Basic Math Examples

$\frac{n}{\frac{35}{8}} = \frac{64}{\frac{35}{200}}$

Step 1

Multiply both sides of the equation by $\frac{35}{8}$ .

$\frac{35}{8} \cdot \frac{n}{\frac{35}{8}} = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{35}{8} \cdot \frac{n}{\frac{35}{8}}$ .

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Step 2.1.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{35}{8} (n \frac{8}{35}) = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.2

Combine $n$ and $\frac{8}{35}$ .

$\frac{35}{8} \cdot \frac{n \cdot 8}{35} = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.3

Cancel the common factor of $35$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{35}{8} \cdot \frac{n \cdot 8}{35} = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{1}{8} (n \cdot 8) = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.4

Cancel the common factor of $8$ .

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Step 2.1.1.4.1

Factor $8$ out of $n \cdot 8$ .

$\frac{1}{8} (8 \cdot n) = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{1}{8} (8 \cdot n) = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.1.1.4.3

Rewrite the expression.

$n = \frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{35}{8} \cdot \frac{64}{\frac{35}{200}}$ .

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Step 2.2.1.1

Cancel the common factor of $8$ .

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Step 2.2.1.1.1

Factor $8$ out of $64$ .

$n = \frac{35}{8} \cdot \frac{8 (8)}{\frac{35}{200}}$

Step 2.2.1.1.2

Cancel the common factor.

$n = \frac{35}{8} \cdot \frac{8 \cdot 8}{\frac{35}{200}}$

Step 2.2.1.1.3

Rewrite the expression.

$n = 35 \frac{8}{\frac{35}{200}}$

Step 2.2.1.2

Combine $35$ and $\frac{8}{\frac{35}{200}}$ .

$n = \frac{35 \cdot 8}{\frac{35}{200}}$

Step 2.2.1.3

Multiply $35$ by $8$ .

$n = \frac{280}{\frac{35}{200}}$

Step 2.2.1.4

Cancel the common factor of $35$ and $200$ .

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Step 2.2.1.4.1

Factor $5$ out of $35$ .

$n = \frac{280}{\frac{5 (7)}{200}}$

Step 2.2.1.4.2

Cancel the common factors.

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Step 2.2.1.4.2.1

Factor $5$ out of $200$ .

$n = \frac{280}{\frac{5 \cdot 7}{5 \cdot 40}}$

Step 2.2.1.4.2.2

Cancel the common factor.

$n = \frac{280}{\frac{5 \cdot 7}{5 \cdot 40}}$

Step 2.2.1.4.2.3

Rewrite the expression.

$n = \frac{280}{\frac{7}{40}}$

Step 2.2.1.5

Multiply the numerator by the reciprocal of the denominator.

$n = 280 (\frac{40}{7})$

Step 2.2.1.6

Cancel the common factor of $7$ .

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Step 2.2.1.6.1

Factor $7$ out of $280$ .

$n = 7 (40) \frac{40}{7}$

Step 2.2.1.6.2

Cancel the common factor.

$n = 7 \cdot 40 \frac{40}{7}$

Step 2.2.1.6.3

Rewrite the expression.

$n = 40 \cdot 40$

Step 2.2.1.7

Multiply $40$ by $40$ .

$n = 1600$