Basic Math Examples

$\frac{7}{4} a + \frac{5}{3} = \frac{31}{6}$

Step 1

Combine $\frac{7}{4}$ and $a$ .

$\frac{7 a}{4} + \frac{5}{3} = \frac{31}{6}$

Step 2

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

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Step 2.1

Subtract $\frac{5}{3}$ from both sides of the equation.

$\frac{7 a}{4} = \frac{31}{6} - \frac{5}{3}$

Step 2.2

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

$\frac{7 a}{4} = \frac{31}{6} - \frac{5}{3} \cdot \frac{2}{2}$

Step 2.3

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

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Step 2.3.1

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

$\frac{7 a}{4} = \frac{31}{6} - \frac{5 \cdot 2}{3 \cdot 2}$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{7 a}{4} = \frac{31}{6} - \frac{5 \cdot 2}{6}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 a}{4} = \frac{31 - 5 \cdot 2}{6}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 5$ by $2$ .

$\frac{7 a}{4} = \frac{31 - 10}{6}$

Step 2.5.2

Subtract $10$ from $31$ .

$\frac{7 a}{4} = \frac{21}{6}$

Step 2.6

Cancel the common factor of $21$ and $6$ .

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Step 2.6.1

Factor $3$ out of $21$ .

$\frac{7 a}{4} = \frac{3 (7)}{6}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $6$ .

$\frac{7 a}{4} = \frac{3 \cdot 7}{3 \cdot 2}$

Step 2.6.2.2

Cancel the common factor.

$\frac{7 a}{4} = \frac{3 \cdot 7}{3 \cdot 2}$

Step 2.6.2.3

Rewrite the expression.

$\frac{7 a}{4} = \frac{7}{2}$

Step 3

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 a}{4} = \frac{4}{7} \cdot \frac{7}{2}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{4}{7} \cdot \frac{7 a}{4}$ .

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 a}{4} = \frac{4}{7} \cdot \frac{7}{2}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 a) = \frac{4}{7} \cdot \frac{7}{2}$

Step 4.1.1.2

Cancel the common factor of $7$ .

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Step 4.1.1.2.1

Factor $7$ out of $7 a$ .

$\frac{1}{7} (7 (a)) = \frac{4}{7} \cdot \frac{7}{2}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 a) = \frac{4}{7} \cdot \frac{7}{2}$

Step 4.1.1.2.3

Rewrite the expression.

$a = \frac{4}{7} \cdot \frac{7}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{7} \cdot \frac{7}{2}$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $4$ .

$a = \frac{2 (2)}{7} \cdot \frac{7}{2}$

Step 4.2.1.1.2

Cancel the common factor.

$a = \frac{2 \cdot 2}{7} \cdot \frac{7}{2}$

Step 4.2.1.1.3

Rewrite the expression.

$a = \frac{2}{7} \cdot 7$

Step 4.2.1.2

Cancel the common factor of $7$ .

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Step 4.2.1.2.1

Cancel the common factor.

$a = \frac{2}{7} \cdot 7$

Step 4.2.1.2.2

Rewrite the expression.

$a = 2$