Basic Math Examples

47.2506 = 4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e

$47.2506 = 4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e$

Step 1

Rewrite the equation as

4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e = 47.2506

$4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e = 47.2506$ .

4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e = 47.2506

$4 a + \frac{7}{b} + 2 c + \frac{5}{d} + 6 e = 47.2506$

Step 2

Move all terms not containing

a

$a$ to the right side of the equation.

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Step 2.1

Subtract

\frac{7}{b}

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

4 a + 2 c + \frac{5}{d} + 6 e = 47.2506 - \frac{7}{b}

$4 a + 2 c + \frac{5}{d} + 6 e = 47.2506 - \frac{7}{b}$

Step 2.2

Subtract

2 c

$2 c$ from both sides of the equation.

4 a + \frac{5}{d} + 6 e = 47.2506 - \frac{7}{b} - 2 c

$4 a + \frac{5}{d} + 6 e = 47.2506 - \frac{7}{b} - 2 c$

Step 2.3

Subtract

\frac{5}{d}

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

4 a + 6 e = 47.2506 - \frac{7}{b} - 2 c - \frac{5}{d}

$4 a + 6 e = 47.2506 - \frac{7}{b} - 2 c - \frac{5}{d}$

Step 2.4

Subtract

6 e

$6 e$ from both sides of the equation.

4 a = 47.2506 - \frac{7}{b} - 2 c - \frac{5}{d} - 6 e

$4 a = 47.2506 - \frac{7}{b} - 2 c - \frac{5}{d} - 6 e$

Step 2.5

Subtract

6 e

$6 e$ from

47.2506

$47.2506$ .

4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902

$4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902$

4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902

$4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902$

Step 3

Divide each term in

4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902

$4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902$ by

4

$4$ and simplify.

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Step 3.1

Divide each term in

4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902

$4 a = - \frac{7}{b} - 2 c - \frac{5}{d} + 30.94090902$ by

4

$4$ .

\frac{4 a}{4} = \frac{- \frac{7}{b}}{4} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}

$\frac{4 a}{4} = \frac{- \frac{7}{b}}{4} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

4

$4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 a}{4} = \frac{- \frac{7}{b}}{4} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.2.1.2

Divide

$a$ by

$1$ .

$a = \frac{- \frac{7}{b}}{4} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$a = - \frac{7}{b} \cdot \frac{1}{4} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.2

Multiply

$\frac{1}{4}$ by

$\frac{7}{b}$ .

$a = - \frac{7}{4 b} + \frac{- 2 c}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.3

Cancel the common factor of

$- 2$ and

$4$ .

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Step 3.3.1.3.1

Factor

$2$ out of

$- 2 c$ .

$a = - \frac{7}{4 b} + \frac{2 (- c)}{4} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

Factor

$2$ out of

$4$ .

$a = - \frac{7}{4 b} + \frac{2 (- c)}{2 (2)} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.3.2.2

Cancel the common factor.

$a = - \frac{7}{4 b} + \frac{2 (- c)}{2 \cdot 2} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.3.2.3

Rewrite the expression.

$a = - \frac{7}{4 b} + \frac{- c}{2} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.4

Move the negative in front of the fraction.

$a = - \frac{7}{4 b} - \frac{c}{2} + \frac{- \frac{5}{d}}{4} + \frac{30.94090902}{4}$

Step 3.3.1.5

Multiply the numerator by the reciprocal of the denominator.

$a = - \frac{7}{4 b} - \frac{c}{2} - \frac{5}{d} \cdot \frac{1}{4} + \frac{30.94090902}{4}$

Step 3.3.1.6

Multiply

$\frac{1}{4}$ by

$\frac{5}{d}$ .

$a = - \frac{7}{4 b} - \frac{c}{2} - \frac{5}{4 d} + \frac{30.94090902}{4}$

Step 3.3.1.7

Divide

$30.94090902$ by

$4$ .

$a = - \frac{7}{4 b} - \frac{c}{2} - \frac{5}{4 d} + 7.73522725$