Basic Math Examples

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

Step 1

Regroup terms.

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

Step 2

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

Tap for more steps...

Step 2.1

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 2.2

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

Tap for more steps...

Step 2.2.1

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 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $5$ by $3$ .

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

Step 2.2.4.2

Add $15$ and $1$ .

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

Step 3

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

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

Step 4

Factor $2$ out of $\frac{16 m}{3} - 30$ .

Tap for more steps...

Step 4.1

Factor $2$ out of $\frac{16 m}{3}$ .

$2 \frac{8 m}{3} - 30 - 1 \frac{1}{9} m - 18$

Step 4.2

Factor $2$ out of $- 30$ .

$2 \frac{8 m}{3} + 2 (- 15) - 1 \frac{1}{9} m - 18$

Step 4.3

Factor $2$ out of $2 \frac{8 m}{3} + 2 (- 15)$ .

$2 (\frac{8 m}{3} - 15) - 1 \frac{1}{9} m - 18$

Step 5

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

Tap for more steps...

Step 5.1

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

$2 (\frac{8 m}{3} - 15) - (1 + \frac{1}{9}) m - 18$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$2 (\frac{8 m}{3} - 15) - (\frac{9}{9} + \frac{1}{9}) m - 18$

Step 5.2.2

Combine the numerators over the common denominator.

$2 (\frac{8 m}{3} - 15) - \frac{9 + 1}{9} m - 18$

Step 5.2.3

Add $9$ and $1$ .

$2 (\frac{8 m}{3} - 15) - \frac{10}{9} m - 18$

Step 6

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

$2 (\frac{8 m}{3} - 15) - \frac{m \cdot 10}{9} - 18$

Step 7

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

$2 (\frac{8 m}{3} - 15) - \frac{10 \cdot m}{9} - 18$

Step 8

Multiply $10$ by $m$ .

$2 (\frac{8 m}{3} - 15) - \frac{10 m}{9} - 18$

Step 9

Rewrite $- \frac{10 m}{9} - 18$ in a factored form.

Tap for more steps...

Step 9.1

Factor $- 2$ out of $- \frac{10 m}{9} - 18$ .

Tap for more steps...

Step 9.1.1

Factor $- 2$ out of $- \frac{10 m}{9}$ .

$2 (\frac{8 m}{3} - 15) - 2 (- \frac{- 5 m}{9}) - 18$

Step 9.1.2

Factor $- 2$ out of $- 18$ .

$2 (\frac{8 m}{3} - 15) - 2 (- \frac{- 5 m}{9}) - 2 (9)$

Step 9.1.3

Factor $- 2$ out of $- 2 (- \frac{- 5 m}{9}) - 2 (9)$ .

$2 (\frac{8 m}{3} - 15) - 2 (- \frac{- 5 m}{9} + 9)$

Step 9.2

Move the negative in front of the fraction.

$2 (\frac{8 m}{3} - 15) - 2 (- - \frac{5 m}{9} + 9)$

Step 9.3

Multiply $- - \frac{5 m}{9}$ .

Tap for more steps...

Step 9.3.1

Multiply $- 1$ by $- 1$ .

$2 (\frac{8 m}{3} - 15) - 2 (1 \frac{5 m}{9} + 9)$

Step 9.3.2

Multiply $\frac{5 m}{9}$ by $1$ .

$2 (\frac{8 m}{3} - 15) - 2 (\frac{5 m}{9} + 9)$

Step 10

Factor $2$ out of $2 (\frac{8 m}{3} - 15) - 2 (\frac{5 m}{9} + 9)$ .

Tap for more steps...

Step 10.1

Factor $2$ out of $- 2 (\frac{5 m}{9} + 9)$ .

$2 (\frac{8 m}{3} - 15) + 2 (- (\frac{5 m}{9} + 9))$

Step 10.2

Factor $2$ out of $2 (\frac{8 m}{3} - 15) + 2 (- (\frac{5 m}{9} + 9))$ .

$2 (\frac{8 m}{3} - 15 - (\frac{5 m}{9} + 9))$

Step 11

Apply the distributive property.

$2 (\frac{8 m}{3} - 15 - \frac{5 m}{9} - 1 \cdot 9)$

Step 12

Multiply $- 1$ by $9$ .

$2 (\frac{8 m}{3} - 15 - \frac{5 m}{9} - 9)$

Step 13

To write $\frac{8 m}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 (\frac{8 m}{3} \cdot \frac{3}{3} - \frac{5 m}{9} - 15 - 9)$

Step 14

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

Tap for more steps...

Step 14.1

Multiply $\frac{8 m}{3}$ by $\frac{3}{3}$ .

$2 (\frac{8 m \cdot 3}{3 \cdot 3} - \frac{5 m}{9} - 15 - 9)$

Step 14.2

Multiply $3$ by $3$ .

$2 (\frac{8 m \cdot 3}{9} - \frac{5 m}{9} - 15 - 9)$

Step 15

Combine the numerators over the common denominator.

$2 (\frac{8 m \cdot 3 - 5 m}{9} - 15 - 9)$

Step 16

To write $- 15$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2 (\frac{8 m \cdot 3 - 5 m}{9} - 15 \cdot \frac{9}{9} - 9)$

Step 17

Combine $- 15$ and $\frac{9}{9}$ .

$2 (\frac{8 m \cdot 3 - 5 m}{9} + \frac{- 15 \cdot 9}{9} - 9)$

Step 18

Combine the numerators over the common denominator.

$2 (\frac{8 m \cdot 3 - 5 m - 15 \cdot 9}{9} - 9)$

Step 19

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

$2 (\frac{8 m \cdot 3 - 5 m - 15 \cdot 9}{9} - 9 \cdot \frac{9}{9})$

Step 20

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

$2 (\frac{8 m \cdot 3 - 5 m - 15 \cdot 9}{9} + \frac{- 9 \cdot 9}{9})$

Step 21

Combine the numerators over the common denominator.

$2 \frac{8 m \cdot 3 - 5 m - 15 \cdot 9 - 9 \cdot 9}{9}$

Step 22

Reorder terms.

$2 \frac{3 \cdot 8 m - 5 m - 9 \cdot 9 - 15 \cdot 9}{9}$

Step 23

Rewrite $\frac{3 \cdot 8 m - 5 m - 9 \cdot 9 - 15 \cdot 9}{9}$ in a factored form.

Tap for more steps...

Step 23.1

Multiply $3$ by $8$ .

$2 \frac{24 m - 5 m - 9 \cdot 9 - 15 \cdot 9}{9}$

Step 23.2

Multiply $- 9$ by $9$ .

$2 \frac{24 m - 5 m - 81 - 15 \cdot 9}{9}$

Step 23.3

Multiply $- 15$ by $9$ .

$2 \frac{24 m - 5 m - 81 - 135}{9}$

Step 23.4

Subtract $5 m$ from $24 m$ .

$2 \frac{19 m - 81 - 135}{9}$

Step 23.5

Subtract $135$ from $- 81$ .

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