Basic Math Examples

$\frac{3060 + 0.04 m}{34000 + m} = 0.05$

Step 1

Factor $0.04$ out of $3060 + 0.04 m$ .

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Step 1.1

Factor $0.04$ out of $3060$ .

$\frac{0.04 \cdot 76500 + 0.04 m}{34000 + m} = 0.05$

Step 1.2

Factor $0.04$ out of $0.04 \cdot 76500 + 0.04 m$ .

$\frac{0.04 \cdot (76500 + m)}{34000 + m} = 0.05$

Step 1.3

Multiply $0.04$ by $76500 + m$ .

$\frac{0.04 (76500 + m)}{34000 + m} = 0.05$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$34000 + m, 1$

Step 2.2

Remove parentheses.

$34000 + m, 1$

Step 2.3

The LCM of one and any expression is the expression.

$34000 + m$

Step 3

Multiply each term in $\frac{0.04 (76500 + m)}{34000 + m} = 0.05$ by $34000 + m$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{0.04 (76500 + m)}{34000 + m} = 0.05$ by $34000 + m$ .

$\frac{0.04 (76500 + m)}{34000 + m} (34000 + m) = 0.05 (34000 + m)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $0.04$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{0.04 (76500 + m)}{34000 + m} (34000 + m) = 0.05 (34000 + m)$

Step 3.2.1.2

Rewrite the expression.

$\frac{76500 + m}{34000 + m} \cdot \frac{34000 + m}{25} = 0.05 (34000 + m)$

Step 3.2.2

Cancel the common factor of $34000 + m$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{76500 + m}{34000 + m} \cdot \frac{34000 + m}{25} = 0.05 (34000 + m)$

Step 3.2.2.2

Rewrite the expression.

$(76500 + m) \frac{1}{25} = 0.05 (34000 + m)$

Step 3.2.3

Apply the distributive property.

$76500 (\frac{1}{25}) + m \frac{1}{25} = 0.05 (34000 + m)$

Step 3.2.4

Cancel the common factor of $25$ .

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Step 3.2.4.1

Factor $25$ out of $76500$ .

$25 (3060) \frac{1}{25} + m \frac{1}{25} = 0.05 (34000 + m)$

Step 3.2.4.2

Cancel the common factor.

$25 \cdot 3060 \frac{1}{25} + m \frac{1}{25} = 0.05 (34000 + m)$

Step 3.2.4.3

Rewrite the expression.

$3060 + m \frac{1}{25} = 0.05 (34000 + m)$

Step 3.2.5

Combine $m$ and $\frac{1}{25}$ .

$3060 + \frac{m}{25} = 0.05 (34000 + m)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$3060 + \frac{m}{25} = 0.05 \cdot 34000 + 0.05 m$

Step 3.3.2

Multiply $0.05$ by $34000$ .

$3060 + \frac{m}{25} = 1700 + 0.05 m$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $0.05 m$ from both sides of the equation.

$3060 + \frac{m}{25} - 0.05 m = 1700$

Step 4.1.2

To write $- 0.05 m$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$3060 + \frac{m}{25} - 0.05 m \cdot \frac{25}{25} = 1700$

Step 4.1.3

Combine $- 0.05 m$ and $\frac{25}{25}$ .

$3060 + \frac{m}{25} + \frac{- 0.05 m \cdot 25}{25} = 1700$

Step 4.1.4

Combine the numerators over the common denominator.

$3060 + \frac{m - 0.05 m \cdot 25}{25} = 1700$

Step 4.1.5

Simplify each term.

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Step 4.1.5.1

Simplify the numerator.

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Step 4.1.5.1.1

Factor $m$ out of $m - 0.05 m \cdot 25$ .

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Step 4.1.5.1.1.1

Raise $m$ to the power of $1$ .

$3060 + \frac{m^{1} - 0.05 m \cdot 25}{25} = 1700$

Step 4.1.5.1.1.2

Factor $m$ out of $m^{1}$ .

$3060 + \frac{m \cdot 1 - 0.05 m \cdot 25}{25} = 1700$

Step 4.1.5.1.1.3

Factor $m$ out of $- 0.05 m \cdot 25$ .

$3060 + \frac{m \cdot 1 + m (- 0.05 \cdot 25)}{25} = 1700$

Step 4.1.5.1.1.4

Factor $m$ out of $m \cdot 1 + m (- 0.05 \cdot 25)$ .

$3060 + \frac{m (1 - 0.05 \cdot 25)}{25} = 1700$

Step 4.1.5.1.2

Multiply $- 0.05$ by $25$ .

$3060 + \frac{m (1 - 1.25)}{25} = 1700$

Step 4.1.5.1.3

Subtract $1.25$ from $1$ .

$3060 + \frac{m \cdot - 0.25}{25} = 1700$

Step 4.1.5.2

Move $- 0.25$ to the left of $m$ .

$3060 + \frac{- 0.25 \cdot m}{25} = 1700$

Step 4.1.5.3

Move the negative in front of the fraction.

$3060 - \frac{0.25 \cdot m}{25} = 1700$

Step 4.1.5.4

Factor $0.25$ out of $0.25 \cdot m$ .

$3060 - \frac{0.25 (m)}{25} = 1700$

Step 4.1.5.5

Factor $25$ out of $25$ .

$3060 - \frac{0.25 (m)}{25 (1)} = 1700$

Step 4.1.5.6

Separate fractions.

$3060 - (\frac{0.25}{25} \cdot \frac{m}{1}) = 1700$

Step 4.1.5.7

Divide $0.25$ by $25$ .

$3060 - (0.01 \frac{m}{1}) = 1700$

Step 4.1.5.8

Cancel the common factor of $0.01$ .

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Step 4.1.5.8.1

Factor $0.01$ out of $1$ .

$3060 - (0.01 \frac{m}{0.01 \cdot 100}) = 1700$

Step 4.1.5.8.2

Cancel the common factor.

$3060 - (0.01 \frac{m}{0.01 \cdot 100}) = 1700$

Step 4.1.5.8.3

Rewrite the expression.

$3060 - \frac{m}{100} = 1700$

Step 4.2

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

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Step 4.2.1

Subtract $3060$ from both sides of the equation.

$- \frac{m}{100} = 1700 - 3060$

Step 4.2.2

Subtract $3060$ from $1700$ .

$- \frac{m}{100} = - 1360$

Step 4.3

Multiply both sides of the equation by $- 100$ .

$- 100 (- \frac{m}{100}) = - 100 \cdot - 1360$

Step 4.4

Simplify both sides of the equation.

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Step 4.4.1

Simplify the left side.

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Step 4.4.1.1

Simplify $- 100 (- \frac{m}{100})$ .

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Step 4.4.1.1.1

Cancel the common factor of $100$ .

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Step 4.4.1.1.1.1

Move the leading negative in $- \frac{m}{100}$ into the numerator.

$- 100 \frac{- m}{100} = - 100 \cdot - 1360$

Step 4.4.1.1.1.2

Factor $100$ out of $- 100$ .

$100 (- 1) \frac{- m}{100} = - 100 \cdot - 1360$

Step 4.4.1.1.1.3

Cancel the common factor.

$100 \cdot - 1 \frac{- m}{100} = - 100 \cdot - 1360$

Step 4.4.1.1.1.4

Rewrite the expression.

$- - m = - 100 \cdot - 1360$

Step 4.4.1.1.2

Multiply.

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Step 4.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 m = - 100 \cdot - 1360$

Step 4.4.1.1.2.2

Multiply $m$ by $1$ .

$m = - 100 \cdot - 1360$

Step 4.4.2

Simplify the right side.

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Step 4.4.2.1

Multiply $- 100$ by $- 1360$ .

$m = 136000$