Pre-Algebra Examples

$1 \frac{3}{4} + \frac{7}{8} + 1 \frac{1}{2}$

Step 1

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

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Step 1.1

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

$1 + \frac{3}{4} + \frac{7}{8} + 1 \frac{1}{2}$

Step 1.2

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

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Step 1.2.1

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

$\frac{4}{4} + \frac{3}{4} + \frac{7}{8} + 1 \frac{1}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} + \frac{7}{8} + 1 \frac{1}{2}$

Step 1.2.3

Add $4$ and $3$ .

$\frac{7}{4} + \frac{7}{8} + 1 \frac{1}{2}$

Step 2

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

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Step 2.1

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

$\frac{7}{4} + \frac{7}{8} + 1 + \frac{1}{2}$

Step 2.2

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

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Step 2.2.1

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

$\frac{7}{4} + \frac{7}{8} + \frac{2}{2} + \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{7}{4} + \frac{7}{8} + \frac{2 + 1}{2}$

Step 2.2.3

Add $2$ and $1$ .

$\frac{7}{4} + \frac{7}{8} + \frac{3}{2}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{7}{4}$ by $\frac{2}{2}$ .

$\frac{7}{4} \cdot \frac{2}{2} + \frac{7}{8} + \frac{3}{2}$

Step 3.2

Multiply $\frac{7}{4}$ by $\frac{2}{2}$ .

$\frac{7 \cdot 2}{4 \cdot 2} + \frac{7}{8} + \frac{3}{2}$

Step 3.3

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 2}{4 \cdot 2} + \frac{7}{8} + \frac{3}{2} \cdot \frac{4}{4}$

Step 3.4

Multiply $\frac{3}{2}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 2}{4 \cdot 2} + \frac{7}{8} + \frac{3 \cdot 4}{2 \cdot 4}$

Step 3.5

Reorder the factors of $4 \cdot 2$ .

$\frac{7 \cdot 2}{2 \cdot 4} + \frac{7}{8} + \frac{3 \cdot 4}{2 \cdot 4}$

Step 3.6

Multiply $2$ by $4$ .

$\frac{7 \cdot 2}{8} + \frac{7}{8} + \frac{3 \cdot 4}{2 \cdot 4}$

Step 3.7

Multiply $2$ by $4$ .

$\frac{7 \cdot 2}{8} + \frac{7}{8} + \frac{3 \cdot 4}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 7 + 3 \cdot 4}{8}$

Step 5

Simplify each term.

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Step 5.1

Multiply $7$ by $2$ .

$\frac{14 + 7 + 3 \cdot 4}{8}$

Step 5.2

Multiply $3$ by $4$ .

$\frac{14 + 7 + 12}{8}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $14$ and $7$ .

$\frac{21 + 12}{8}$

Step 6.2

Add $21$ and $12$ .

$\frac{33}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{33}{8}$

Decimal Form:

$4.125$

Mixed Number Form:

$4 \frac{1}{8}$