Basic Math Examples

$(\frac{3}{8} + \frac{1}{7}) - (\frac{5}{3} - \frac{1}{2})$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{3}{8}$ by $\frac{7}{7}$ .

$\frac{3}{8} \cdot \frac{7}{7} + \frac{1}{7} - (\frac{5}{3} - \frac{1}{2})$

Step 1.2

Multiply $\frac{3}{8}$ by $\frac{7}{7}$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{1}{7} - (\frac{5}{3} - \frac{1}{2})$

Step 1.3

Multiply $\frac{1}{7}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{1}{7} \cdot \frac{8}{8} - (\frac{5}{3} - \frac{1}{2})$

Step 1.4

Multiply $\frac{1}{7}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{8}{7 \cdot 8} - (\frac{5}{3} - \frac{1}{2})$

Step 1.5

Write $- (\frac{5}{3} - \frac{1}{2})$ as a fraction with denominator $1$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{8}{7 \cdot 8} + \frac{- (\frac{5}{3} - \frac{1}{2})}{1}$

Step 1.6

Multiply $\frac{- (\frac{5}{3} - \frac{1}{2})}{1}$ by $\frac{56}{56}$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{8}{7 \cdot 8} + \frac{- (\frac{5}{3} - \frac{1}{2})}{1} \cdot \frac{56}{56}$

Step 1.7

Multiply $\frac{- (\frac{5}{3} - \frac{1}{2})}{1}$ by $\frac{56}{56}$ .

$\frac{3 \cdot 7}{8 \cdot 7} + \frac{8}{7 \cdot 8} + \frac{- (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 1.8

Reorder the factors of $8 \cdot 7$ .

$\frac{3 \cdot 7}{7 \cdot 8} + \frac{8}{7 \cdot 8} + \frac{- (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 1.9

Multiply $7$ by $8$ .

$\frac{3 \cdot 7}{56} + \frac{8}{7 \cdot 8} + \frac{- (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 1.10

Multiply $7$ by $8$ .

$\frac{3 \cdot 7}{56} + \frac{8}{56} + \frac{- (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 7 + 8 - (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $7$ .

$\frac{21 + 8 - (\frac{5}{3} - \frac{1}{2}) \cdot 56}{56}$

Step 3.2

To write $\frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{21 + 8 - (\frac{5}{3} \cdot \frac{2}{2} - \frac{1}{2}) \cdot 56}{56}$

Step 3.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{21 + 8 - (\frac{5}{3} \cdot \frac{2}{2} - \frac{1}{2} \cdot \frac{3}{3}) \cdot 56}{56}$

Step 3.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

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

$\frac{21 + 8 - (\frac{5 \cdot 2}{3 \cdot 2} - \frac{1}{2} \cdot \frac{3}{3}) \cdot 56}{56}$

Step 3.4.2

Multiply $3$ by $2$ .

$\frac{21 + 8 - (\frac{5 \cdot 2}{6} - \frac{1}{2} \cdot \frac{3}{3}) \cdot 56}{56}$

Step 3.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{21 + 8 - (\frac{5 \cdot 2}{6} - \frac{3}{2 \cdot 3}) \cdot 56}{56}$

Step 3.4.4

Multiply $2$ by $3$ .

$\frac{21 + 8 - (\frac{5 \cdot 2}{6} - \frac{3}{6}) \cdot 56}{56}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{21 + 8 - \frac{5 \cdot 2 - 3}{6} \cdot 56}{56}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $5$ by $2$ .

$\frac{21 + 8 - \frac{10 - 3}{6} \cdot 56}{56}$

Step 3.6.2

Subtract $3$ from $10$ .

$\frac{21 + 8 - \frac{7}{6} \cdot 56}{56}$

Step 3.7

Cancel the common factor of $2$ .

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Step 3.7.1

Move the leading negative in $- \frac{7}{6}$ into the numerator.

$\frac{21 + 8 + \frac{- 7}{6} \cdot 56}{56}$

Step 3.7.2

Factor $2$ out of $6$ .

$\frac{21 + 8 + \frac{- 7}{2 (3)} \cdot 56}{56}$

Step 3.7.3

Factor $2$ out of $56$ .

$\frac{21 + 8 + \frac{- 7}{2 \cdot 3} \cdot (2 \cdot 28)}{56}$

Step 3.7.4

Cancel the common factor.

$\frac{21 + 8 + \frac{- 7}{2 \cdot 3} \cdot (2 \cdot 28)}{56}$

Step 3.7.5

Rewrite the expression.

$\frac{21 + 8 + \frac{- 7}{3} \cdot 28}{56}$

Step 3.8

Combine $\frac{- 7}{3}$ and $28$ .

$\frac{21 + 8 + \frac{- 7 \cdot 28}{3}}{56}$

Step 3.9

Multiply $- 7$ by $28$ .

$\frac{21 + 8 + \frac{- 196}{3}}{56}$

Step 3.10

Move the negative in front of the fraction.

$\frac{21 + 8 - \frac{196}{3}}{56}$

Step 4

Find the common denominator.

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Step 4.1

Write $21$ as a fraction with denominator $1$ .

$\frac{\frac{21}{1} + 8 - \frac{196}{3}}{56}$

Step 4.2

Multiply $\frac{21}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{21}{1} \cdot \frac{3}{3} + 8 - \frac{196}{3}}{56}$

Step 4.3

Multiply $\frac{21}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{21 \cdot 3}{3} + 8 - \frac{196}{3}}{56}$

Step 4.4

Write $8$ as a fraction with denominator $1$ .

$\frac{\frac{21 \cdot 3}{3} + \frac{8}{1} - \frac{196}{3}}{56}$

Step 4.5

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{21 \cdot 3}{3} + \frac{8}{1} \cdot \frac{3}{3} - \frac{196}{3}}{56}$

Step 4.6

Multiply $\frac{8}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{21 \cdot 3}{3} + \frac{8 \cdot 3}{3} - \frac{196}{3}}{56}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{21 \cdot 3 + 8 \cdot 3 - 196}{3}}{56}$

Step 6

Simplify each term.

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Step 6.1

Multiply $21$ by $3$ .

$\frac{\frac{63 + 8 \cdot 3 - 196}{3}}{56}$

Step 6.2

Multiply $8$ by $3$ .

$\frac{\frac{63 + 24 - 196}{3}}{56}$

Step 7

Simplify the expression.

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Step 7.1

Add $63$ and $24$ .

$\frac{\frac{87 - 196}{3}}{56}$

Step 7.2

Subtract $196$ from $87$ .

$\frac{\frac{- 109}{3}}{56}$

Step 7.3

Move the negative in front of the fraction.

$\frac{- \frac{109}{3}}{56}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$- \frac{109}{3} \cdot \frac{1}{56}$

Step 9

Multiply $- \frac{109}{3} \cdot \frac{1}{56}$ .

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Step 9.1

Multiply $\frac{1}{56}$ by $\frac{109}{3}$ .

$- \frac{109}{56 \cdot 3}$

Step 9.2

Multiply $56$ by $3$ .

$- \frac{109}{168}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{109}{168}$

Decimal Form:

$- 0.64880952 \dots$