Basic Math Examples

$- \frac{- 3}{3 \frac{3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1

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

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Step 1.1

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

$- \frac{- 3}{3 + \frac{3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1.2

Add $3$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{- 3}{3 \cdot \frac{4}{4} + \frac{3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$- \frac{- 3}{\frac{3 \cdot 4}{4} + \frac{3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{- 3}{\frac{3 \cdot 4 + 3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$- \frac{- 3}{\frac{12 + 3}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 1.2.4.2

Add $12$ and $3$ .

$- \frac{- 3}{\frac{15}{4}} - \frac{2}{- 3} + \frac{2}{5}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{- 3}{\frac{15}{4}}$ by $\frac{15}{15}$ .

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

Step 2.2

Multiply $\frac{- 3}{\frac{15}{4}}$ by $\frac{15}{15}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2}{- 3} + \frac{2}{5}$

Step 2.3

Multiply $\frac{2}{- 3}$ by $\frac{\frac{- 15 \cdot 5}{4}}{\frac{- 15 \cdot 5}{4}}$ .

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

Step 2.4

Multiply $\frac{2}{- 3}$ by $\frac{\frac{- 15 \cdot 5}{4}}{\frac{- 15 \cdot 5}{4}}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{- 3 \frac{- 15 \cdot 5}{4}} + \frac{2}{5}$

Step 2.5

Multiply $\frac{2}{5}$ by $\frac{\frac{3 \cdot 15}{4}}{\frac{3 \cdot 15}{4}}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{- 3 \frac{- 15 \cdot 5}{4}} + \frac{2}{5} \cdot \frac{\frac{3 \cdot 15}{4}}{\frac{3 \cdot 15}{4}}$

Step 2.6

Multiply $\frac{2}{5}$ by $\frac{\frac{3 \cdot 15}{4}}{\frac{3 \cdot 15}{4}}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{- 3 \frac{- 15 \cdot 5}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{5 \frac{3 \cdot 15}{4}}$

Step 2.7

Multiply $- 15$ by $5$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{- 3 (\frac{- 75}{4})} + \frac{2 \frac{3 \cdot 15}{4}}{5 \frac{3 \cdot 15}{4}}$

Step 2.8

Combine $- 3$ and $\frac{- 75}{4}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{\frac{- 3 \cdot - 75}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{5 \frac{3 \cdot 15}{4}}$

Step 2.9

Multiply $- 3$ by $- 75$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{\frac{225}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{5 \frac{3 \cdot 15}{4}}$

Step 2.10

Multiply $3$ by $15$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{\frac{225}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{5 (\frac{45}{4})}$

Step 2.11

Combine $5$ and $\frac{45}{4}$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{\frac{225}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{\frac{5 \cdot 45}{4}}$

Step 2.12

Multiply $5$ by $45$ .

$- \frac{- 3 \cdot 15}{\frac{15}{4} \cdot 15} - \frac{2 \frac{- 15 \cdot 5}{4}}{\frac{225}{4}} + \frac{2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{- 2 \frac{- 15 \cdot 5}{4} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $- 2$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{2 (- 1) \frac{- 15 \cdot 5}{4} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.1.2

Factor $2$ out of $4$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{2 \cdot - 1 \frac{- 15 \cdot 5}{2 \cdot 2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.1.3

Cancel the common factor.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{2 \cdot - 1 \frac{- 15 \cdot 5}{2 \cdot 2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.1.4

Rewrite the expression.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{- \frac{- 15 \cdot 5}{2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.2

Multiply $- 15$ by $5$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{- \frac{- 75}{2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.3

Move the negative in front of the fraction.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{- - \frac{75}{2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.4

Multiply $- - \frac{75}{2}$ .

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Step 4.4.1

Multiply $- 1$ by $- 1$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{1 (\frac{75}{2}) + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.4.2

Multiply $\frac{75}{2}$ by $1$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75}{2} + 2 \frac{3 \cdot 15}{4}}{\frac{225}{4}}$

Step 4.5

Cancel the common factor of $2$ .

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Step 4.5.1

Factor $2$ out of $4$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75}{2} + 2 \frac{3 \cdot 15}{2 (2)}}{\frac{225}{4}}$

Step 4.5.2

Cancel the common factor.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75}{2} + 2 \frac{3 \cdot 15}{2 \cdot 2}}{\frac{225}{4}}$

Step 4.5.3

Rewrite the expression.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75}{2} + \frac{3 \cdot 15}{2}}{\frac{225}{4}}$

Step 4.6

Multiply $3$ by $15$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75}{2} + \frac{45}{2}}{\frac{225}{4}}$

Step 5

Combine fractions.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{75 + 45}{2}}{\frac{225}{4}}$

Step 5.2

Simplify the expression.

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Step 5.2.1

Add $75$ and $45$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{\frac{120}{2}}{\frac{225}{4}}$

Step 5.2.2

Divide $120$ by $2$ .

$\frac{3 \cdot 15}{15 (\frac{15}{4})} + \frac{60}{\frac{225}{4}}$

Step 5.2.3

Multiply $3$ by $15$ .

$\frac{45}{15 (\frac{15}{4})} + \frac{60}{\frac{225}{4}}$

Step 6

Simplify each term.

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Step 6.1

Cancel the common factor of $45$ and $15$ .

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Step 6.1.1

Factor $15$ out of $45$ .

$\frac{15 \cdot 3}{15 (\frac{15}{4})} + \frac{60}{\frac{225}{4}}$

Step 6.1.2

Cancel the common factors.

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Step 6.1.2.1

Cancel the common factor.

$\frac{15 \cdot 3}{15 (\frac{15}{4})} + \frac{60}{\frac{225}{4}}$

Step 6.1.2.2

Rewrite the expression.

$\frac{3}{\frac{15}{4}} + \frac{60}{\frac{225}{4}}$

Step 6.2

Multiply the numerator by the reciprocal of the denominator.

$3 (\frac{4}{15}) + \frac{60}{\frac{225}{4}}$

Step 6.3

Cancel the common factor of $3$ .

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Step 6.3.1

Factor $3$ out of $15$ .

$3 \frac{4}{3 (5)} + \frac{60}{\frac{225}{4}}$

Step 6.3.2

Cancel the common factor.

$3 \frac{4}{3 \cdot 5} + \frac{60}{\frac{225}{4}}$

Step 6.3.3

Rewrite the expression.

$\frac{4}{5} + \frac{60}{\frac{225}{4}}$

Step 6.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{4}{5} + 60 (\frac{4}{225})$

Step 6.5

Cancel the common factor of $15$ .

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Step 6.5.1

Factor $15$ out of $60$ .

$\frac{4}{5} + 15 (4) \frac{4}{225}$

Step 6.5.2

Factor $15$ out of $225$ .

$\frac{4}{5} + 15 \cdot 4 \frac{4}{15 \cdot 15}$

Step 6.5.3

Cancel the common factor.

$\frac{4}{5} + 15 \cdot 4 \frac{4}{15 \cdot 15}$

Step 6.5.4

Rewrite the expression.

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

Step 6.6

Combine $4$ and $\frac{4}{15}$ .

$\frac{4}{5} + \frac{4 \cdot 4}{15}$

Step 6.7

Multiply $4$ by $4$ .

$\frac{4}{5} + \frac{16}{15}$

Step 7

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{4}{5} \cdot \frac{3}{3} + \frac{16}{15}$

Step 8

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

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Step 8.1

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$\frac{4 \cdot 3}{5 \cdot 3} + \frac{16}{15}$

Step 8.2

Multiply $5$ by $3$ .

$\frac{4 \cdot 3}{15} + \frac{16}{15}$

Step 9

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 16}{15}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $4$ by $3$ .

$\frac{12 + 16}{15}$

Step 10.2

Add $12$ and $16$ .

$\frac{28}{15}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{28}{15}$

Decimal Form:

$1.8\overline{6}$

Mixed Number Form:

$1 \frac{13}{15}$