Basic Math Examples

$0.9 = \frac{4 \cdot \frac{8388608}{R}}{0.0047652 + \frac{8388608}{R}}$

Step 1

Rewrite the equation as $\frac{4 \cdot \frac{8388608}{R}}{0.0047652 + \frac{8388608}{R}} = 0.9$ .

$\frac{4 \cdot \frac{8388608}{R}}{0.0047652 + \frac{8388608}{R}} = 0.9$

Step 2

Factor each term.

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Step 2.1

Factor $0.0000004$ out of $0.0047652 + \frac{8388608}{R}$ .

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Step 2.1.1

Factor $0.0000004$ out of $0.0047652$ .

$\frac{4 \cdot \frac{8388608}{R}}{0.0000004 (11913) + \frac{8388608}{R}} = 0.9$

Step 2.1.2

Factor $0.0000004$ out of $\frac{8388608}{R}$ .

$\frac{4 \cdot \frac{8388608}{R}}{0.0000004 \cdot 11913 + 0.0000004 \frac{20971520000000}{R}} = 0.9$

Step 2.1.3

Factor $0.0000004$ out of $0.0000004 \cdot 11913 + 0.0000004 \frac{20971520000000}{R}$ .

$\frac{4 \cdot \frac{8388608}{R}}{0.0000004 \cdot (11913 + \frac{20971520000000}{R})} = 0.9$

Step 2.1.4

Multiply $0.0000004$ by $11913 + \frac{20971520000000}{R}$ .

$\frac{4 \cdot \frac{8388608}{R}}{0.0000004 (11913 + \frac{20971520000000}{R})} = 0.9$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Multiply $4$ by $\frac{8388608}{R}$ .

$\frac{4 \frac{8388608}{R}}{0.0000004 (11913 + \frac{20971520000000}{R})} = 0.9$

Step 2.2.2

Combine $4$ and $\frac{8388608}{R}$ .

$\frac{\frac{4 \cdot 8388608}{R}}{0.0000004 (11913 + \frac{20971520000000}{R})} = 0.9$

Step 2.3

Simplify the denominator.

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Step 2.3.1

To write $11913$ as a fraction with a common denominator, multiply by $\frac{R}{R}$ .

$\frac{\frac{4 \cdot 8388608}{R}}{0.0000004 (\frac{11913 R}{R} + \frac{20971520000000}{R})} = 0.9$

Step 2.3.2

Combine the numerators over the common denominator.

$\frac{\frac{4 \cdot 8388608}{R}}{0.0000004 \frac{11913 R + 20971520000000}{R}} = 0.9$

Step 2.4

Multiply $4$ by $8388608$ .

$\frac{\frac{33554432}{R}}{0.0000004 \frac{11913 R + 20971520000000}{R}} = 0.9$

Step 2.5

Combine $0.0000004$ and $\frac{11913 R + 20971520000000}{R}$ .

$\frac{\frac{33554432}{R}}{\frac{0.0000004 (11913 R + 20971520000000)}{R}} = 0.9$

Step 2.6

Multiply the numerator by the reciprocal of the denominator.

$\frac{33554432}{R} \cdot \frac{R}{0.0000004 (11913 R + 20971520000000)} = 0.9$

Step 2.7

Cancel the common factor of $0.0000004$ .

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Step 2.7.1

Factor $0.0000004$ out of $33554432$ .

$\frac{0.0000004 (83886080000000)}{R} \cdot \frac{R}{0.0000004 (11913 R + 20971520000000)} = 0.9$

Step 2.7.2

Cancel the common factor.

$\frac{0.0000004 \cdot 83886080000000}{R} \cdot \frac{R}{0.0000004 (11913 R + 20971520000000)} = 0.9$

Step 2.7.3

Rewrite the expression.

$\frac{83886080000000}{R} \cdot \frac{R}{11913 R + 20971520000000} = 0.9$

Step 2.8

Cancel the common factor of $R$ .

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Step 2.8.1

Cancel the common factor.

$\frac{83886080000000}{R} \cdot \frac{R}{11913 R + 20971520000000} = 0.9$

Step 2.8.2

Rewrite the expression.

$83886080000000 \frac{1}{11913 R + 20971520000000} = 0.9$

Step 2.9

Combine $83886080000000$ and $\frac{1}{11913 R + 20971520000000}$ .

$\frac{83886080000000}{11913 R + 20971520000000} = 0.9$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

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

$11913 R + 20971520000000, 1$

Step 3.2

Remove parentheses.

$11913 R + 20971520000000, 1$

Step 3.3

The LCM of one and any expression is the expression.

$11913 R + 20971520000000$

Step 4

Multiply each term in $\frac{83886080000000}{11913 R + 20971520000000} = 0.9$ by $11913 R + 20971520000000$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{83886080000000}{11913 R + 20971520000000} = 0.9$ by $11913 R + 20971520000000$ .

$\frac{83886080000000}{11913 R + 20971520000000} (11913 R + 20971520000000) = 0.9 (11913 R + 20971520000000)$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $11913 R + 20971520000000$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{83886080000000}{11913 R + 20971520000000} (11913 R + 20971520000000) = 0.9 (11913 R + 20971520000000)$

Step 4.2.1.2

Rewrite the expression.

$83886080000000 = 0.9 (11913 R + 20971520000000)$

Step 4.3

Simplify the right side.

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Step 4.3.1

Apply the distributive property.

$83886080000000 = 0.9 (11913 R) + 0.9 \cdot 20971520000000$

Step 4.3.2

Multiply.

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Step 4.3.2.1

Multiply $11913$ by $0.9$ .

$83886080000000 = 10721.7 R + 0.9 \cdot 20971520000000$

Step 4.3.2.2

Multiply $0.9$ by $20971520000000$ .

$83886080000000 = 10721.7 R + 18874368000000$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $10721.7 R + 18874368000000 = 83886080000000$ .

$10721.7 R + 18874368000000 = 83886080000000$

Step 5.2

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

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Step 5.2.1

Subtract $18874368000000$ from both sides of the equation.

$10721.7 R = 83886080000000 - 18874368000000$

Step 5.2.2

Subtract $18874368000000$ from $83886080000000$ .

$10721.7 R = 65011712000000$

Step 5.3

Divide each term in $10721.7 R = 65011712000000$ by $10721.7$ and simplify.

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Step 5.3.1

Divide each term in $10721.7 R = 65011712000000$ by $10721.7$ .

$\frac{10721.7 R}{10721.7} = \frac{65011712000000}{10721.7}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $10721.7$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{10721.7 R}{10721.7} = \frac{65011712000000}{10721.7}$

Step 5.3.2.1.2

Divide $R$ by $1$ .

$R = \frac{65011712000000}{10721.7}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $65011712000000$ by $10721.7$ .

$R = 6063563800.5167091$