Basic Math Examples

$\frac{5}{3} a + 7 = \frac{17}{3}$

Step 1

Combine $\frac{5}{3}$ and $a$ .

$\frac{5 a}{3} + 7 = \frac{17}{3}$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the equation.

$\frac{5 a}{3} = \frac{17}{3} - 7$

Step 2.2

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

$\frac{5 a}{3} = \frac{17}{3} - 7 \cdot \frac{3}{3}$

Step 2.3

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

$\frac{5 a}{3} = \frac{17}{3} + \frac{- 7 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{5 a}{3} = \frac{17 - 7 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 7$ by $3$ .

$\frac{5 a}{3} = \frac{17 - 21}{3}$

Step 2.5.2

Subtract $21$ from $17$ .

$\frac{5 a}{3} = \frac{- 4}{3}$

Step 2.6

Move the negative in front of the fraction.

$\frac{5 a}{3} = - \frac{4}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$5 a = - 4$

Step 4

Divide each term in $5 a = - 4$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 a = - 4$ by $5$ .

$\frac{5 a}{5} = \frac{- 4}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 a}{5} = \frac{- 4}{5}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 4}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Move the negative in front of the fraction.

$a = - \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{4}{5}$

Decimal Form:

$a = - 0.8$