Basic Math Examples

$\frac{- 1}{3} = \frac{7}{8} + b$

Step 1

Rewrite the equation as $\frac{7}{8} + b = \frac{- 1}{3}$ .

$\frac{7}{8} + b = \frac{- 1}{3}$

Step 2

Move the negative in front of the fraction.

$\frac{7}{8} + b = - \frac{1}{3}$

Step 3

Move all terms not containing $b$ to the right side of the equation.

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Step 3.1

Subtract $\frac{7}{8}$ from both sides of the equation.

$b = - \frac{1}{3} - \frac{7}{8}$

Step 3.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$b = - \frac{1}{3} \cdot \frac{8}{8} - \frac{7}{8}$

Step 3.3

To write $- \frac{7}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b = - \frac{1}{3} \cdot \frac{8}{8} - \frac{7}{8} \cdot \frac{3}{3}$

Step 3.4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

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

$b = - \frac{8}{3 \cdot 8} - \frac{7}{8} \cdot \frac{3}{3}$

Step 3.4.2

Multiply $3$ by $8$ .

$b = - \frac{8}{24} - \frac{7}{8} \cdot \frac{3}{3}$

Step 3.4.3

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

$b = - \frac{8}{24} - \frac{7 \cdot 3}{8 \cdot 3}$

Step 3.4.4

Multiply $8$ by $3$ .

$b = - \frac{8}{24} - \frac{7 \cdot 3}{24}$

Step 3.5

Combine the numerators over the common denominator.

$b = \frac{- 8 - 7 \cdot 3}{24}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 7$ by $3$ .

$b = \frac{- 8 - 21}{24}$

Step 3.6.2

Subtract $21$ from $- 8$ .

$b = \frac{- 29}{24}$

Step 3.7

Move the negative in front of the fraction.

$b = - \frac{29}{24}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{29}{24}$

Decimal Form:

$b = - 1.208\overline{3}$

Mixed Number Form:

$b = - 1 \frac{5}{24}$