Pre-Algebra Examples

$Q - 7 \frac{5}{6} = 6 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Convert $7 \frac{5}{6}$ to an improper fraction.

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Step 1.1.1

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

$Q - (7 + \frac{5}{6}) = 6 \frac{1}{2}$

Step 1.1.2

Add $7$ and $\frac{5}{6}$ .

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Step 1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$Q - (7 \cdot \frac{6}{6} + \frac{5}{6}) = 6 \frac{1}{2}$

Step 1.1.2.2

Combine $7$ and $\frac{6}{6}$ .

$Q - (\frac{7 \cdot 6}{6} + \frac{5}{6}) = 6 \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$Q - \frac{7 \cdot 6 + 5}{6} = 6 \frac{1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $6$ .

$Q - \frac{42 + 5}{6} = 6 \frac{1}{2}$

Step 1.1.2.4.2

Add $42$ and $5$ .

$Q - \frac{47}{6} = 6 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $6 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

$Q - \frac{47}{6} = 6 + \frac{1}{2}$

Step 2.1.2

Add $6$ and $\frac{1}{2}$ .

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Step 2.1.2.1

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

$Q - \frac{47}{6} = 6 \cdot \frac{2}{2} + \frac{1}{2}$

Step 2.1.2.2

Combine $6$ and $\frac{2}{2}$ .

$Q - \frac{47}{6} = \frac{6 \cdot 2}{2} + \frac{1}{2}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$Q - \frac{47}{6} = \frac{6 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $6$ by $2$ .

$Q - \frac{47}{6} = \frac{12 + 1}{2}$

Step 2.1.2.4.2

Add $12$ and $1$ .

$Q - \frac{47}{6} = \frac{13}{2}$

Step 3

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

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Step 3.1

Add $\frac{47}{6}$ to both sides of the equation.

$Q = \frac{13}{2} + \frac{47}{6}$

Step 3.2

To write $\frac{13}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$Q = \frac{13}{2} \cdot \frac{3}{3} + \frac{47}{6}$

Step 3.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{13}{2}$ by $\frac{3}{3}$ .

$Q = \frac{13 \cdot 3}{2 \cdot 3} + \frac{47}{6}$

Step 3.3.2

Multiply $2$ by $3$ .

$Q = \frac{13 \cdot 3}{6} + \frac{47}{6}$

Step 3.4

Combine the numerators over the common denominator.

$Q = \frac{13 \cdot 3 + 47}{6}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $13$ by $3$ .

$Q = \frac{39 + 47}{6}$

Step 3.5.2

Add $39$ and $47$ .

$Q = \frac{86}{6}$

Step 3.6

Cancel the common factor of $86$ and $6$ .

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Step 3.6.1

Factor $2$ out of $86$ .

$Q = \frac{2 (43)}{6}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $2$ out of $6$ .

$Q = \frac{2 \cdot 43}{2 \cdot 3}$

Step 3.6.2.2

Cancel the common factor.

$Q = \frac{2 \cdot 43}{2 \cdot 3}$

Step 3.6.2.3

Rewrite the expression.

$Q = \frac{43}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$Q = \frac{43}{3}$

Decimal Form:

$Q = 14.\overline{3}$

Mixed Number Form:

$Q = 14 \frac{1}{3}$