Basic Math Examples

$(5 \frac{1}{3}) m - 30 - 1 \frac{1}{9} m - 18$

Step 1

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$(5 + \frac{1}{3}) m - 30 - 1 \frac{1}{9} m - 18$

Step 1.2

Add $5$ and $\frac{1}{3}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(5 \cdot \frac{3}{3} + \frac{1}{3}) m - 30 - 1 \frac{1}{9} m - 18$

Step 1.2.2

Combine $5$ and $\frac{3}{3}$ .

$(\frac{5 \cdot 3}{3} + \frac{1}{3}) m - 30 - 1 \frac{1}{9} m - 18$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 1}{3} m - 30 - 1 \frac{1}{9} m - 18$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $3$ .

$\frac{15 + 1}{3} m - 30 - 1 \frac{1}{9} m - 18$

Step 1.2.4.2

Add $15$ and $1$ .

$\frac{16}{3} m - 30 - 1 \frac{1}{9} m - 18$

Step 2

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

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Step 2.1

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

$\frac{16}{3} m - 30 - (1 + \frac{1}{9}) m - 18$

Step 2.2

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

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Step 2.2.1

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

$\frac{16}{3} m - 30 - (\frac{9}{9} + \frac{1}{9}) m - 18$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{16}{3} m - 30 - \frac{9 + 1}{9} m - 18$

Step 2.2.3

Add $9$ and $1$ .

$\frac{16}{3} m - 30 - \frac{10}{9} m - 18$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{16}{3}$ and $m$ .

$\frac{16 m}{3} - 30 - \frac{10}{9} m - 18$

Step 3.2

Combine $m$ and $\frac{10}{9}$ .

$\frac{16 m}{3} - 30 - \frac{m \cdot 10}{9} - 18$

Step 3.3

Move $10$ to the left of $m$ .

$\frac{16 m}{3} - 30 - \frac{10 m}{9} - 18$

Step 4

To write $\frac{16 m}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16 m}{3} \cdot \frac{3}{3} - \frac{10 m}{9} - 30 - 18$

Step 5

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{16 m}{3}$ by $\frac{3}{3}$ .

$\frac{16 m \cdot 3}{3 \cdot 3} - \frac{10 m}{9} - 30 - 18$

Step 5.2

Multiply $3$ by $3$ .

$\frac{16 m \cdot 3}{9} - \frac{10 m}{9} - 30 - 18$

Step 6

Combine the numerators over the common denominator.

$\frac{16 m \cdot 3 - 10 m}{9} - 30 - 18$

Step 7

Find the common denominator.

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Step 7.1

Write $- 30$ as a fraction with denominator $1$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30}{1} - 18$

Step 7.2

Multiply $\frac{- 30}{1}$ by $\frac{9}{9}$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30}{1} \cdot \frac{9}{9} - 18$

Step 7.3

Multiply $\frac{- 30}{1}$ by $\frac{9}{9}$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30 \cdot 9}{9} - 18$

Step 7.4

Write $- 18$ as a fraction with denominator $1$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30 \cdot 9}{9} + \frac{- 18}{1}$

Step 7.5

Multiply $\frac{- 18}{1}$ by $\frac{9}{9}$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30 \cdot 9}{9} + \frac{- 18}{1} \cdot \frac{9}{9}$

Step 7.6

Multiply $\frac{- 18}{1}$ by $\frac{9}{9}$ .

$\frac{16 m \cdot 3 - 10 m}{9} + \frac{- 30 \cdot 9}{9} + \frac{- 18 \cdot 9}{9}$

Step 8

Combine the numerators over the common denominator.

$\frac{16 m \cdot 3 - 10 m - 30 \cdot 9 - 18 \cdot 9}{9}$

Step 9

Simplify each term.

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Step 9.1

Multiply $3$ by $16$ .

$\frac{48 m - 10 m - 30 \cdot 9 - 18 \cdot 9}{9}$

Step 9.2

Multiply $- 30$ by $9$ .

$\frac{48 m - 10 m - 270 - 18 \cdot 9}{9}$

Step 9.3

Multiply $- 18$ by $9$ .

$\frac{48 m - 10 m - 270 - 162}{9}$

Step 10

Simplify terms.

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Step 10.1

Subtract $10 m$ from $48 m$ .

$\frac{38 m - 270 - 162}{9}$

Step 10.2

Subtract $162$ from $- 270$ .

$\frac{38 m - 432}{9}$

Step 10.3

Factor $2$ out of $38 m - 432$ .

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Step 10.3.1

Factor $2$ out of $38 m$ .

$\frac{2 (19 m) - 432}{9}$

Step 10.3.2

Factor $2$ out of $- 432$ .

$\frac{2 (19 m) + 2 (- 216)}{9}$

Step 10.3.3

Factor $2$ out of $2 (19 m) + 2 (- 216)$ .

$\frac{2 (19 m - 216)}{9}$