Basic Math Examples

$4 \frac{2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1

Simplify the left side.

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Step 1.1

Simplify $4 \frac{2}{3} + 1 \frac{1}{6}$ .

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Step 1.1.1

Convert $4 \frac{2}{3}$ 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.

$4 + \frac{2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.1.2

Add $4$ and $\frac{2}{3}$ .

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Step 1.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 \cdot \frac{3}{3} + \frac{2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.1.2.2

Combine $4$ and $\frac{3}{3}$ .

$\frac{4 \cdot 3}{3} + \frac{2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $4$ by $3$ .

$\frac{12 + 2}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.1.2.4.2

Add $12$ and $2$ .

$\frac{14}{3} + 1 \frac{1}{6} = s i m l i f y$

Step 1.1.2

Convert $1 \frac{1}{6}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{14}{3} + 1 + \frac{1}{6} = s i m l i f y$

Step 1.1.2.2

Add $1$ and $\frac{1}{6}$ .

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Step 1.1.2.2.1

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

$\frac{14}{3} + \frac{6}{6} + \frac{1}{6} = s i m l i f y$

Step 1.1.2.2.2

Combine the numerators over the common denominator.

$\frac{14}{3} + \frac{6 + 1}{6} = s i m l i f y$

Step 1.1.2.2.3

Add $6$ and $1$ .

$\frac{14}{3} + \frac{7}{6} = s i m l i f y$

Step 1.1.3

To write $\frac{14}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{14}{3} \cdot \frac{2}{2} + \frac{7}{6} = s i m l i f y$

Step 1.1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.4.1

Multiply $\frac{14}{3}$ by $\frac{2}{2}$ .

$\frac{14 \cdot 2}{3 \cdot 2} + \frac{7}{6} = s i m l i f y$

Step 1.1.4.2

Multiply $3$ by $2$ .

$\frac{14 \cdot 2}{6} + \frac{7}{6} = s i m l i f y$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{14 \cdot 2 + 7}{6} = s i m l i f y$

Step 1.1.6

Simplify the numerator.

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Step 1.1.6.1

Multiply $14$ by $2$ .

$\frac{28 + 7}{6} = s i m l i f y$

Step 1.1.6.2

Add $28$ and $7$ .

$\frac{35}{6} = s i m l i f y$

Step 2

Simplify the right side.

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Step 2.1

Simplify $s i m l i f y$ .

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Step 2.1.1

Multiply $s i m l i$ .

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Step 2.1.1.1

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

$\frac{35}{6} = s m l (i^{1} i) f y$

Step 2.1.1.2

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

$\frac{35}{6} = s m l (i^{1} i^{1}) f y$

Step 2.1.1.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{35}{6} = s m l i^{1 + 1} f y$

Step 2.1.1.4

Add $1$ and $1$ .

$\frac{35}{6} = s m l i^{2} f y$

Step 2.1.2

Rewrite $i^{2}$ as $- 1$ .

$\frac{35}{6} = s m l \cdot - 1 f y$

Step 2.1.3

Move $- 1$ to the left of $s m l$ .

$\frac{35}{6} = - 1 \cdot (s m l) f y$

Step 2.1.4

Rewrite $- 1 (s m l)$ as $- (s m l)$ .

$\frac{35}{6} = - s m l f y$

Step 3

Rewrite the equation as $- s m l f y = \frac{35}{6}$ .

$- s m l f y = \frac{35}{6}$

Step 4

Divide each term in $- s m l f y = \frac{35}{6}$ by $- s m l f$ and simplify.

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Step 4.1

Divide each term in $- s m l f y = \frac{35}{6}$ by $- s m l f$ .

$\frac{- s m l f y}{- s m l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{s m l f y}{s m l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.2

Cancel the common factor of $s$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{s m l f y}{s m l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.2.2

Rewrite the expression.

$\frac{m l f y}{m l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.3

Cancel the common factor of $m$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{m l f y}{m l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.3.2

Rewrite the expression.

$\frac{l f y}{l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.4

Cancel the common factor of $l$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{l f y}{l f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.4.2

Rewrite the expression.

$\frac{f y}{f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.5

Cancel the common factor of $f$ .

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Step 4.2.5.1

Cancel the common factor.

$\frac{f y}{f} = \frac{\frac{35}{6}}{- s m l f}$

Step 4.2.5.2

Divide $y$ by $1$ .

$y = \frac{\frac{35}{6}}{- s m l f}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{35}{6} \cdot \frac{1}{- s m l f}$

Step 4.3.2

Cancel the common factor of $1$ and $- 1$ .

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Step 4.3.2.1

Rewrite $1$ as $- 1 (- 1)$ .

$y = \frac{35}{6} \cdot \frac{- 1 (- 1)}{- s m l f}$

Step 4.3.2.2

Move the negative in front of the fraction.

$y = \frac{35}{6} (- \frac{1}{s m l f})$

Step 4.3.3

Multiply $\frac{35}{6}$ by $\frac{1}{s m l f}$ .

$y = - \frac{35}{6 s m l f}$