Basic Math Examples

$5 \frac{1}{6} + q = 5 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

Convert $5 \frac{1}{6}$ to an improper fraction.

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Step 1.1.1

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

$5 + \frac{1}{6} + q = 5 \frac{1}{4}$

Step 1.1.2

Add $5$ and $\frac{1}{6}$ .

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Step 1.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$5 \cdot \frac{6}{6} + \frac{1}{6} + q = 5 \frac{1}{4}$

Step 1.1.2.2

Combine $5$ and $\frac{6}{6}$ .

$\frac{5 \cdot 6}{6} + \frac{1}{6} + q = 5 \frac{1}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 6 + 1}{6} + q = 5 \frac{1}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $5$ by $6$ .

$\frac{30 + 1}{6} + q = 5 \frac{1}{4}$

Step 1.1.2.4.2

Add $30$ and $1$ .

$\frac{31}{6} + q = 5 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $5 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

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

$\frac{31}{6} + q = 5 + \frac{1}{4}$

Step 2.1.2

Add $5$ and $\frac{1}{4}$ .

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Step 2.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{31}{6} + q = 5 \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.1.2.2

Combine $5$ and $\frac{4}{4}$ .

$\frac{31}{6} + q = \frac{5 \cdot 4}{4} + \frac{1}{4}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{31}{6} + q = \frac{5 \cdot 4 + 1}{4}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $5$ by $4$ .

$\frac{31}{6} + q = \frac{20 + 1}{4}$

Step 2.1.2.4.2

Add $20$ and $1$ .

$\frac{31}{6} + q = \frac{21}{4}$

Step 3

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

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Step 3.1

Subtract $\frac{31}{6}$ from both sides of the equation.

$q = \frac{21}{4} - \frac{31}{6}$

Step 3.2

To write $\frac{21}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$q = \frac{21}{4} \cdot \frac{3}{3} - \frac{31}{6}$

Step 3.3

To write $- \frac{31}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$q = \frac{21}{4} \cdot \frac{3}{3} - \frac{31}{6} \cdot \frac{2}{2}$

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 $\frac{21}{4}$ by $\frac{3}{3}$ .

$q = \frac{21 \cdot 3}{4 \cdot 3} - \frac{31}{6} \cdot \frac{2}{2}$

Step 3.4.2

Multiply $4$ by $3$ .

$q = \frac{21 \cdot 3}{12} - \frac{31}{6} \cdot \frac{2}{2}$

Step 3.4.3

Multiply $\frac{31}{6}$ by $\frac{2}{2}$ .

$q = \frac{21 \cdot 3}{12} - \frac{31 \cdot 2}{6 \cdot 2}$

Step 3.4.4

Multiply $6$ by $2$ .

$q = \frac{21 \cdot 3}{12} - \frac{31 \cdot 2}{12}$

Step 3.5

Combine the numerators over the common denominator.

$q = \frac{21 \cdot 3 - 31 \cdot 2}{12}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $21$ by $3$ .

$q = \frac{63 - 31 \cdot 2}{12}$

Step 3.6.2

Multiply $- 31$ by $2$ .

$q = \frac{63 - 62}{12}$

Step 3.6.3

Subtract $62$ from $63$ .

$q = \frac{1}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$q = \frac{1}{12}$

Decimal Form:

$q = 0.08\overline{3}$