Finite Math Examples

$\frac{3}{4} - (- \frac{7}{3} - \frac{1}{4})$

Step 1

Simplify each term.

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Step 1.1

To write $- \frac{7}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} - (- \frac{7}{3} \cdot \frac{4}{4} - \frac{1}{4})$

Step 1.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{4} - (- \frac{7}{3} \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{3}{3})$

Step 1.3

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

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Step 1.3.1

Multiply $\frac{7}{3}$ by $\frac{4}{4}$ .

$\frac{3}{4} - (- \frac{7 \cdot 4}{3 \cdot 4} - \frac{1}{4} \cdot \frac{3}{3})$

Step 1.3.2

Multiply $3$ by $4$ .

$\frac{3}{4} - (- \frac{7 \cdot 4}{12} - \frac{1}{4} \cdot \frac{3}{3})$

Step 1.3.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{3}{4} - (- \frac{7 \cdot 4}{12} - \frac{3}{4 \cdot 3})$

Step 1.3.4

Multiply $4$ by $3$ .

$\frac{3}{4} - (- \frac{7 \cdot 4}{12} - \frac{3}{12})$

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 7$ by $4$ .

$\frac{3}{4} - \frac{- 28 - 3}{12}$

Step 1.5.2

Subtract $3$ from $- 28$ .

$\frac{3}{4} - \frac{- 31}{12}$

Step 1.6

Move the negative in front of the fraction.

$\frac{3}{4} - - \frac{31}{12}$

Step 1.7

Multiply $- - \frac{31}{12}$ .

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Step 1.7.1

Multiply $- 1$ by $- 1$ .

$\frac{3}{4} + 1 (\frac{31}{12})$

Step 1.7.2

Multiply $\frac{31}{12}$ by $1$ .

$\frac{3}{4} + \frac{31}{12}$

Step 2

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

$\frac{3}{4} \cdot \frac{3}{3} + \frac{31}{12}$

Step 3

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

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Step 3.1

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

$\frac{3 \cdot 3}{4 \cdot 3} + \frac{31}{12}$

Step 3.2

Multiply $4$ by $3$ .

$\frac{3 \cdot 3}{12} + \frac{31}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 31}{12}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 + 31}{12}$

Step 5.2

Add $9$ and $31$ .

$\frac{40}{12}$

Step 6

Cancel the common factor of $40$ and $12$ .

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Step 6.1

Factor $4$ out of $40$ .

$\frac{4 (10)}{12}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $12$ .

$\frac{4 \cdot 10}{4 \cdot 3}$

Step 6.2.2

Cancel the common factor.

$\frac{4 \cdot 10}{4 \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{10}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$