Basic Math Examples

$- \frac{7}{9} + 3 \frac{1}{5} \cdot \frac{17}{20}$

Step 1

Convert $3 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$- \frac{7}{9} + (3 + \frac{1}{5}) \cdot \frac{17}{20}$

Step 1.2

Add $3$ and $\frac{1}{5}$ .

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Step 1.2.1

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

$- \frac{7}{9} + (3 \cdot \frac{5}{5} + \frac{1}{5}) \cdot \frac{17}{20}$

Step 1.2.2

Combine $3$ and $\frac{5}{5}$ .

$- \frac{7}{9} + (\frac{3 \cdot 5}{5} + \frac{1}{5}) \cdot \frac{17}{20}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{7}{9} + \frac{3 \cdot 5 + 1}{5} \cdot \frac{17}{20}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $5$ .

$- \frac{7}{9} + \frac{15 + 1}{5} \cdot \frac{17}{20}$

Step 1.2.4.2

Add $15$ and $1$ .

$- \frac{7}{9} + \frac{16}{5} \cdot \frac{17}{20}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $4$ .

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Step 2.1.1

Factor $4$ out of $16$ .

$- \frac{7}{9} + \frac{4 (4)}{5} \cdot \frac{17}{20}$

Step 2.1.2

Factor $4$ out of $20$ .

$- \frac{7}{9} + \frac{4 \cdot 4}{5} \cdot \frac{17}{4 \cdot 5}$

Step 2.1.3

Cancel the common factor.

$- \frac{7}{9} + \frac{4 \cdot 4}{5} \cdot \frac{17}{4 \cdot 5}$

Step 2.1.4

Rewrite the expression.

$- \frac{7}{9} + \frac{4}{5} \cdot \frac{17}{5}$

Step 2.2

Multiply $\frac{4}{5}$ by $\frac{17}{5}$ .

$- \frac{7}{9} + \frac{4 \cdot 17}{5 \cdot 5}$

Step 2.3

Multiply $4$ by $17$ .

$- \frac{7}{9} + \frac{68}{5 \cdot 5}$

Step 2.4

Multiply $5$ by $5$ .

$- \frac{7}{9} + \frac{68}{25}$

Step 3

To write $- \frac{7}{9}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$- \frac{7}{9} \cdot \frac{25}{25} + \frac{68}{25}$

Step 4

To write $\frac{68}{25}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$- \frac{7}{9} \cdot \frac{25}{25} + \frac{68}{25} \cdot \frac{9}{9}$

Step 5

Write each expression with a common denominator of $225$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{7}{9}$ by $\frac{25}{25}$ .

$- \frac{7 \cdot 25}{9 \cdot 25} + \frac{68}{25} \cdot \frac{9}{9}$

Step 5.2

Multiply $9$ by $25$ .

$- \frac{7 \cdot 25}{225} + \frac{68}{25} \cdot \frac{9}{9}$

Step 5.3

Multiply $\frac{68}{25}$ by $\frac{9}{9}$ .

$- \frac{7 \cdot 25}{225} + \frac{68 \cdot 9}{25 \cdot 9}$

Step 5.4

Multiply $25$ by $9$ .

$- \frac{7 \cdot 25}{225} + \frac{68 \cdot 9}{225}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 7 \cdot 25 + 68 \cdot 9}{225}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $- 7$ by $25$ .

$\frac{- 175 + 68 \cdot 9}{225}$

Step 7.2

Multiply $68$ by $9$ .

$\frac{- 175 + 612}{225}$

Step 7.3

Add $- 175$ and $612$ .

$\frac{437}{225}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{437}{225}$

Decimal Form:

$1.94\overline{2}$

Mixed Number Form:

$1 \frac{212}{225}$