Basic Math Examples

$2 \frac{5}{12} = z - 3 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{5}{12}$ to an improper fraction.

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Step 1.1.1

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

$2 + \frac{5}{12} = z - 3 \frac{1}{4}$

Step 1.1.2

Add $2$ and $\frac{5}{12}$ .

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Step 1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$2 \cdot \frac{12}{12} + \frac{5}{12} = z - 3 \frac{1}{4}$

Step 1.1.2.2

Combine $2$ and $\frac{12}{12}$ .

$\frac{2 \cdot 12}{12} + \frac{5}{12} = z - 3 \frac{1}{4}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 12 + 5}{12} = z - 3 \frac{1}{4}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $12$ .

$\frac{24 + 5}{12} = z - 3 \frac{1}{4}$

Step 1.1.2.4.2

Add $24$ and $5$ .

$\frac{29}{12} = z - 3 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 2.1.1

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

$\frac{29}{12} = z - (3 + \frac{1}{4})$

Step 2.1.2

Add $3$ and $\frac{1}{4}$ .

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Step 2.1.2.1

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

$\frac{29}{12} = z - (3 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.1.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{29}{12} = z - (\frac{3 \cdot 4}{4} + \frac{1}{4})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{29}{12} = z - \frac{3 \cdot 4 + 1}{4}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $3$ by $4$ .

$\frac{29}{12} = z - \frac{12 + 1}{4}$

Step 2.1.2.4.2

Add $12$ and $1$ .

$\frac{29}{12} = z - \frac{13}{4}$

Step 3

Rewrite the equation as $z - \frac{13}{4} = \frac{29}{12}$ .

$z - \frac{13}{4} = \frac{29}{12}$

Step 4

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

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Step 4.1

Add $\frac{13}{4}$ to both sides of the equation.

$z = \frac{29}{12} + \frac{13}{4}$

Step 4.2

To write $\frac{13}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z = \frac{29}{12} + \frac{13}{4} \cdot \frac{3}{3}$

Step 4.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{13}{4}$ by $\frac{3}{3}$ .

$z = \frac{29}{12} + \frac{13 \cdot 3}{4 \cdot 3}$

Step 4.3.2

Multiply $4$ by $3$ .

$z = \frac{29}{12} + \frac{13 \cdot 3}{12}$

Step 4.4

Combine the numerators over the common denominator.

$z = \frac{29 + 13 \cdot 3}{12}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $13$ by $3$ .

$z = \frac{29 + 39}{12}$

Step 4.5.2

Add $29$ and $39$ .

$z = \frac{68}{12}$

Step 4.6

Cancel the common factor of $68$ and $12$ .

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Step 4.6.1

Factor $4$ out of $68$ .

$z = \frac{4 (17)}{12}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $4$ out of $12$ .

$z = \frac{4 \cdot 17}{4 \cdot 3}$

Step 4.6.2.2

Cancel the common factor.

$z = \frac{4 \cdot 17}{4 \cdot 3}$

Step 4.6.2.3

Rewrite the expression.

$z = \frac{17}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$z = \frac{17}{3}$

Decimal Form:

$z = 5.\overline{6}$

Mixed Number Form:

$z = 5 \frac{2}{3}$