Basic Math Examples

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot 3 \frac{3}{8}$

Step 1

Convert $3 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot (3 + \frac{3}{8})$

Step 1.2

Add $3$ and $\frac{3}{8}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot (3 \cdot \frac{8}{8} + \frac{3}{8})$

Step 1.2.2

Combine $3$ and $\frac{8}{8}$ .

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot (\frac{3 \cdot 8}{8} + \frac{3}{8})$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{3 \cdot 8 + 3}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $8$ .

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{24 + 3}{8}$

Step 1.2.4.2

Add $24$ and $3$ .

$(\frac{5}{7} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 2

To write $\frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$(\frac{5}{7} \cdot \frac{9}{9} + \frac{5}{9}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 3

To write $\frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(\frac{5}{7} \cdot \frac{9}{9} + \frac{5}{9} \cdot \frac{7}{7}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 4

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{7}$ by $\frac{9}{9}$ .

$(\frac{5 \cdot 9}{7 \cdot 9} + \frac{5}{9} \cdot \frac{7}{7}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 4.2

Multiply $7$ by $9$ .

$(\frac{5 \cdot 9}{63} + \frac{5}{9} \cdot \frac{7}{7}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 4.3

Multiply $\frac{5}{9}$ by $\frac{7}{7}$ .

$(\frac{5 \cdot 9}{63} + \frac{5 \cdot 7}{9 \cdot 7}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 4.4

Multiply $9$ by $7$ .

$(\frac{5 \cdot 9}{63} + \frac{5 \cdot 7}{63}) \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 \cdot 9 + 5 \cdot 7}{63} \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $9$ .

$\frac{45 + 5 \cdot 7}{63} \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 6.2

Multiply $5$ by $7$ .

$\frac{45 + 35}{63} \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 6.3

Add $45$ and $35$ .

$\frac{80}{63} \div \frac{5}{63} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7

Simplify each term.

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Step 7.1

To divide by a fraction, multiply by its reciprocal.

$\frac{80}{63} \cdot \frac{63}{5} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.2

Cancel the common factor of $5$ .

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Step 7.2.1

Factor $5$ out of $80$ .

$\frac{5 (16)}{63} \cdot \frac{63}{5} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.2.2

Cancel the common factor.

$\frac{5 \cdot 16}{63} \cdot \frac{63}{5} + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.2.3

Rewrite the expression.

$\frac{16}{63} \cdot 63 + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.3

Cancel the common factor of $63$ .

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Step 7.3.1

Cancel the common factor.

$\frac{16}{63} \cdot 63 + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.3.2

Rewrite the expression.

$16 + (\frac{7}{9} - \frac{2}{3}) \cdot \frac{27}{8}$

Step 7.4

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$16 + (\frac{7}{9} - \frac{2}{3} \cdot \frac{3}{3}) \cdot \frac{27}{8}$

Step 7.5

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.5.1

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

$16 + (\frac{7}{9} - \frac{2 \cdot 3}{3 \cdot 3}) \cdot \frac{27}{8}$

Step 7.5.2

Multiply $3$ by $3$ .

$16 + (\frac{7}{9} - \frac{2 \cdot 3}{9}) \cdot \frac{27}{8}$

Step 7.6

Combine the numerators over the common denominator.

$16 + \frac{7 - 2 \cdot 3}{9} \cdot \frac{27}{8}$

Step 7.7

Simplify the numerator.

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Step 7.7.1

Multiply $- 2$ by $3$ .

$16 + \frac{7 - 6}{9} \cdot \frac{27}{8}$

Step 7.7.2

Subtract $6$ from $7$ .

$16 + \frac{1}{9} \cdot \frac{27}{8}$

Step 7.8

Cancel the common factor of $9$ .

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Step 7.8.1

Factor $9$ out of $27$ .

$16 + \frac{1}{9} \cdot \frac{9 (3)}{8}$

Step 7.8.2

Cancel the common factor.

$16 + \frac{1}{9} \cdot \frac{9 \cdot 3}{8}$

Step 7.8.3

Rewrite the expression.

$16 + \frac{3}{8}$

Step 8

To write $16$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$16 \cdot \frac{8}{8} + \frac{3}{8}$

Step 9

Combine $16$ and $\frac{8}{8}$ .

$\frac{16 \cdot 8}{8} + \frac{3}{8}$

Step 10

Combine the numerators over the common denominator.

$\frac{16 \cdot 8 + 3}{8}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $16$ by $8$ .

$\frac{128 + 3}{8}$

Step 11.2

Add $128$ and $3$ .

$\frac{131}{8}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{131}{8}$

Decimal Form:

$16.375$

Mixed Number Form:

$16 \frac{3}{8}$