Basic Math Examples

(4 \frac{2}{3} - 1 \frac{4}{15}) - (1 \frac{3}{5} + \frac{7}{15})

$(4 \frac{2}{3} - 1 \frac{4}{15}) - (1 \frac{3}{5} + \frac{7}{15})$

Step 1

Convert

$4 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{2}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 1.2

Add

$4$ and

$\frac{2}{3}$ .

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Step 1.2.1

To write

$4$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$4 \cdot \frac{3}{3} + \frac{2}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 1.2.2

Combine

$4$ and

$\frac{3}{3}$ .

$\frac{4 \cdot 3}{3} + \frac{2}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 2}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$3$ .

$\frac{12 + 2}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 1.2.4.2

Add

$12$ and

$2$ .

$\frac{14}{3} - 1 \frac{4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 2

Convert

$1 \frac{4}{15}$ to an improper fraction.

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Step 2.1

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

$\frac{14}{3} - (1 + \frac{4}{15}) - (1 \frac{3}{5} + \frac{7}{15})$

Step 2.2

Add

$1$ and

$\frac{4}{15}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{14}{3} - (\frac{15}{15} + \frac{4}{15}) - (1 \frac{3}{5} + \frac{7}{15})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{14}{3} - \frac{15 + 4}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 2.2.3

Add

$15$ and

$4$ .

$\frac{14}{3} - \frac{19}{15} - (1 \frac{3}{5} + \frac{7}{15})$

Step 3

Convert

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

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Step 3.1

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

$\frac{14}{3} - \frac{19}{15} - (1 + \frac{3}{5} + \frac{7}{15})$

Step 3.2

Add

$1$ and

$\frac{3}{5}$ .

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Step 3.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{14}{3} - \frac{19}{15} - (\frac{5}{5} + \frac{3}{5} + \frac{7}{15})$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{14}{3} - \frac{19}{15} - (\frac{5 + 3}{5} + \frac{7}{15})$

Step 3.2.3

Add

$5$ and

$3$ .

$\frac{14}{3} - \frac{19}{15} - (\frac{8}{5} + \frac{7}{15})$

Step 4

Find the common denominator.

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Step 4.1

Multiply

$\frac{14}{3}$ by

$\frac{5}{5}$ .

$\frac{14}{3} \cdot \frac{5}{5} - \frac{19}{15} - (\frac{8}{5} + \frac{7}{15})$

Step 4.2

Multiply

$\frac{14}{3}$ by

$\frac{5}{5}$ .

$\frac{14 \cdot 5}{3 \cdot 5} - \frac{19}{15} - (\frac{8}{5} + \frac{7}{15})$

Step 4.3

Write

$- (\frac{8}{5} + \frac{7}{15})$ as a fraction with denominator

$1$ .

$\frac{14 \cdot 5}{3 \cdot 5} - \frac{19}{15} + \frac{- (\frac{8}{5} + \frac{7}{15})}{1}$

Step 4.4

Multiply

$\frac{- (\frac{8}{5} + \frac{7}{15})}{1}$ by

$\frac{15}{15}$ .

$\frac{14 \cdot 5}{3 \cdot 5} - \frac{19}{15} + \frac{- (\frac{8}{5} + \frac{7}{15})}{1} \cdot \frac{15}{15}$

Step 4.5

Multiply

$\frac{- (\frac{8}{5} + \frac{7}{15})}{1}$ by

$\frac{15}{15}$ .

$\frac{14 \cdot 5}{3 \cdot 5} - \frac{19}{15} + \frac{- (\frac{8}{5} + \frac{7}{15}) \cdot 15}{15}$

Step 4.6

Multiply

$3$ by

$5$ .

$\frac{14 \cdot 5}{15} - \frac{19}{15} + \frac{- (\frac{8}{5} + \frac{7}{15}) \cdot 15}{15}$

Step 5

Combine the numerators over the common denominator.

$\frac{14 \cdot 5 - 19 - (\frac{8}{5} + \frac{7}{15}) \cdot 15}{15}$

Step 6

Simplify each term.

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Step 6.1

Multiply

$14$ by

$5$ .

$\frac{70 - 19 - (\frac{8}{5} + \frac{7}{15}) \cdot 15}{15}$

Step 6.2

To write

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

$\frac{3}{3}$ .

$\frac{70 - 19 - (\frac{8}{5} \cdot \frac{3}{3} + \frac{7}{15}) \cdot 15}{15}$

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

$\frac{8}{5}$ by

$\frac{3}{3}$ .

$\frac{70 - 19 - (\frac{8 \cdot 3}{5 \cdot 3} + \frac{7}{15}) \cdot 15}{15}$

Step 6.3.2

Multiply

$5$ by

$3$ .

$\frac{70 - 19 - (\frac{8 \cdot 3}{15} + \frac{7}{15}) \cdot 15}{15}$

Step 6.4

Combine the numerators over the common denominator.

$\frac{70 - 19 - \frac{8 \cdot 3 + 7}{15} \cdot 15}{15}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply

$8$ by

$3$ .

$\frac{70 - 19 - \frac{24 + 7}{15} \cdot 15}{15}$

Step 6.5.2

Add

$24$ and

$7$ .

$\frac{70 - 19 - \frac{31}{15} \cdot 15}{15}$

Step 6.6

Cancel the common factor of

$15$ .

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Step 6.6.1

Move the leading negative in

$- \frac{31}{15}$ into the numerator.

$\frac{70 - 19 + \frac{- 31}{15} \cdot 15}{15}$

Step 6.6.2

Cancel the common factor.

$\frac{70 - 19 + \frac{- 31}{15} \cdot 15}{15}$

Step 6.6.3

Rewrite the expression.

$\frac{70 - 19 - 31}{15}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Subtract

$19$ from

$70$ .

$\frac{51 - 31}{15}$

Step 7.2

Subtract

$31$ from

$51$ .

$\frac{20}{15}$

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:

$1 \frac{1}{3}$