Basic Math Examples

$8 \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1

Simplify the left side.

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Step 1.1

Simplify $8 \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6}$ .

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Step 1.1.1

Convert $8 \frac{3}{4}$ 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.

$8 + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.1.2

Add $8$ and $\frac{3}{4}$ .

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Step 1.1.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.1.2.2

Combine $8$ and $\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $8$ by $4$ .

$\frac{32 + 3}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.1.2.4.2

Add $32$ and $3$ .

$\frac{35}{4} + 3 \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2

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

$\frac{35}{4} + 3 + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2.2

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

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Step 1.1.2.2.1

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

$\frac{35}{4} + 3 \cdot \frac{3}{3} + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2.2.2

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

$\frac{35}{4} + \frac{3 \cdot 3}{3} + \frac{2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{3 \cdot 3 + 2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $3$ by $3$ .

$\frac{35}{4} + \frac{9 + 2}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.2.2.4.2

Add $9$ and $2$ .

$\frac{35}{4} + \frac{11}{3} + 6 \frac{5}{6} = s i m p l i f y$

Step 1.1.3

Convert $6 \frac{5}{6}$ to an improper fraction.

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Step 1.1.3.1

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

$\frac{35}{4} + \frac{11}{3} + 6 + \frac{5}{6} = s i m p l i f y$

Step 1.1.3.2

Add $6$ and $\frac{5}{6}$ .

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Step 1.1.3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{35}{4} + \frac{11}{3} + 6 \cdot \frac{6}{6} + \frac{5}{6} = s i m p l i f y$

Step 1.1.3.2.2

Combine $6$ and $\frac{6}{6}$ .

$\frac{35}{4} + \frac{11}{3} + \frac{6 \cdot 6}{6} + \frac{5}{6} = s i m p l i f y$

Step 1.1.3.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{11}{3} + \frac{6 \cdot 6 + 5}{6} = s i m p l i f y$

Step 1.1.3.2.4

Simplify the numerator.

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Step 1.1.3.2.4.1

Multiply $6$ by $6$ .

$\frac{35}{4} + \frac{11}{3} + \frac{36 + 5}{6} = s i m p l i f y$

Step 1.1.3.2.4.2

Add $36$ and $5$ .

$\frac{35}{4} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Step 1.1.4

Find the common denominator.

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Step 1.1.4.1

Multiply $\frac{35}{4}$ by $\frac{3}{3}$ .

$\frac{35}{4} \cdot \frac{3}{3} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Step 1.1.4.2

Multiply $\frac{35}{4}$ by $\frac{3}{3}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11}{3} + \frac{41}{6} = s i m p l i f y$

Step 1.1.4.3

Multiply $\frac{11}{3}$ by $\frac{4}{4}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11}{3} \cdot \frac{4}{4} + \frac{41}{6} = s i m p l i f y$

Step 1.1.4.4

Multiply $\frac{11}{3}$ by $\frac{4}{4}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41}{6} = s i m p l i f y$

Step 1.1.4.5

Multiply $\frac{41}{6}$ by $\frac{2}{2}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41}{6} \cdot \frac{2}{2} = s i m p l i f y$

Step 1.1.4.6

Multiply $\frac{41}{6}$ by $\frac{2}{2}$ .

$\frac{35 \cdot 3}{4 \cdot 3} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Step 1.1.4.7

Reorder the factors of $4 \cdot 3$ .

$\frac{35 \cdot 3}{3 \cdot 4} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Step 1.1.4.8

Multiply $3$ by $4$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{3 \cdot 4} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Step 1.1.4.9

Multiply $3$ by $4$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{6 \cdot 2} = s i m p l i f y$

Step 1.1.4.10

Reorder the factors of $6 \cdot 2$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{2 \cdot 6} = s i m p l i f y$

Step 1.1.4.11

Multiply $2$ by $6$ .

$\frac{35 \cdot 3}{12} + \frac{11 \cdot 4}{12} + \frac{41 \cdot 2}{12} = s i m p l i f y$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{35 \cdot 3 + 11 \cdot 4 + 41 \cdot 2}{12} = s i m p l i f y$

Step 1.1.6

Simplify each term.

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Step 1.1.6.1

Multiply $35$ by $3$ .

$\frac{105 + 11 \cdot 4 + 41 \cdot 2}{12} = s i m p l i f y$

Step 1.1.6.2

Multiply $11$ by $4$ .

$\frac{105 + 44 + 41 \cdot 2}{12} = s i m p l i f y$

Step 1.1.6.3

Multiply $41$ by $2$ .

$\frac{105 + 44 + 82}{12} = s i m p l i f y$

Step 1.1.7

Reduce the expression by cancelling the common factors.

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Step 1.1.7.1

Add $105$ and $44$ .

$\frac{149 + 82}{12} = s i m p l i f y$

Step 1.1.7.2

Add $149$ and $82$ .

$\frac{231}{12} = s i m p l i f y$

Step 1.1.7.3

Cancel the common factor of $231$ and $12$ .

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Step 1.1.7.3.1

Factor $3$ out of $231$ .

$\frac{3 (77)}{12} = s i m p l i f y$

Step 1.1.7.3.2

Cancel the common factors.

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Step 1.1.7.3.2.1

Factor $3$ out of $12$ .

$\frac{3 \cdot 77}{3 \cdot 4} = s i m p l i f y$

Step 1.1.7.3.2.2

Cancel the common factor.

$\frac{3 \cdot 77}{3 \cdot 4} = s i m p l i f y$

Step 1.1.7.3.2.3

Rewrite the expression.

$\frac{77}{4} = s i m p l i f y$

Step 2

Simplify the right side.

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Step 2.1

Simplify $s i m p l i f y$ .

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Step 2.1.1

Multiply $s i m p l i$ .

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Step 2.1.1.1

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

$\frac{77}{4} = s m p l (i^{1} i) f y$

Step 2.1.1.2

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

$\frac{77}{4} = s m p l (i^{1} i^{1}) f y$

Step 2.1.1.3

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

$\frac{77}{4} = s m p l i^{1 + 1} f y$

Step 2.1.1.4

Add $1$ and $1$ .

$\frac{77}{4} = s m p l i^{2} f y$

Step 2.1.2

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

$\frac{77}{4} = s m p l \cdot - 1 f y$

Step 2.1.3

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

$\frac{77}{4} = - 1 \cdot (s m p l) f y$

Step 2.1.4

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

$\frac{77}{4} = - s m p l f y$

Step 3

Rewrite the equation as $- s m p l f y = \frac{77}{4}$ .

$- s m p l f y = \frac{77}{4}$

Step 4

Divide each term in $- s m p l f y = \frac{77}{4}$ by $- s m p l f$ and simplify.

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Step 4.1

Divide each term in $- s m p l f y = \frac{77}{4}$ by $- s m p l f$ .

$\frac{- s m p l f y}{- s m p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{s m p l f y}{s m p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.2

Cancel the common factor of $s$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{s m p l f y}{s m p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.2.2

Rewrite the expression.

$\frac{m p l f y}{m p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.3

Cancel the common factor of $m$ .

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Step 4.2.3.1

Cancel the common factor.

$\frac{m p l f y}{m p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.3.2

Rewrite the expression.

$\frac{p l f y}{p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.4

Cancel the common factor of $p$ .

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Step 4.2.4.1

Cancel the common factor.

$\frac{p l f y}{p l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.4.2

Rewrite the expression.

$\frac{l f y}{l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.5

Cancel the common factor of $l$ .

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Step 4.2.5.1

Cancel the common factor.

$\frac{l f y}{l f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.5.2

Rewrite the expression.

$\frac{f y}{f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.6

Cancel the common factor of $f$ .

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Step 4.2.6.1

Cancel the common factor.

$\frac{f y}{f} = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.2.6.2

Divide $y$ by $1$ .

$y = \frac{\frac{77}{4}}{- s m p l f}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{77}{4} \cdot \frac{1}{- s m p l f}$

Step 4.3.2

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

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Step 4.3.2.1

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

$y = \frac{77}{4} \cdot \frac{- 1 (- 1)}{- s m p l f}$

Step 4.3.2.2

Move the negative in front of the fraction.

$y = \frac{77}{4} (- \frac{1}{s m p l f})$

Step 4.3.3

Multiply $\frac{77}{4}$ by $\frac{1}{s m p l f}$ .

$y = - \frac{77}{4 s m p l f}$