Algebra Examples

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

Step 1

Convert $1 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{2}{5}) m - \frac{3}{5} \cdot (\frac{2}{3} m + 1)$

Step 1.2

Add $1$ and $\frac{2}{5}$ .

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Step 1.2.1

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

$(\frac{5}{5} + \frac{2}{5}) m - \frac{3}{5} \cdot (\frac{2}{3} m + 1)$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{5 + 2}{5} m - \frac{3}{5} \cdot (\frac{2}{3} m + 1)$

Step 1.2.3

Add $5$ and $2$ .

$\frac{7}{5} m - \frac{3}{5} \cdot (\frac{2}{3} m + 1)$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{7}{5}$ and $m$ .

$\frac{7 m}{5} - \frac{3}{5} \cdot (\frac{2}{3} m + 1)$

Step 2.2

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

$\frac{7 m}{5} - \frac{3}{5} \cdot (\frac{2 m}{3} + 1)$

Step 2.3

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

$\frac{7 m}{5} - \frac{3}{5} \cdot (\frac{2 m}{3} + \frac{3}{3})$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 m}{5} - \frac{3}{5} \cdot \frac{2 m + 3}{3}$

Step 2.5

Cancel the common factor of $3$ .

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Step 2.5.1

Move the leading negative in $- \frac{3}{5}$ into the numerator.

$\frac{7 m}{5} + \frac{- 3}{5} \cdot \frac{2 m + 3}{3}$

Step 2.5.2

Factor $3$ out of $- 3$ .

$\frac{7 m}{5} + \frac{3 (- 1)}{5} \cdot \frac{2 m + 3}{3}$

Step 2.5.3

Cancel the common factor.

$\frac{7 m}{5} + \frac{3 \cdot - 1}{5} \cdot \frac{2 m + 3}{3}$

Step 2.5.4

Rewrite the expression.

$\frac{7 m}{5} + \frac{- 1}{5} \cdot (2 m + 3)$

Step 2.6

Move the negative in front of the fraction.

$\frac{7 m}{5} - \frac{1}{5} \cdot (2 m + 3)$

Step 2.7

Apply the distributive property.

$\frac{7 m}{5} - \frac{1}{5} (2 m) - \frac{1}{5} \cdot 3$

Step 2.8

Multiply $- \frac{1}{5} (2 m)$ .

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Step 2.8.1

Multiply $2$ by $- 1$ .

$\frac{7 m}{5} - 2 (\frac{1}{5}) m - \frac{1}{5} \cdot 3$

Step 2.8.2

Combine $- 2$ and $\frac{1}{5}$ .

$\frac{7 m}{5} + \frac{- 2}{5} m - \frac{1}{5} \cdot 3$

Step 2.8.3

Combine $\frac{- 2}{5}$ and $m$ .

$\frac{7 m}{5} + \frac{- 2 m}{5} - \frac{1}{5} \cdot 3$

Step 2.9

Multiply $- \frac{1}{5} \cdot 3$ .

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Step 2.9.1

Multiply $3$ by $- 1$ .

$\frac{7 m}{5} + \frac{- 2 m}{5} - 3 (\frac{1}{5})$

Step 2.9.2

Combine $- 3$ and $\frac{1}{5}$ .

$\frac{7 m}{5} + \frac{- 2 m}{5} + \frac{- 3}{5}$

Step 2.10

Combine the numerators over the common denominator.

$\frac{7 m}{5} + \frac{- 2 m - 3}{5}$

Step 3

Simplify terms.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{7 m - 2 m - 3}{5}$

Step 3.2

Subtract $2 m$ from $7 m$ .

$\frac{5 m - 3}{5}$