the numerators over the common denominator.

$- \frac{11}{4} - \frac{6 + 5}{6}$

Step 2.2.3

Add $6$ and $5$ .

$- \frac{11}{4} - \frac{11}{6}$

Step 3

To write $- \frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{11}{4} \cdot \frac{3}{3} - \frac{11}{6}$

Step 4

To write $- \frac{11}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{11}{4} \cdot \frac{3}{3} - \frac{11}{6} \cdot \frac{2}{2}$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$- \frac{11 \cdot 3}{4 \cdot 3} - \frac{11}{6} \cdot \frac{2}{2}$

Step 5.2

Multiply $4$ by $3$ .

$- \frac{11 \cdot 3}{12} - \frac{11}{6} \cdot \frac{2}{2}$

Step 5.3

Multiply $\frac{11}{6}$ by $\frac{2}{2}$ .

$- \frac{11 \cdot 3}{12} - \frac{11 \cdot 2}{6 \cdot 2}$

Step 5.4

Multiply $6$ by $2$ .

$- \frac{11 \cdot 3}{12} - \frac{11 \cdot 2}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 11 \cdot 3 - 11 \cdot 2}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 11$ by $3$ .

$\frac{- 33 - 11 \cdot 2}{12}$

Step 7.2

Multiply $- 11$ by $2$ .

$\frac{- 33 - 22}{12}$

Step 7.3

Subtract $22$ from $- 33$ .

$\frac{- 55}{12}$

Step 8

Move the negative in front of the fraction.

$- \frac{55}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{55}{12}$

Decimal Form:

$- 4.58\overline{3}$

Mixed Number Form:

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