Basic Math Examples

$\frac{8}{49} + \frac{7}{24} \div (- \frac{2}{14})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{8}{49} + \frac{7}{24} (- \frac{14}{2})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Move the leading negative in $- \frac{14}{2}$ into the numerator.

$\frac{8}{49} + \frac{7}{24} \cdot \frac{- 14}{2}$

Step 1.2.2

Factor $2$ out of $24$ .

$\frac{8}{49} + \frac{7}{2 (12)} \cdot \frac{- 14}{2}$

Step 1.2.3

Factor $2$ out of $- 14$ .

$\frac{8}{49} + \frac{7}{2 \cdot 12} \cdot \frac{2 \cdot - 7}{2}$

Step 1.2.4

Cancel the common factor.

$\frac{8}{49} + \frac{7}{2 \cdot 12} \cdot \frac{2 \cdot - 7}{2}$

Step 1.2.5

Rewrite the expression.

$\frac{8}{49} + \frac{7}{12} \cdot \frac{- 7}{2}$

Step 1.3

Multiply $\frac{7}{12}$ by $\frac{- 7}{2}$ .

$\frac{8}{49} + \frac{7 \cdot - 7}{12 \cdot 2}$

Step 1.4

Multiply $7$ by $- 7$ .

$\frac{8}{49} + \frac{- 49}{12 \cdot 2}$

Step 1.5

Multiply $12$ by $2$ .

$\frac{8}{49} + \frac{- 49}{24}$

Step 1.6

Move the negative in front of the fraction.

$\frac{8}{49} - \frac{49}{24}$

Step 2

To write $\frac{8}{49}$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{8}{49} \cdot \frac{24}{24} - \frac{49}{24}$

Step 3

To write $- \frac{49}{24}$ as a fraction with a common denominator, multiply by $\frac{49}{49}$ .

$\frac{8}{49} \cdot \frac{24}{24} - \frac{49}{24} \cdot \frac{49}{49}$

Step 4

Write each expression with a common denominator of $1176$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{8}{49}$ by $\frac{24}{24}$ .

$\frac{8 \cdot 24}{49 \cdot 24} - \frac{49}{24} \cdot \frac{49}{49}$

Step 4.2

Multiply $49$ by $24$ .

$\frac{8 \cdot 24}{1176} - \frac{49}{24} \cdot \frac{49}{49}$

Step 4.3

Multiply $\frac{49}{24}$ by $\frac{49}{49}$ .

$\frac{8 \cdot 24}{1176} - \frac{49 \cdot 49}{24 \cdot 49}$

Step 4.4

Multiply $24$ by $49$ .

$\frac{8 \cdot 24}{1176} - \frac{49 \cdot 49}{1176}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 \cdot 24 - 49 \cdot 49}{1176}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $24$ .

$\frac{192 - 49 \cdot 49}{1176}$

Step 6.2

Multiply $- 49$ by $49$ .

$\frac{192 - 2401}{1176}$

Step 6.3

Subtract $2401$ from $192$ .

$\frac{- 2209}{1176}$

Step 7

Move the negative in front of the fraction.

$- \frac{2209}{1176}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{2209}{1176}$

Decimal Form:

$- 1.87840136 \dots$

Mixed Number Form:

$- 1 \frac{1033}{1176}$