Basic Math Examples

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

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.

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

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 $\frac{4}{4}$ .

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{1}{2} - 4 - \frac{8 + 3}{4} \cdot 1 \frac{1}{4}$

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{1}{2} - 4 - \frac{11}{4} \cdot 1 \frac{1}{4}$

Step 2

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

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Step 2.1

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

$\frac{1}{2} - 4 - \frac{11}{4} \cdot (1 + \frac{1}{4})$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{2} - 4 - \frac{11}{4} \cdot (\frac{4}{4} + \frac{1}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{1}{2} - 4 - \frac{11}{4} \cdot \frac{4 + 1}{4}$

Step 2.2.3

Add $4$ and $1$ .

$\frac{1}{2} - 4 - \frac{11}{4} \cdot \frac{5}{4}$

Step 3

Multiply $- \frac{11}{4} \cdot \frac{5}{4}$ .

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Step 3.1

Multiply $\frac{5}{4}$ by $\frac{11}{4}$ .

$\frac{1}{2} - 4 - \frac{5 \cdot 11}{4 \cdot 4}$

Step 3.2

Multiply $5$ by $11$ .

$\frac{1}{2} - 4 - \frac{55}{4 \cdot 4}$

Step 3.3

Multiply $4$ by $4$ .

$\frac{1}{2} - 4 - \frac{55}{16}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{8}{8}$ .

$\frac{1}{2} \cdot \frac{8}{8} - 4 - \frac{55}{16}$

Step 4.2

Multiply $\frac{1}{2}$ by $\frac{8}{8}$ .

$\frac{8}{2 \cdot 8} - 4 - \frac{55}{16}$

Step 4.3

Write $- 4$ as a fraction with denominator $1$ .

$\frac{8}{2 \cdot 8} + \frac{- 4}{1} - \frac{55}{16}$

Step 4.4

Multiply $\frac{- 4}{1}$ by $\frac{16}{16}$ .

$\frac{8}{2 \cdot 8} + \frac{- 4}{1} \cdot \frac{16}{16} - \frac{55}{16}$

Step 4.5

Multiply $\frac{- 4}{1}$ by $\frac{16}{16}$ .

$\frac{8}{2 \cdot 8} + \frac{- 4 \cdot 16}{16} - \frac{55}{16}$

Step 4.6

Multiply $2$ by $8$ .

$\frac{8}{16} + \frac{- 4 \cdot 16}{16} - \frac{55}{16}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 - 4 \cdot 16 - 55}{16}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $- 4$ by $16$ .

$\frac{8 - 64 - 55}{16}$

Step 6.2

Subtract $64$ from $8$ .

$\frac{- 56 - 55}{16}$

Step 6.3

Subtract $55$ from $- 56$ .

$\frac{- 111}{16}$

Step 6.4

Move the negative in front of the fraction.

$- \frac{111}{16}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{111}{16}$

Decimal Form:

$- 6.9375$

Mixed Number Form:

$- 6 \frac{15}{16}$