Basic Math Examples

$\frac{2}{3} a + \frac{1}{3} = \frac{3}{7} - \frac{1}{3} a + \frac{3}{7}$

Step 1

Combine $\frac{2}{3}$ and $a$ .

$\frac{2 a}{3} + \frac{1}{3} = \frac{3}{7} - \frac{1}{3} a + \frac{3}{7}$

Step 2

Simplify $\frac{3}{7} - \frac{1}{3} a + \frac{3}{7}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 a}{3} + \frac{1}{3} = - \frac{1}{3} a + \frac{3 + 3}{7}$

Step 2.2

Add $3$ and $3$ .

$\frac{2 a}{3} + \frac{1}{3} = - \frac{1}{3} a + \frac{6}{7}$

Step 2.3

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

$\frac{2 a}{3} + \frac{1}{3} = - \frac{a}{3} + \frac{6}{7}$

Step 3

Move all terms containing $a$ to the left side of the equation.

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Step 3.1

Add $\frac{a}{3}$ to both sides of the equation.

$\frac{2 a}{3} + \frac{1}{3} + \frac{a}{3} = \frac{6}{7}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 a + 1 + a}{3} = \frac{6}{7}$

Step 3.3

Add $2 a$ and $a$ .

$\frac{3 a + 1}{3} = \frac{6}{7}$

Step 4

Multiply both sides by $3$ .

$\frac{3 a + 1}{3} \cdot 3 = \frac{6}{7} \cdot 3$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{3 a + 1}{3} \cdot 3 = \frac{6}{7} \cdot 3$

Step 5.1.1.2

Rewrite the expression.

$3 a + 1 = \frac{6}{7} \cdot 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{6}{7} \cdot 3$ .

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Step 5.2.1.1

Combine $\frac{6}{7}$ and $3$ .

$3 a + 1 = \frac{6 \cdot 3}{7}$

Step 5.2.1.2

Multiply $6$ by $3$ .

$3 a + 1 = \frac{18}{7}$

Step 6

Solve for $a$ .

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Step 6.1

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

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Step 6.1.1

Subtract $1$ from both sides of the equation.

$3 a = \frac{18}{7} - 1$

Step 6.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$3 a = \frac{18}{7} - 1 \cdot \frac{7}{7}$

Step 6.1.3

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

$3 a = \frac{18}{7} + \frac{- 1 \cdot 7}{7}$

Step 6.1.4

Combine the numerators over the common denominator.

$3 a = \frac{18 - 1 \cdot 7}{7}$

Step 6.1.5

Simplify the numerator.

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Step 6.1.5.1

Multiply $- 1$ by $7$ .

$3 a = \frac{18 - 7}{7}$

Step 6.1.5.2

Subtract $7$ from $18$ .

$3 a = \frac{11}{7}$

Step 6.2

Divide each term in $3 a = \frac{11}{7}$ by $3$ and simplify.

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Step 6.2.1

Divide each term in $3 a = \frac{11}{7}$ by $3$ .

$\frac{3 a}{3} = \frac{\frac{11}{7}}{3}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $3$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{3 a}{3} = \frac{\frac{11}{7}}{3}$

Step 6.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{\frac{11}{7}}{3}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$a = \frac{11}{7} \cdot \frac{1}{3}$

Step 6.2.3.2

Multiply $\frac{11}{7} \cdot \frac{1}{3}$ .

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Step 6.2.3.2.1

Multiply $\frac{11}{7}$ by $\frac{1}{3}$ .

$a = \frac{11}{7 \cdot 3}$

Step 6.2.3.2.2

Multiply $7$ by $3$ .

$a = \frac{11}{21}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{11}{21}$

Decimal Form:

$a = 0.\overline{523809}$