Finite Math Examples

$\frac{8}{4} \cdot \frac{5}{3} \cdot \frac{4}{8} + \frac{2}{6} \div \frac{7}{4}$

Step 1

Simplify each term.

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Step 1.1

Divide $8$ by $4$ .

$2 \cdot \frac{5}{3} \cdot \frac{4}{8} + \frac{2}{6} \div \frac{7}{4}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $2 \cdot \frac{5}{3}$ .

$2 (\frac{5}{3}) \cdot \frac{4}{8} + \frac{2}{6} \div \frac{7}{4}$

Step 1.2.2

Factor $2$ out of $8$ .

$2 (\frac{5}{3}) \cdot \frac{4}{2 (4)} + \frac{2}{6} \div \frac{7}{4}$

Step 1.2.3

Cancel the common factor.

$2 (\frac{5}{3}) \cdot \frac{4}{2 \cdot 4} + \frac{2}{6} \div \frac{7}{4}$

Step 1.2.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{4}{4} + \frac{2}{6} \div \frac{7}{4}$

Step 1.3

Multiply $\frac{5}{3}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 4}{3 \cdot 4} + \frac{2}{6} \div \frac{7}{4}$

Step 1.4

Multiply $5$ by $4$ .

$\frac{20}{3 \cdot 4} + \frac{2}{6} \div \frac{7}{4}$

Step 1.5

Multiply $3$ by $4$ .

$\frac{20}{12} + \frac{2}{6} \div \frac{7}{4}$

Step 1.6

Cancel the common factor of $20$ and $12$ .

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Step 1.6.1

Factor $4$ out of $20$ .

$\frac{4 (5)}{12} + \frac{2}{6} \div \frac{7}{4}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $4$ out of $12$ .

$\frac{4 \cdot 5}{4 \cdot 3} + \frac{2}{6} \div \frac{7}{4}$

Step 1.6.2.2

Cancel the common factor.

$\frac{4 \cdot 5}{4 \cdot 3} + \frac{2}{6} \div \frac{7}{4}$

Step 1.6.2.3

Rewrite the expression.

$\frac{5}{3} + \frac{2}{6} \div \frac{7}{4}$

Step 1.7

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{3} + \frac{2}{6} \cdot \frac{4}{7}$

Step 1.8

Cancel the common factor of $2$ .

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Step 1.8.1

Factor $2$ out of $6$ .

$\frac{5}{3} + \frac{2}{2 (3)} \cdot \frac{4}{7}$

Step 1.8.2

Factor $2$ out of $4$ .

$\frac{5}{3} + \frac{2}{2 \cdot 3} \cdot \frac{2 \cdot 2}{7}$

Step 1.8.3

Cancel the common factor.

$\frac{5}{3} + \frac{2}{2 \cdot 3} \cdot \frac{2 \cdot 2}{7}$

Step 1.8.4

Rewrite the expression.

$\frac{5}{3} + \frac{2}{3} \cdot \frac{2}{7}$

Step 1.9

Multiply $\frac{2}{3}$ by $\frac{2}{7}$ .

$\frac{5}{3} + \frac{2 \cdot 2}{3 \cdot 7}$

Step 1.10

Multiply $2$ by $2$ .

$\frac{5}{3} + \frac{4}{3 \cdot 7}$

Step 1.11

Multiply $3$ by $7$ .

$\frac{5}{3} + \frac{4}{21}$

Step 2

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5}{3} \cdot \frac{7}{7} + \frac{4}{21}$

Step 3

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5}{3}$ by $\frac{7}{7}$ .

$\frac{5 \cdot 7}{3 \cdot 7} + \frac{4}{21}$

Step 3.2

Multiply $3$ by $7$ .

$\frac{5 \cdot 7}{21} + \frac{4}{21}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 7 + 4}{21}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $7$ .

$\frac{35 + 4}{21}$

Step 5.2

Add $35$ and $4$ .

$\frac{39}{21}$

Step 6

Cancel the common factor of $39$ and $21$ .

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Step 6.1

Factor $3$ out of $39$ .

$\frac{3 (13)}{21}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $21$ .

$\frac{3 \cdot 13}{3 \cdot 7}$

Step 6.2.2

Cancel the common factor.

$\frac{3 \cdot 13}{3 \cdot 7}$

Step 6.2.3

Rewrite the expression.

$\frac{13}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{7}$

Decimal Form:

$1.\overline{857142}$

Mixed Number Form:

$1 \frac{6}{7}$