Basic Math Examples

$\frac{3}{5} - (\frac{8}{7} - \frac{5}{4} \cdot (- \frac{6}{3}))$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $2$ .

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Step 1.1.1.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{4} \cdot (- \frac{6}{3}))$

Step 1.1.1.2

Move the leading negative in $- \frac{6}{3}$ into the numerator.

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{4} \cdot \frac{- 6}{3})$

Step 1.1.1.3

Factor $2$ out of $4$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{2 (2)} \cdot \frac{- 6}{3})$

Step 1.1.1.4

Factor $2$ out of $- 6$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{2 \cdot 2} \cdot \frac{2 \cdot - 3}{3})$

Step 1.1.1.5

Cancel the common factor.

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{2 \cdot 2} \cdot \frac{2 \cdot - 3}{3})$

Step 1.1.1.6

Rewrite the expression.

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5}{2} \cdot \frac{- 3}{3})$

Step 1.1.2

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

$\frac{3}{5} - (\frac{8}{7} + \frac{- 5 \cdot - 3}{2 \cdot 3})$

Step 1.1.3

Multiply $- 5$ by $- 3$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{15}{2 \cdot 3})$

Step 1.1.4

Multiply $2$ by $3$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{15}{6})$

Step 1.1.5

Cancel the common factor of $15$ and $6$ .

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Step 1.1.5.1

Factor $3$ out of $15$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{3 (5)}{6})$

Step 1.1.5.2

Cancel the common factors.

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Step 1.1.5.2.1

Factor $3$ out of $6$ .

$\frac{3}{5} - (\frac{8}{7} + \frac{3 \cdot 5}{3 \cdot 2})$

Step 1.1.5.2.2

Cancel the common factor.

$\frac{3}{5} - (\frac{8}{7} + \frac{3 \cdot 5}{3 \cdot 2})$

Step 1.1.5.2.3

Rewrite the expression.

$\frac{3}{5} - (\frac{8}{7} + \frac{5}{2})$

Step 1.2

To write $\frac{8}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{5} - (\frac{8}{7} \cdot \frac{2}{2} + \frac{5}{2})$

Step 1.3

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3}{5} - (\frac{8}{7} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{7}{7})$

Step 1.4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{8}{7}$ by $\frac{2}{2}$ .

$\frac{3}{5} - (\frac{8 \cdot 2}{7 \cdot 2} + \frac{5}{2} \cdot \frac{7}{7})$

Step 1.4.2

Multiply $7$ by $2$ .

$\frac{3}{5} - (\frac{8 \cdot 2}{14} + \frac{5}{2} \cdot \frac{7}{7})$

Step 1.4.3

Multiply $\frac{5}{2}$ by $\frac{7}{7}$ .

$\frac{3}{5} - (\frac{8 \cdot 2}{14} + \frac{5 \cdot 7}{2 \cdot 7})$

Step 1.4.4

Multiply $2$ by $7$ .

$\frac{3}{5} - (\frac{8 \cdot 2}{14} + \frac{5 \cdot 7}{14})$

Step 1.5

Combine the numerators over the common denominator.

$\frac{3}{5} - \frac{8 \cdot 2 + 5 \cdot 7}{14}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $8$ by $2$ .

$\frac{3}{5} - \frac{16 + 5 \cdot 7}{14}$

Step 1.6.2

Multiply $5$ by $7$ .

$\frac{3}{5} - \frac{16 + 35}{14}$

Step 1.6.3

Add $16$ and $35$ .

$\frac{3}{5} - \frac{51}{14}$

Step 2

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

$\frac{3}{5} \cdot \frac{14}{14} - \frac{51}{14}$

Step 3

To write $- \frac{51}{14}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{5} \cdot \frac{14}{14} - \frac{51}{14} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $70$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{5}$ by $\frac{14}{14}$ .

$\frac{3 \cdot 14}{5 \cdot 14} - \frac{51}{14} \cdot \frac{5}{5}$

Step 4.2

Multiply $5$ by $14$ .

$\frac{3 \cdot 14}{70} - \frac{51}{14} \cdot \frac{5}{5}$

Step 4.3

Multiply $\frac{51}{14}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 14}{70} - \frac{51 \cdot 5}{14 \cdot 5}$

Step 4.4

Multiply $14$ by $5$ .

$\frac{3 \cdot 14}{70} - \frac{51 \cdot 5}{70}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 14 - 51 \cdot 5}{70}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $14$ .

$\frac{42 - 51 \cdot 5}{70}$

Step 6.2

Multiply $- 51$ by $5$ .

$\frac{42 - 255}{70}$

Step 6.3

Subtract $255$ from $42$ .

$\frac{- 213}{70}$

Step 7

Move the negative in front of the fraction.

$- \frac{213}{70}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{213}{70}$

Decimal Form:

$- 3.04285714 \dots$

Mixed Number Form:

$- 3 \frac{3}{70}$