Pre-Algebra Examples

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + 1 \frac{1}{2} + \frac{1}{2} + 1 \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 1

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

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Step 1.1

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

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + 1 + \frac{1}{2} + \frac{1}{2} + 1 \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 1.2

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

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Step 1.2.1

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

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{2}{2} + \frac{1}{2} + \frac{1}{2} + 1 \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{2 + 1}{2} + \frac{1}{2} + 1 \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 1.2.3

Add $2$ and $1$ .

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + 1 \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 2

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

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Step 2.1

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

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + 1 + \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 2.2

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

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Step 2.2.1

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

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{4}{4} + \frac{3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{4 + 3}{4} + \frac{1}{2} + \frac{1}{2}$

Step 2.2.3

Add $4$ and $3$ .

$\frac{1}{4} + \frac{1}{2} + \frac{1}{4} + \frac{3}{4} + 1 + \frac{3}{2} + \frac{1}{2} + \frac{7}{4} + \frac{1}{2} + \frac{1}{2}$

Step 3

Combine the numerators over the common denominator.

$1 + \frac{1 + 1 + 3 + 7}{4} + \frac{1 + 3 + 1 + 1 + 1}{2}$

Step 4

Simplify by adding numbers.

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Step 4.1

Add $1$ and $1$ .

$1 + \frac{2 + 3 + 7}{4} + \frac{1 + 3 + 1 + 1 + 1}{2}$

Step 4.2

Add $2$ and $3$ .

$1 + \frac{5 + 7}{4} + \frac{1 + 3 + 1 + 1 + 1}{2}$

Step 4.3

Add $5$ and $7$ .

$1 + \frac{12}{4} + \frac{1 + 3 + 1 + 1 + 1}{2}$

Step 4.4

Add $1$ and $3$ .

$1 + \frac{12}{4} + \frac{4 + 1 + 1 + 1}{2}$

Step 4.5

Add $4$ and $1$ .

$1 + \frac{12}{4} + \frac{5 + 1 + 1}{2}$

Step 4.6

Add $5$ and $1$ .

$1 + \frac{12}{4} + \frac{6 + 1}{2}$

Step 4.7

Add $6$ and $1$ .

$1 + \frac{12}{4} + \frac{7}{2}$

Step 5

Find the common denominator.

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Step 5.1

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

$\frac{1}{1} + \frac{12}{4} + \frac{7}{2}$

Step 5.2

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$\frac{1}{1} \cdot \frac{4}{4} + \frac{12}{4} + \frac{7}{2}$

Step 5.3

Multiply $\frac{1}{1}$ by $\frac{4}{4}$ .

$\frac{4}{4} + \frac{12}{4} + \frac{7}{2}$

Step 5.4

Multiply $\frac{7}{2}$ by $\frac{2}{2}$ .

$\frac{4}{4} + \frac{12}{4} + \frac{7}{2} \cdot \frac{2}{2}$

Step 5.5

Multiply $\frac{7}{2}$ by $\frac{2}{2}$ .

$\frac{4}{4} + \frac{12}{4} + \frac{7 \cdot 2}{2 \cdot 2}$

Step 5.6

Multiply $2$ by $2$ .

$\frac{4}{4} + \frac{12}{4} + \frac{7 \cdot 2}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{4 + 12 + 7 \cdot 2}{4}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $7$ by $2$ .

$\frac{4 + 12 + 14}{4}$

Step 7.2

Add $4$ and $12$ .

$\frac{16 + 14}{4}$

Step 7.3

Add $16$ and $14$ .

$\frac{30}{4}$

Step 8

Cancel the common factor of $30$ and $4$ .

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Step 8.1

Factor $2$ out of $30$ .

$\frac{2 (15)}{4}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 15}{2 \cdot 2}$

Step 8.2.2

Cancel the common factor.

$\frac{2 \cdot 15}{2 \cdot 2}$

Step 8.2.3

Rewrite the expression.

$\frac{15}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{2}$

Decimal Form:

$7.5$

Mixed Number Form:

$7 \frac{1}{2}$