Basic Math Examples

$\frac{k}{2} + \frac{3 k}{4} = 7$

Step 1

Simplify $\frac{k}{2} + \frac{3 k}{4}$ .

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Step 1.1

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

$\frac{k}{2} \cdot \frac{2}{2} + \frac{3 k}{4} = 7$

Step 1.2

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{k}{2}$ by $\frac{2}{2}$ .

$\frac{k \cdot 2}{2 \cdot 2} + \frac{3 k}{4} = 7$

Step 1.2.2

Multiply $2$ by $2$ .

$\frac{k \cdot 2}{4} + \frac{3 k}{4} = 7$

Step 1.3

Combine the numerators over the common denominator.

$\frac{k \cdot 2 + 3 k}{4} = 7$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $k$ .

$\frac{2 \cdot k + 3 k}{4} = 7$

Step 1.4.2

Add $2 k$ and $3 k$ .

$\frac{5 k}{4} = 7$

Step 2

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 k}{4} = \frac{4}{5} \cdot 7$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{5} \cdot \frac{5 k}{4}$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 k}{4} = \frac{4}{5} \cdot 7$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 k) = \frac{4}{5} \cdot 7$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 k$ .

$\frac{1}{5} (5 (k)) = \frac{4}{5} \cdot 7$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 k) = \frac{4}{5} \cdot 7$

Step 3.1.1.2.3

Rewrite the expression.

$k = \frac{4}{5} \cdot 7$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{4}{5} \cdot 7$ .

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Step 3.2.1.1

Combine $\frac{4}{5}$ and $7$ .

$k = \frac{4 \cdot 7}{5}$

Step 3.2.1.2

Multiply $4$ by $7$ .

$k = \frac{28}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{28}{5}$

Decimal Form:

$k = 5.6$

Mixed Number Form:

$k = 5 \frac{3}{5}$