Basic Math Examples

$\frac{8}{9} = d + \frac{1}{3} \cdot 7$

Step 1

Rewrite the equation as $d + \frac{1}{3} \cdot 7 = \frac{8}{9}$ .

$d + \frac{1}{3} \cdot 7 = \frac{8}{9}$

Step 2

Combine $\frac{1}{3}$ and $7$ .

$d + \frac{7}{3} = \frac{8}{9}$

Step 3

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

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Step 3.1

Subtract $\frac{7}{3}$ from both sides of the equation.

$d = \frac{8}{9} - \frac{7}{3}$

Step 3.2

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

$d = \frac{8}{9} - \frac{7}{3} \cdot \frac{3}{3}$

Step 3.3

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

$d = \frac{8}{9} - \frac{7 \cdot 3}{3 \cdot 3}$

Step 3.3.2

Multiply $3$ by $3$ .

$d = \frac{8}{9} - \frac{7 \cdot 3}{9}$

Step 3.4

Combine the numerators over the common denominator.

$d = \frac{8 - 7 \cdot 3}{9}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 7$ by $3$ .

$d = \frac{8 - 21}{9}$

Step 3.5.2

Subtract $21$ from $8$ .

$d = \frac{- 13}{9}$

Step 3.6

Move the negative in front of the fraction.

$d = - \frac{13}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = - \frac{13}{9}$

Decimal Form:

$d = - 1.\overline{4}$

Mixed Number Form:

$d = - 1 \frac{4}{9}$