Basic Math Examples

$- 2 \frac{1}{4} \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1

Simplify the left side.

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Step 1.1

Simplify $- 2 \frac{1}{4} \cdot m - \frac{989}{120}$ .

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Step 1.1.1

Convert $2 \frac{1}{4}$ 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.

$- (2 + \frac{1}{4}) \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{1}{4}) \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{1}{4}) \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 4 + 1}{4} \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 1}{4} \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.1.2.4.2

Add $8$ and $1$ .

$- \frac{9}{4} \cdot m - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.2

Simplify each term.

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Step 1.1.2.1

Combine $m$ and $\frac{9}{4}$ .

$- \frac{m \cdot 9}{4} - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 1.1.2.2

Move $9$ to the left of $m$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{17}{6} \cdot (m + \frac{13}{5})$

Step 2

Simplify the right side.

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Step 2.1

Simplify $- \frac{17}{6} \cdot (m + \frac{13}{5})$ .

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Step 2.1.1

Apply the distributive property.

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{17}{6} m - \frac{17}{6} \cdot \frac{13}{5}$

Step 2.1.2

Combine $m$ and $\frac{17}{6}$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{m \cdot 17}{6} - \frac{17}{6} \cdot \frac{13}{5}$

Step 2.1.3

Multiply $- \frac{17}{6} \cdot \frac{13}{5}$ .

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Step 2.1.3.1

Multiply $\frac{13}{5}$ by $\frac{17}{6}$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{m \cdot 17}{6} - \frac{13 \cdot 17}{5 \cdot 6}$

Step 2.1.3.2

Multiply $13$ by $17$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{m \cdot 17}{6} - \frac{221}{5 \cdot 6}$

Step 2.1.3.3

Multiply $5$ by $6$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{m \cdot 17}{6} - \frac{221}{30}$

Step 2.1.4

Move $17$ to the left of $m$ .

$- \frac{9 m}{4} - \frac{989}{120} = - \frac{17 m}{6} - \frac{221}{30}$

Step 3

Move all terms containing $m$ to the left side of the equation.

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Step 3.1

Add $\frac{17 m}{6}$ to both sides of the equation.

$- \frac{9 m}{4} - \frac{989}{120} + \frac{17 m}{6} = - \frac{221}{30}$

Step 3.2

To write $- \frac{9 m}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{9 m}{4} \cdot \frac{3}{3} + \frac{17 m}{6} - \frac{989}{120} = - \frac{221}{30}$

Step 3.3

To write $\frac{17 m}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9 m}{4} \cdot \frac{3}{3} + \frac{17 m}{6} \cdot \frac{2}{2} - \frac{989}{120} = - \frac{221}{30}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{9 m}{4}$ by $\frac{3}{3}$ .

$- \frac{9 m \cdot 3}{4 \cdot 3} + \frac{17 m}{6} \cdot \frac{2}{2} - \frac{989}{120} = - \frac{221}{30}$

Step 3.4.2

Multiply $4$ by $3$ .

$- \frac{9 m \cdot 3}{12} + \frac{17 m}{6} \cdot \frac{2}{2} - \frac{989}{120} = - \frac{221}{30}$

Step 3.4.3

Multiply $\frac{17 m}{6}$ by $\frac{2}{2}$ .

$- \frac{9 m \cdot 3}{12} + \frac{17 m \cdot 2}{6 \cdot 2} - \frac{989}{120} = - \frac{221}{30}$

Step 3.4.4

Multiply $6$ by $2$ .

$- \frac{9 m \cdot 3}{12} + \frac{17 m \cdot 2}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 9 m \cdot 3 + 17 m \cdot 2}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $m$ out of $- 9 m \cdot 3 + 17 m \cdot 2$ .

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Step 3.6.1.1.1

Factor $m$ out of $- 9 m \cdot 3$ .

$\frac{m (- 9 \cdot 3) + 17 m \cdot 2}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.1.1.2

Factor $m$ out of $17 m \cdot 2$ .

$\frac{m (- 9 \cdot 3) + m (17 \cdot 2)}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.1.1.3

Factor $m$ out of $m (- 9 \cdot 3) + m (17 \cdot 2)$ .

$\frac{m (- 9 \cdot 3 + 17 \cdot 2)}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.1.2

Multiply $- 9$ by $3$ .

$\frac{m (- 27 + 17 \cdot 2)}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.1.3

Multiply $17$ by $2$ .

$\frac{m (- 27 + 34)}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.1.4

Add $- 27$ and $34$ .

$\frac{m \cdot 7}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 3.6.2

Move $7$ to the left of $m$ .

$\frac{7 m}{12} - \frac{989}{120} = - \frac{221}{30}$

Step 4

Move all terms not containing $m$ to the right side of the equation.

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Step 4.1

Add $\frac{989}{120}$ to both sides of the equation.

$\frac{7 m}{12} = - \frac{221}{30} + \frac{989}{120}$

Step 4.2

To write $- \frac{221}{30}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{7 m}{12} = - \frac{221}{30} \cdot \frac{4}{4} + \frac{989}{120}$

Step 4.3

Write each expression with a common denominator of $120$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{221}{30}$ by $\frac{4}{4}$ .

$\frac{7 m}{12} = - \frac{221 \cdot 4}{30 \cdot 4} + \frac{989}{120}$

Step 4.3.2

Multiply $30$ by $4$ .

$\frac{7 m}{12} = - \frac{221 \cdot 4}{120} + \frac{989}{120}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{7 m}{12} = \frac{- 221 \cdot 4 + 989}{120}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 221$ by $4$ .

$\frac{7 m}{12} = \frac{- 884 + 989}{120}$

Step 4.5.2

Add $- 884$ and $989$ .

$\frac{7 m}{12} = \frac{105}{120}$

Step 4.6

Cancel the common factor of $105$ and $120$ .

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Step 4.6.1

Factor $15$ out of $105$ .

$\frac{7 m}{12} = \frac{15 (7)}{120}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $15$ out of $120$ .

$\frac{7 m}{12} = \frac{15 \cdot 7}{15 \cdot 8}$

Step 4.6.2.2

Cancel the common factor.

$\frac{7 m}{12} = \frac{15 \cdot 7}{15 \cdot 8}$

Step 4.6.2.3

Rewrite the expression.

$\frac{7 m}{12} = \frac{7}{8}$

Step 5

Multiply both sides of the equation by $\frac{12}{7}$ .

$\frac{12}{7} \cdot \frac{7 m}{12} = \frac{12}{7} \cdot \frac{7}{8}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{12}{7} \cdot \frac{7 m}{12}$ .

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Step 6.1.1.1

Cancel the common factor of $12$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{12}{7} \cdot \frac{7 m}{12} = \frac{12}{7} \cdot \frac{7}{8}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{7} (7 m) = \frac{12}{7} \cdot \frac{7}{8}$

Step 6.1.1.2

Cancel the common factor of $7$ .

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Step 6.1.1.2.1

Factor $7$ out of $7 m$ .

$\frac{1}{7} (7 (m)) = \frac{12}{7} \cdot \frac{7}{8}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{7} (7 m) = \frac{12}{7} \cdot \frac{7}{8}$

Step 6.1.1.2.3

Rewrite the expression.

$m = \frac{12}{7} \cdot \frac{7}{8}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{12}{7} \cdot \frac{7}{8}$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Factor $4$ out of $12$ .

$m = \frac{4 (3)}{7} \cdot \frac{7}{8}$

Step 6.2.1.1.2

Factor $4$ out of $8$ .

$m = \frac{4 \cdot 3}{7} \cdot \frac{7}{4 \cdot 2}$

Step 6.2.1.1.3

Cancel the common factor.

$m = \frac{4 \cdot 3}{7} \cdot \frac{7}{4 \cdot 2}$

Step 6.2.1.1.4

Rewrite the expression.

$m = \frac{3}{7} \cdot \frac{7}{2}$

Step 6.2.1.2

Cancel the common factor of $7$ .

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Step 6.2.1.2.1

Cancel the common factor.

$m = \frac{3}{7} \cdot \frac{7}{2}$

Step 6.2.1.2.2

Rewrite the expression.

$m = 3 (\frac{1}{2})$

Step 6.2.1.3

Combine $3$ and $\frac{1}{2}$ .

$m = \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$m = \frac{3}{2}$

Decimal Form:

$m = 1.5$

Mixed Number Form:

$m = 1 \frac{1}{2}$