Pre-Algebra Examples

$1 + \frac{49}{\frac{4}{1 - \frac{7}{2}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$1 + 49 \frac{1 - \frac{7}{2}}{4}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

$1 + 49 \frac{\frac{2}{2} - \frac{7}{2}}{4}$

Step 1.2.2

Combine the numerators over the common denominator.

$1 + 49 \frac{\frac{2 - 7}{2}}{4}$

Step 1.2.3

Subtract $7$ from $2$ .

$1 + 49 \frac{\frac{- 5}{2}}{4}$

Step 1.2.4

Move the negative in front of the fraction.

$1 + 49 \frac{- \frac{5}{2}}{4}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$1 + 49 (- \frac{5}{2} \cdot \frac{1}{4})$

Step 1.4

Multiply $- \frac{5}{2} \cdot \frac{1}{4}$ .

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Step 1.4.1

Multiply $\frac{1}{4}$ by $\frac{5}{2}$ .

$1 + 49 (- \frac{5}{4 \cdot 2})$

Step 1.4.2

Multiply $4$ by $2$ .

$1 + 49 (- \frac{5}{8})$

Step 1.5

Multiply $49 (- \frac{5}{8})$ .

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Step 1.5.1

Multiply $- 1$ by $49$ .

$1 - 49 (\frac{5}{8})$

Step 1.5.2

Combine $- 49$ and $\frac{5}{8}$ .

$1 + \frac{- 49 \cdot 5}{8}$

Step 1.5.3

Multiply $- 49$ by $5$ .

$1 + \frac{- 245}{8}$

Step 1.6

Move the negative in front of the fraction.

$1 - \frac{245}{8}$

Step 2

Simplify the expression.

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Step 2.1

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

$\frac{8}{8} - \frac{245}{8}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{8 - 245}{8}$

Step 2.3

Subtract $245$ from $8$ .

$\frac{- 237}{8}$

Step 2.4

Move the negative in front of the fraction.

$- \frac{237}{8}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{237}{8}$

Decimal Form:

$- 29.625$

Mixed Number Form:

$- 29 \frac{5}{8}$