Basic Math Examples

$\frac{15}{8} a + \frac{7}{4} = \frac{7}{4} a$

Step 1

Combine $\frac{15}{8}$ and $a$ .

$\frac{15 a}{8} + \frac{7}{4} = \frac{7}{4} a$

Step 2

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

$\frac{15 a}{8} + \frac{7}{4} = \frac{7 a}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{7 a}{4}$ from both sides of the equation.

$\frac{15 a}{8} + \frac{7}{4} - \frac{7 a}{4} = 0$

Step 3.2

To write $- \frac{7 a}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15 a}{8} - \frac{7 a}{4} \cdot \frac{2}{2} + \frac{7}{4} = 0$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{7 a}{4}$ by $\frac{2}{2}$ .

$\frac{15 a}{8} - \frac{7 a \cdot 2}{4 \cdot 2} + \frac{7}{4} = 0$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{15 a}{8} - \frac{7 a \cdot 2}{8} + \frac{7}{4} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{15 a - 7 a \cdot 2}{8} + \frac{7}{4} = 0$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $a$ out of $15 a - 7 a \cdot 2$ .

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Step 3.5.1.1.1

Factor $a$ out of $15 a$ .

$\frac{a \cdot 15 - 7 a \cdot 2}{8} + \frac{7}{4} = 0$

Step 3.5.1.1.2

Factor $a$ out of $- 7 a \cdot 2$ .

$\frac{a \cdot 15 + a (- 7 \cdot 2)}{8} + \frac{7}{4} = 0$

Step 3.5.1.1.3

Factor $a$ out of $a \cdot 15 + a (- 7 \cdot 2)$ .

$\frac{a (15 - 7 \cdot 2)}{8} + \frac{7}{4} = 0$

Step 3.5.1.2

Multiply $- 7$ by $2$ .

$\frac{a (15 - 14)}{8} + \frac{7}{4} = 0$

Step 3.5.1.3

Subtract $14$ from $15$ .

$\frac{a \cdot 1}{8} + \frac{7}{4} = 0$

Step 3.5.2

Multiply $a$ by $1$ .

$\frac{a}{8} + \frac{7}{4} = 0$

Step 4

Subtract $\frac{7}{4}$ from both sides of the equation.

$\frac{a}{8} = - \frac{7}{4}$

Step 5

Multiply both sides of the equation by $8$ .

$8 \frac{a}{8} = 8 (- \frac{7}{4})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1

Cancel the common factor.

$8 \frac{a}{8} = 8 (- \frac{7}{4})$

Step 6.1.1.2

Rewrite the expression.

$a = 8 (- \frac{7}{4})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $8 (- \frac{7}{4})$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$a = 8 (\frac{- 7}{4})$

Step 6.2.1.1.2

Factor $4$ out of $8$ .

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

Step 6.2.1.1.3

Cancel the common factor.

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

Step 6.2.1.1.4

Rewrite the expression.

$a = 2 \cdot - 7$

Step 6.2.1.2

Multiply $2$ by $- 7$ .

$a = - 14$