Pre-Algebra Examples

\frac{1}{4} + \frac{1}{8} + \frac{1}{4} + \frac{1}{8}

$\frac{1}{4} + \frac{1}{8} + \frac{1}{4} + \frac{1}{8}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

\frac{1 + 1}{4} + \frac{1 + 1}{8}

$\frac{1 + 1}{4} + \frac{1 + 1}{8}$

Step 1.2

Simplify by adding numbers.

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Step 1.2.1

Add

1

$1$ and

1

$1$ .

\frac{2}{4} + \frac{1 + 1}{8}

$\frac{2}{4} + \frac{1 + 1}{8}$

Step 1.2.2

Add

1

$1$ and

1

$1$ .

\frac{2}{4} + \frac{2}{8}

$\frac{2}{4} + \frac{2}{8}$

\frac{2}{4} + \frac{2}{8}

$\frac{2}{4} + \frac{2}{8}$

\frac{2}{4} + \frac{2}{8}

$\frac{2}{4} + \frac{2}{8}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of

2

$2$ and

4

$4$ .

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Step 2.1.1

Factor

2

$2$ out of

2

$2$ .

\frac{2 (1)}{4} + \frac{2}{8}

$\frac{2 (1)}{4} + \frac{2}{8}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor

2

$2$ out of

4

$4$ .

\frac{2 \cdot 1}{2 \cdot 2} + \frac{2}{8}

$\frac{2 \cdot 1}{2 \cdot 2} + \frac{2}{8}$

Step 2.1.2.2

Cancel the common factor.

\frac{2 \cdot 1}{2 \cdot 2} + \frac{2}{8}

$\frac{2 \cdot 1}{2 \cdot 2} + \frac{2}{8}$

Step 2.1.2.3

Rewrite the expression.

\frac{1}{2} + \frac{2}{8}

$\frac{1}{2} + \frac{2}{8}$

\frac{1}{2} + \frac{2}{8}

$\frac{1}{2} + \frac{2}{8}$

\frac{1}{2} + \frac{2}{8}

$\frac{1}{2} + \frac{2}{8}$

Step 2.2

Cancel the common factor of

2

$2$ and

8

$8$ .

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Step 2.2.1

Factor

2

$2$ out of

2

$2$ .

\frac{1}{2} + \frac{2 (1)}{8}

$\frac{1}{2} + \frac{2 (1)}{8}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor

2

$2$ out of

8

$8$ .

\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 4}

$\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 4}$

Step 2.2.2.2

Cancel the common factor.

\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 4}

$\frac{1}{2} + \frac{2 \cdot 1}{2 \cdot 4}$

Step 2.2.2.3

Rewrite the expression.

\frac{1}{2} + \frac{1}{4}

$\frac{1}{2} + \frac{1}{4}$

\frac{1}{2} + \frac{1}{4}

$\frac{1}{2} + \frac{1}{4}$

\frac{1}{2} + \frac{1}{4}

$\frac{1}{2} + \frac{1}{4}$

\frac{1}{2} + \frac{1}{4}

$\frac{1}{2} + \frac{1}{4}$

Step 3

To write

\frac{1}{2}

$\frac{1}{2}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}

$\frac{1}{2} \cdot \frac{2}{2} + \frac{1}{4}$

Step 4

Write each expression with a common denominator of

4

$4$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{2}{2 \cdot 2} + \frac{1}{4}

$\frac{2}{2 \cdot 2} + \frac{1}{4}$

Step 4.2

Multiply

2

$2$ by

2

$2$ .

\frac{2}{4} + \frac{1}{4}

$\frac{2}{4} + \frac{1}{4}$

\frac{2}{4} + \frac{1}{4}

$\frac{2}{4} + \frac{1}{4}$

Step 5

Combine the numerators over the common denominator.

\frac{2 + 1}{4}

$\frac{2 + 1}{4}$

Step 6

Add

2

$2$ and

1

$1$ .

\frac{3}{4}

$\frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{3}{4}

$\frac{3}{4}$

Decimal Form:

0.75

$0.75$