Pre-Algebra Examples

$4 \frac{7}{12} = x + 1 \frac{1}{12}$

Step 1

Simplify the left side.

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Step 1.1

Convert $4 \frac{7}{12}$ to an improper fraction.

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Step 1.1.1

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

$4 + \frac{7}{12} = x + 1 \frac{1}{12}$

Step 1.1.2

Add $4$ and $\frac{7}{12}$ .

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Step 1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$4 \cdot \frac{12}{12} + \frac{7}{12} = x + 1 \frac{1}{12}$

Step 1.1.2.2

Combine $4$ and $\frac{12}{12}$ .

$\frac{4 \cdot 12}{12} + \frac{7}{12} = x + 1 \frac{1}{12}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 12 + 7}{12} = x + 1 \frac{1}{12}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $4$ by $12$ .

$\frac{48 + 7}{12} = x + 1 \frac{1}{12}$

Step 1.1.2.4.2

Add $48$ and $7$ .

$\frac{55}{12} = x + 1 \frac{1}{12}$

Step 2

Simplify the right side.

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Step 2.1

Convert $1 \frac{1}{12}$ to an improper fraction.

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Step 2.1.1

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

$\frac{55}{12} = x + 1 + \frac{1}{12}$

Step 2.1.2

Add $1$ and $\frac{1}{12}$ .

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Step 2.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{55}{12} = x + \frac{12}{12} + \frac{1}{12}$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{55}{12} = x + \frac{12 + 1}{12}$

Step 2.1.2.3

Add $12$ and $1$ .

$\frac{55}{12} = x + \frac{13}{12}$

Step 3

Rewrite the equation as $x + \frac{13}{12} = \frac{55}{12}$ .

$x + \frac{13}{12} = \frac{55}{12}$

Step 4

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

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Step 4.1

Subtract $\frac{13}{12}$ from both sides of the equation.

$x = \frac{55}{12} - \frac{13}{12}$

Step 4.2

Combine the numerators over the common denominator.

$x = \frac{55 - 13}{12}$

Step 4.3

Subtract $13$ from $55$ .

$x = \frac{42}{12}$

Step 4.4

Cancel the common factor of $42$ and $12$ .

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Step 4.4.1

Factor $6$ out of $42$ .

$x = \frac{6 (7)}{12}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 7}{6 \cdot 2}$

Step 4.4.2.2

Cancel the common factor.

$x = \frac{6 \cdot 7}{6 \cdot 2}$

Step 4.4.2.3

Rewrite the expression.

$x = \frac{7}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

$x = 3 \frac{1}{2}$