Basic Math Examples

$11 \frac{2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1

Simplify the left side.

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Step 1.1

Convert $11 \frac{2}{5}$ to an improper fraction.

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Step 1.1.1

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

$11 + \frac{2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1.1.2

Add $11$ and $\frac{2}{5}$ .

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Step 1.1.2.1

To write $11$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$11 \cdot \frac{5}{5} + \frac{2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1.1.2.2

Combine $11$ and $\frac{5}{5}$ .

$\frac{11 \cdot 5}{5} + \frac{2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{11 \cdot 5 + 2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $11$ by $5$ .

$\frac{55 + 2}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 1.1.2.4.2

Add $55$ and $2$ .

$\frac{57}{5} = q - 4 \frac{2}{7} + 2 \frac{1}{7}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $q - 4 \frac{2}{7} + 2 \frac{1}{7}$ .

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Step 2.1.1

Convert $4 \frac{2}{7}$ to an improper fraction.

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Step 2.1.1.1

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

$\frac{57}{5} = q - (4 + \frac{2}{7}) + 2 \frac{1}{7}$

Step 2.1.1.2

Add $4$ and $\frac{2}{7}$ .

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Step 2.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{57}{5} = q - (4 \cdot \frac{7}{7} + \frac{2}{7}) + 2 \frac{1}{7}$

Step 2.1.1.2.2

Combine $4$ and $\frac{7}{7}$ .

$\frac{57}{5} = q - (\frac{4 \cdot 7}{7} + \frac{2}{7}) + 2 \frac{1}{7}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{57}{5} = q - \frac{4 \cdot 7 + 2}{7} + 2 \frac{1}{7}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $4$ by $7$ .

$\frac{57}{5} = q - \frac{28 + 2}{7} + 2 \frac{1}{7}$

Step 2.1.1.2.4.2

Add $28$ and $2$ .

$\frac{57}{5} = q - \frac{30}{7} + 2 \frac{1}{7}$

Step 2.1.2

Convert $2 \frac{1}{7}$ to an improper fraction.

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Step 2.1.2.1

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

$\frac{57}{5} = q - \frac{30}{7} + 2 + \frac{1}{7}$

Step 2.1.2.2

Add $2$ and $\frac{1}{7}$ .

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Step 2.1.2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{57}{5} = q - \frac{30}{7} + 2 \cdot \frac{7}{7} + \frac{1}{7}$

Step 2.1.2.2.2

Combine $2$ and $\frac{7}{7}$ .

$\frac{57}{5} = q - \frac{30}{7} + \frac{2 \cdot 7}{7} + \frac{1}{7}$

Step 2.1.2.2.3

Combine the numerators over the common denominator.

$\frac{57}{5} = q - \frac{30}{7} + \frac{2 \cdot 7 + 1}{7}$

Step 2.1.2.2.4

Simplify the numerator.

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Step 2.1.2.2.4.1

Multiply $2$ by $7$ .

$\frac{57}{5} = q - \frac{30}{7} + \frac{14 + 1}{7}$

Step 2.1.2.2.4.2

Add $14$ and $1$ .

$\frac{57}{5} = q - \frac{30}{7} + \frac{15}{7}$

Step 2.1.3

Combine the numerators over the common denominator.

$\frac{57}{5} = q + \frac{- 30 + 15}{7}$

Step 2.1.4

Simplify the expression.

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Step 2.1.4.1

Add $- 30$ and $15$ .

$\frac{57}{5} = q + \frac{- 15}{7}$

Step 2.1.4.2

Move the negative in front of the fraction.

$\frac{57}{5} = q - \frac{15}{7}$

Step 3

Rewrite the equation as $q - \frac{15}{7} = \frac{57}{5}$ .

$q - \frac{15}{7} = \frac{57}{5}$

Step 4

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

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Step 4.1

Add $\frac{15}{7}$ to both sides of the equation.

$q = \frac{57}{5} + \frac{15}{7}$

Step 4.2

To write $\frac{57}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$q = \frac{57}{5} \cdot \frac{7}{7} + \frac{15}{7}$

Step 4.3

To write $\frac{15}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$q = \frac{57}{5} \cdot \frac{7}{7} + \frac{15}{7} \cdot \frac{5}{5}$

Step 4.4

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{57}{5}$ by $\frac{7}{7}$ .

$q = \frac{57 \cdot 7}{5 \cdot 7} + \frac{15}{7} \cdot \frac{5}{5}$

Step 4.4.2

Multiply $5$ by $7$ .

$q = \frac{57 \cdot 7}{35} + \frac{15}{7} \cdot \frac{5}{5}$

Step 4.4.3

Multiply $\frac{15}{7}$ by $\frac{5}{5}$ .

$q = \frac{57 \cdot 7}{35} + \frac{15 \cdot 5}{7 \cdot 5}$

Step 4.4.4

Multiply $7$ by $5$ .

$q = \frac{57 \cdot 7}{35} + \frac{15 \cdot 5}{35}$

Step 4.5

Combine the numerators over the common denominator.

$q = \frac{57 \cdot 7 + 15 \cdot 5}{35}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $57$ by $7$ .

$q = \frac{399 + 15 \cdot 5}{35}$

Step 4.6.2

Multiply $15$ by $5$ .

$q = \frac{399 + 75}{35}$

Step 4.6.3

Add $399$ and $75$ .

$q = \frac{474}{35}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$q = \frac{474}{35}$

Decimal Form:

$q = 13.54285714 \dots$

Mixed Number Form:

$q = 13 \frac{19}{35}$