Basic Math Examples

$1 \frac{9}{18} \cdot (l e s \cdot s t h) = 3 \frac{7}{9}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $1 \frac{9}{18} \cdot (l e s \cdot s t h)$ .

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Step 1.1.1

Convert $1 \frac{9}{18}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(1 + \frac{9}{18}) \cdot (l e s \cdot s t h) = 3 \frac{7}{9}$

Step 1.1.1.2

Add $1$ and $\frac{9}{18}$ .

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Step 1.1.1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{18}{18} + \frac{9}{18}) \cdot (l e s \cdot s t h) = 3 \frac{7}{9}$

Step 1.1.1.2.2

Combine the numerators over the common denominator.

$\frac{18 + 9}{18} \cdot (l e s \cdot s t h) = 3 \frac{7}{9}$

Step 1.1.1.2.3

Add $18$ and $9$ .

$\frac{27}{18} \cdot (l e s \cdot s t h) = 3 \frac{7}{9}$

Step 1.1.2

Multiply $s$ by $s$ by adding the exponents.

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Step 1.1.2.1

Move $s$ .

$\frac{27}{18} \cdot (l e (s \cdot s) t h) = 3 \frac{7}{9}$

Step 1.1.2.2

Multiply $s$ by $s$ .

$\frac{27}{18} \cdot (l e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.3

Cancel the common factor of $27$ and $18$ .

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Step 1.1.3.1

Factor $9$ out of $27$ .

$\frac{9 (3)}{18} \cdot (l e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor $9$ out of $18$ .

$\frac{9 \cdot 3}{9 \cdot 2} \cdot (l e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.3.2.2

Cancel the common factor.

$\frac{9 \cdot 3}{9 \cdot 2} \cdot (l e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.3.2.3

Rewrite the expression.

$\frac{3}{2} \cdot (l e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.4

Multiply $\frac{3}{2} (l e s^{2} t h)$ .

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Step 1.1.4.1

Combine $l$ and $\frac{3}{2}$ .

$\frac{l \cdot 3}{2} (e s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.4.2

Combine $e$ and $\frac{l \cdot 3}{2}$ .

$\frac{e (l \cdot 3)}{2} (s^{2} t h) = 3 \frac{7}{9}$

Step 1.1.4.3

Combine $s^{2}$ and $\frac{e (l \cdot 3)}{2}$ .

$\frac{s^{2} (e (l \cdot 3))}{2} (t h) = 3 \frac{7}{9}$

Step 1.1.4.4

Combine $t$ and $\frac{s^{2} (e (l \cdot 3))}{2}$ .

$\frac{t (s^{2} (e (l \cdot 3)))}{2} h = 3 \frac{7}{9}$

Step 1.1.4.5

Combine $\frac{t (s^{2} (e (l \cdot 3)))}{2}$ and $h$ .

$\frac{t (s^{2} (e (l \cdot 3))) h}{2} = 3 \frac{7}{9}$

Step 1.1.5

Move $3$ to the left of $t s^{2} e l$ .

$\frac{3 t s^{2} e l h}{2} = 3 \frac{7}{9}$

Step 2

Simplify the right side.

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Step 2.1

Convert $3 \frac{7}{9}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{3 t s^{2} e l h}{2} = 3 + \frac{7}{9}$

Step 2.1.2

Add $3$ and $\frac{7}{9}$ .

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Step 2.1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{3 t s^{2} e l h}{2} = 3 \cdot \frac{9}{9} + \frac{7}{9}$

Step 2.1.2.2

Combine $3$ and $\frac{9}{9}$ .

$\frac{3 t s^{2} e l h}{2} = \frac{3 \cdot 9}{9} + \frac{7}{9}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{3 t s^{2} e l h}{2} = \frac{3 \cdot 9 + 7}{9}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $3$ by $9$ .

$\frac{3 t s^{2} e l h}{2} = \frac{27 + 7}{9}$

Step 2.1.2.4.2

Add $27$ and $7$ .

$\frac{3 t s^{2} e l h}{2} = \frac{34}{9}$

Step 3

Multiply both sides of the equation by $\frac{1}{3 \frac{e}{2}}$ .

$\frac{1}{3 \frac{e}{2}} \cdot \frac{3 t s^{2} e l h}{2} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{1}{3 \frac{e}{2}} \cdot \frac{3 t s^{2} e l h}{2}$ .

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Step 4.1.1.1

Combine.

$\frac{1 (3 t s^{2} e l h)}{3 \frac{e}{2} \cdot 2} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

$\frac{1 (3 t s^{2} e l h)}{3 \frac{e}{2} \cdot 2} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.2.2

Rewrite the expression.

$\frac{1 (t s^{2} e l h)}{\frac{e}{2} \cdot 2} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.3

Multiply $t$ by $1$ .

$\frac{t s^{2} e l h}{\frac{e}{2} \cdot 2} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.4

Combine $\frac{e}{2}$ and $2$ .

$\frac{t s^{2} e l h}{\frac{e \cdot 2}{2}} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.5

Reduce the expression by cancelling the common factors.

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Step 4.1.1.5.1

Reduce the expression $\frac{e \cdot 2}{2}$ by cancelling the common factors.

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Step 4.1.1.5.1.1

Cancel the common factor.

$\frac{t s^{2} e l h}{\frac{e \cdot 2}{2}} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.5.1.2

Rewrite the expression.

$\frac{t s^{2} e l h}{\frac{e}{1}} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.5.2

Divide $e$ by $1$ .

$\frac{t s^{2} e l h}{e} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.6

Cancel the common factor of $e$ .

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Step 4.1.1.6.1

Cancel the common factor.

$\frac{t s^{2} e l h}{e} = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.1.1.6.2

Divide $t s^{2} l h$ by $1$ .

$t s^{2} l h = \frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{1}{3 \frac{e}{2}} \cdot \frac{34}{9}$ .

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Step 4.2.1.1

Combine $3$ and $\frac{e}{2}$ .

$t s^{2} l h = \frac{1}{\frac{3 e}{2}} \cdot \frac{34}{9}$

Step 4.2.1.2

Multiply the numerator by the reciprocal of the denominator.

$t s^{2} l h = 1 \frac{2}{3 e} \frac{34}{9}$

Step 4.2.1.3

Multiply $\frac{2}{3 e}$ by $1$ .

$t s^{2} l h = \frac{2}{3 e} \cdot \frac{34}{9}$

Step 4.2.1.4

Multiply $\frac{2}{3 e} \cdot \frac{34}{9}$ .

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Step 4.2.1.4.1

Multiply $\frac{2}{3 e}$ by $\frac{34}{9}$ .

$t s^{2} l h = \frac{2 \cdot 34}{3 e \cdot 9}$

Step 4.2.1.4.2

Multiply $2$ by $34$ .

$t s^{2} l h = \frac{68}{3 e \cdot 9}$

Step 4.2.1.4.3

Multiply $9$ by $3$ .

$t s^{2} l h = \frac{68}{27 e}$

Step 5

Divide each term in $t s^{2} l h = \frac{68}{27 e}$ by $s^{2} l h$ and simplify.

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Step 5.1

Divide each term in $t s^{2} l h = \frac{68}{27 e}$ by $s^{2} l h$ .

$\frac{t s^{2} l h}{s^{2} l h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $s^{2}$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{t s^{2} l h}{s^{2} l h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2.1.2

Rewrite the expression.

$\frac{t l h}{l h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2.2

Cancel the common factor of $l$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{t l h}{l h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2.2.2

Rewrite the expression.

$\frac{t h}{h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2.3

Cancel the common factor of $h$ .

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Step 5.2.3.1

Cancel the common factor.

$\frac{t h}{h} = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.2.3.2

Divide $t$ by $1$ .

$t = \frac{\frac{68}{27 e}}{s^{2} l h}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$t = \frac{68}{27 e} \cdot \frac{1}{s^{2} l h}$

Step 5.3.2

Combine.

$t = \frac{68 \cdot 1}{27 e (s^{2} l h)}$

Step 5.3.3

Multiply $68$ by $1$ .

$t = \frac{68}{27 e s^{2} l h}$