Basic Math Examples

$(5 \frac{3}{5} - 1 \frac{2}{15}) - (2 \frac{2}{3} + \frac{7}{15})$

Step 1

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

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Step 1.1

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

$5 + \frac{3}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 1.2

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

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Step 1.2.1

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

$5 \cdot \frac{5}{5} + \frac{3}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 1.2.2

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

$\frac{5 \cdot 5}{5} + \frac{3}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 3}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $5$ .

$\frac{25 + 3}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 1.2.4.2

Add $25$ and $3$ .

$\frac{28}{5} - 1 \frac{2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 2

Convert $1 \frac{2}{15}$ to an improper fraction.

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Step 2.1

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

$\frac{28}{5} - (1 + \frac{2}{15}) - (2 \frac{2}{3} + \frac{7}{15})$

Step 2.2

Add $1$ and $\frac{2}{15}$ .

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Step 2.2.1

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

$\frac{28}{5} - (\frac{15}{15} + \frac{2}{15}) - (2 \frac{2}{3} + \frac{7}{15})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{28}{5} - \frac{15 + 2}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 2.2.3

Add $15$ and $2$ .

$\frac{28}{5} - \frac{17}{15} - (2 \frac{2}{3} + \frac{7}{15})$

Step 3

Convert $2 \frac{2}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{28}{5} - \frac{17}{15} - (2 + \frac{2}{3} + \frac{7}{15})$

Step 3.2

Add $2$ and $\frac{2}{3}$ .

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Step 3.2.1

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

$\frac{28}{5} - \frac{17}{15} - (2 \cdot \frac{3}{3} + \frac{2}{3} + \frac{7}{15})$

Step 3.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{28}{5} - \frac{17}{15} - (\frac{2 \cdot 3}{3} + \frac{2}{3} + \frac{7}{15})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{28}{5} - \frac{17}{15} - (\frac{2 \cdot 3 + 2}{3} + \frac{7}{15})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $3$ .

$\frac{28}{5} - \frac{17}{15} - (\frac{6 + 2}{3} + \frac{7}{15})$

Step 3.2.4.2

Add $6$ and $2$ .

$\frac{28}{5} - \frac{17}{15} - (\frac{8}{3} + \frac{7}{15})$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{28}{5}$ by $\frac{3}{3}$ .

$\frac{28}{5} \cdot \frac{3}{3} - \frac{17}{15} - (\frac{8}{3} + \frac{7}{15})$

Step 4.2

Multiply $\frac{28}{5}$ by $\frac{3}{3}$ .

$\frac{28 \cdot 3}{5 \cdot 3} - \frac{17}{15} - (\frac{8}{3} + \frac{7}{15})$

Step 4.3

Write $- (\frac{8}{3} + \frac{7}{15})$ as a fraction with denominator $1$ .

$\frac{28 \cdot 3}{5 \cdot 3} - \frac{17}{15} + \frac{- (\frac{8}{3} + \frac{7}{15})}{1}$

Step 4.4

Multiply $\frac{- (\frac{8}{3} + \frac{7}{15})}{1}$ by $\frac{15}{15}$ .

$\frac{28 \cdot 3}{5 \cdot 3} - \frac{17}{15} + \frac{- (\frac{8}{3} + \frac{7}{15})}{1} \cdot \frac{15}{15}$

Step 4.5

Multiply $\frac{- (\frac{8}{3} + \frac{7}{15})}{1}$ by $\frac{15}{15}$ .

$\frac{28 \cdot 3}{5 \cdot 3} - \frac{17}{15} + \frac{- (\frac{8}{3} + \frac{7}{15}) \cdot 15}{15}$

Step 4.6

Reorder the factors of $5 \cdot 3$ .

$\frac{28 \cdot 3}{3 \cdot 5} - \frac{17}{15} + \frac{- (\frac{8}{3} + \frac{7}{15}) \cdot 15}{15}$

Step 4.7

Multiply $3$ by $5$ .

$\frac{28 \cdot 3}{15} - \frac{17}{15} + \frac{- (\frac{8}{3} + \frac{7}{15}) \cdot 15}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{28 \cdot 3 - 17 - (\frac{8}{3} + \frac{7}{15}) \cdot 15}{15}$

Step 6

Simplify each term.

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Step 6.1

Multiply $28$ by $3$ .

$\frac{84 - 17 - (\frac{8}{3} + \frac{7}{15}) \cdot 15}{15}$

Step 6.2

To write $\frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{84 - 17 - (\frac{8}{3} \cdot \frac{5}{5} + \frac{7}{15}) \cdot 15}{15}$

Step 6.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.3.1

Multiply $\frac{8}{3}$ by $\frac{5}{5}$ .

$\frac{84 - 17 - (\frac{8 \cdot 5}{3 \cdot 5} + \frac{7}{15}) \cdot 15}{15}$

Step 6.3.2

Multiply $3$ by $5$ .

$\frac{84 - 17 - (\frac{8 \cdot 5}{15} + \frac{7}{15}) \cdot 15}{15}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{84 - 17 - \frac{8 \cdot 5 + 7}{15} \cdot 15}{15}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $8$ by $5$ .

$\frac{84 - 17 - \frac{40 + 7}{15} \cdot 15}{15}$

Step 6.5.2

Add $40$ and $7$ .

$\frac{84 - 17 - \frac{47}{15} \cdot 15}{15}$

Step 6.6

Cancel the common factor of $15$ .

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Step 6.6.1

Move the leading negative in $- \frac{47}{15}$ into the numerator.

$\frac{84 - 17 + \frac{- 47}{15} \cdot 15}{15}$

Step 6.6.2

Cancel the common factor.

$\frac{84 - 17 + \frac{- 47}{15} \cdot 15}{15}$

Step 6.6.3

Rewrite the expression.

$\frac{84 - 17 - 47}{15}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract $17$ from $84$ .

$\frac{67 - 47}{15}$

Step 7.2

Subtract $47$ from $67$ .

$\frac{20}{15}$

Step 7.3

Cancel the common factor of $20$ and $15$ .

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Step 7.3.1

Factor $5$ out of $20$ .

$\frac{5 (4)}{15}$

Step 7.3.2

Cancel the common factors.

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Step 7.3.2.1

Factor $5$ out of $15$ .

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

Step 7.3.2.2

Cancel the common factor.

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

Step 7.3.2.3

Rewrite the expression.

$\frac{4}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$