Basic Math Examples

$(7 \frac{5}{9} \cdot 1 \frac{11}{18}) - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1

Convert $7 \frac{5}{9}$ to an improper fraction.

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Step 1.1

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

$(7 + \frac{5}{9}) \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1.2

Add $7$ and $\frac{5}{9}$ .

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Step 1.2.1

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

$(7 \cdot \frac{9}{9} + \frac{5}{9}) \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1.2.2

Combine $7$ and $\frac{9}{9}$ .

$(\frac{7 \cdot 9}{9} + \frac{5}{9}) \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 9 + 5}{9} \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $9$ .

$\frac{63 + 5}{9} \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 1.2.4.2

Add $63$ and $5$ .

$\frac{68}{9} \cdot 1 \frac{11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 2

Convert $1 \frac{11}{18}$ to an improper fraction.

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Step 2.1

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

$\frac{68}{9} \cdot (1 + \frac{11}{18}) - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 2.2

Add $1$ and $\frac{11}{18}$ .

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Step 2.2.1

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

$\frac{68}{9} \cdot (\frac{18}{18} + \frac{11}{18}) - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{68}{9} \cdot \frac{18 + 11}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 2.2.3

Add $18$ and $11$ .

$\frac{68}{9} \cdot \frac{29}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $68$ .

$\frac{2 (34)}{9} \cdot \frac{29}{18} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 3.2

Factor $2$ out of $18$ .

$\frac{2 \cdot 34}{9} \cdot \frac{29}{2 \cdot 9} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 3.3

Cancel the common factor.

$\frac{2 \cdot 34}{9} \cdot \frac{29}{2 \cdot 9} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 3.4

Rewrite the expression.

$\frac{34}{9} \cdot \frac{29}{9} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 4

Multiply $\frac{34}{9}$ by $\frac{29}{9}$ .

$\frac{34 \cdot 29}{9 \cdot 9} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 5

Multiply $34$ by $29$ .

$\frac{986}{9 \cdot 9} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 6

Multiply $9$ by $9$ .

$\frac{986}{81} - {(\frac{5}{8} + \frac{7}{8})}^{2}$

Step 7

Combine the numerators over the common denominator.

$\frac{986}{81} - {(\frac{5 + 7}{8})}^{2}$

Step 8

Add $5$ and $7$ .

$\frac{986}{81} - {(\frac{12}{8})}^{2}$

Step 9

Cancel the common factor of $12$ and $8$ .

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Step 9.1

Factor $4$ out of $12$ .

$\frac{986}{81} - {(\frac{4 (3)}{8})}^{2}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $4$ out of $8$ .

$\frac{986}{81} - {(\frac{4 \cdot 3}{4 \cdot 2})}^{2}$

Step 9.2.2

Cancel the common factor.

$\frac{986}{81} - {(\frac{4 \cdot 3}{4 \cdot 2})}^{2}$

Step 9.2.3

Rewrite the expression.

$\frac{986}{81} - {(\frac{3}{2})}^{2}$

Step 10

Apply the product rule to $\frac{3}{2}$ .

$\frac{986}{81} - \frac{3^{2}}{2^{2}}$

Step 11

Raise $3$ to the power of $2$ .

$\frac{986}{81} - \frac{9}{2^{2}}$

Step 12

Raise $2$ to the power of $2$ .

$\frac{986}{81} - \frac{9}{4}$

Step 13

To write $\frac{986}{81}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{986}{81} \cdot \frac{4}{4} - \frac{9}{4}$

Step 14

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{81}{81}$ .

$\frac{986}{81} \cdot \frac{4}{4} - \frac{9}{4} \cdot \frac{81}{81}$

Step 15

Write each expression with a common denominator of $324$ , by multiplying each by an appropriate factor of $1$ .

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Step 15.1

Multiply $\frac{986}{81}$ by $\frac{4}{4}$ .

$\frac{986 \cdot 4}{81 \cdot 4} - \frac{9}{4} \cdot \frac{81}{81}$

Step 15.2

Multiply $81$ by $4$ .

$\frac{986 \cdot 4}{324} - \frac{9}{4} \cdot \frac{81}{81}$

Step 15.3

Multiply $\frac{9}{4}$ by $\frac{81}{81}$ .

$\frac{986 \cdot 4}{324} - \frac{9 \cdot 81}{4 \cdot 81}$

Step 15.4

Multiply $4$ by $81$ .

$\frac{986 \cdot 4}{324} - \frac{9 \cdot 81}{324}$

Step 16

Combine the numerators over the common denominator.

$\frac{986 \cdot 4 - 9 \cdot 81}{324}$

Step 17

Simplify the numerator.

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Step 17.1

Multiply $986$ by $4$ .

$\frac{3944 - 9 \cdot 81}{324}$

Step 17.2

Multiply $- 9$ by $81$ .

$\frac{3944 - 729}{324}$

Step 17.3

Subtract $729$ from $3944$ .

$\frac{3215}{324}$