Algebra Examples

$7 \frac{1}{9} = 2 \frac{4}{5} + m$

Step 1

Simplify the left side.

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Step 1.1

Convert $7 \frac{1}{9}$ to an improper fraction.

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Step 1.1.1

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

$7 + \frac{1}{9} = 2 \frac{4}{5} + m$

Step 1.1.2

Add $7$ and $\frac{1}{9}$ .

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Step 1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$7 \cdot \frac{9}{9} + \frac{1}{9} = 2 \frac{4}{5} + m$

Step 1.1.2.2

Combine $7$ and $\frac{9}{9}$ .

$\frac{7 \cdot 9}{9} + \frac{1}{9} = 2 \frac{4}{5} + m$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 9 + 1}{9} = 2 \frac{4}{5} + m$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $9$ .

$\frac{63 + 1}{9} = 2 \frac{4}{5} + m$

Step 1.1.2.4.2

Add $63$ and $1$ .

$\frac{64}{9} = 2 \frac{4}{5} + m$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{4}{5}$ to an improper fraction.

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Step 2.1.1

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

$\frac{64}{9} = 2 + \frac{4}{5} + m$

Step 2.1.2

Add $2$ and $\frac{4}{5}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{64}{9} = 2 \cdot \frac{5}{5} + \frac{4}{5} + m$

Step 2.1.2.2

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

$\frac{64}{9} = \frac{2 \cdot 5}{5} + \frac{4}{5} + m$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{64}{9} = \frac{2 \cdot 5 + 4}{5} + m$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $5$ .

$\frac{64}{9} = \frac{10 + 4}{5} + m$

Step 2.1.2.4.2

Add $10$ and $4$ .

$\frac{64}{9} = \frac{14}{5} + m$

Step 3

Rewrite the equation as $\frac{14}{5} + m = \frac{64}{9}$ .

$\frac{14}{5} + m = \frac{64}{9}$

Step 4

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

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Step 4.1

Subtract $\frac{14}{5}$ from both sides of the equation.

$m = \frac{64}{9} - \frac{14}{5}$

Step 4.2

To write $\frac{64}{9}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$m = \frac{64}{9} \cdot \frac{5}{5} - \frac{14}{5}$

Step 4.3

To write $- \frac{14}{5}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$m = \frac{64}{9} \cdot \frac{5}{5} - \frac{14}{5} \cdot \frac{9}{9}$

Step 4.4

Write each expression with a common denominator of $45$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{64}{9}$ by $\frac{5}{5}$ .

$m = \frac{64 \cdot 5}{9 \cdot 5} - \frac{14}{5} \cdot \frac{9}{9}$

Step 4.4.2

Multiply $9$ by $5$ .

$m = \frac{64 \cdot 5}{45} - \frac{14}{5} \cdot \frac{9}{9}$

Step 4.4.3

Multiply $\frac{14}{5}$ by $\frac{9}{9}$ .

$m = \frac{64 \cdot 5}{45} - \frac{14 \cdot 9}{5 \cdot 9}$

Step 4.4.4

Multiply $5$ by $9$ .

$m = \frac{64 \cdot 5}{45} - \frac{14 \cdot 9}{45}$

Step 4.5

Combine the numerators over the common denominator.

$m = \frac{64 \cdot 5 - 14 \cdot 9}{45}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $64$ by $5$ .

$m = \frac{320 - 14 \cdot 9}{45}$

Step 4.6.2

Multiply $- 14$ by $9$ .

$m = \frac{320 - 126}{45}$

Step 4.6.3

Subtract $126$ from $320$ .

$m = \frac{194}{45}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$m = \frac{194}{45}$

Decimal Form:

$m = 4.3\overline{1}$

Mixed Number Form:

$m = 4 \frac{14}{45}$