Basic Math Examples

$\frac{1}{2} \cdot 8 \frac{3}{8} \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1

Convert $8 \frac{3}{8}$ to an improper fraction.

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Step 1.1

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

$\frac{1}{2} \cdot (8 + \frac{3}{8}) \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1.2

Add $8$ and $\frac{3}{8}$ .

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Step 1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{2} \cdot (8 \cdot \frac{8}{8} + \frac{3}{8}) \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1.2.2

Combine $8$ and $\frac{8}{8}$ .

$\frac{1}{2} \cdot (\frac{8 \cdot 8}{8} + \frac{3}{8}) \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{8 \cdot 8 + 3}{8} \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $8$ by $8$ .

$\frac{1}{2} \cdot \frac{64 + 3}{8} \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 1.2.4.2

Add $64$ and $3$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot 1 \frac{7}{8} \cdot 3 \frac{4}{5}$

Step 2

Convert $1 \frac{7}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{1}{2} \cdot \frac{67}{8} \cdot (1 + \frac{7}{8}) \cdot 3 \frac{4}{5}$

Step 2.2

Add $1$ and $\frac{7}{8}$ .

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Step 2.2.1

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

$\frac{1}{2} \cdot \frac{67}{8} \cdot (\frac{8}{8} + \frac{7}{8}) \cdot 3 \frac{4}{5}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{8 + 7}{8} \cdot 3 \frac{4}{5}$

Step 2.2.3

Add $8$ and $7$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot 3 \frac{4}{5}$

Step 3

Convert $3 \frac{4}{5}$ to an improper fraction.

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Step 3.1

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

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot (3 + \frac{4}{5})$

Step 3.2

Add $3$ and $\frac{4}{5}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot (3 \cdot \frac{5}{5} + \frac{4}{5})$

Step 3.2.2

Combine $3$ and $\frac{5}{5}$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot (\frac{3 \cdot 5}{5} + \frac{4}{5})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot \frac{3 \cdot 5 + 4}{5}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $5$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot \frac{15 + 4}{5}$

Step 3.2.4.2

Add $15$ and $4$ .

$\frac{1}{2} \cdot \frac{67}{8} \cdot \frac{15}{8} \cdot \frac{19}{5}$

Step 4

Multiply $\frac{1}{2} \cdot \frac{67}{8}$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{67}{8}$ .

$\frac{67}{2 \cdot 8} \cdot \frac{15}{8} \cdot \frac{19}{5}$

Step 4.2

Multiply $2$ by $8$ .

$\frac{67}{16} \cdot \frac{15}{8} \cdot \frac{19}{5}$

Step 5

Multiply $\frac{67}{16} \cdot \frac{15}{8}$ .

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Step 5.1

Multiply $\frac{67}{16}$ by $\frac{15}{8}$ .

$\frac{67 \cdot 15}{16 \cdot 8} \cdot \frac{19}{5}$

Step 5.2

Multiply $67$ by $15$ .

$\frac{1005}{16 \cdot 8} \cdot \frac{19}{5}$

Step 5.3

Multiply $16$ by $8$ .

$\frac{1005}{128} \cdot \frac{19}{5}$

Step 6

Cancel the common factor of $5$ .

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Step 6.1

Factor $5$ out of $1005$ .

$\frac{5 (201)}{128} \cdot \frac{19}{5}$

Step 6.2

Cancel the common factor.

$\frac{5 \cdot 201}{128} \cdot \frac{19}{5}$

Step 6.3

Rewrite the expression.

$\frac{201}{128} \cdot 19$

Step 7

Combine $\frac{201}{128}$ and $19$ .

$\frac{201 \cdot 19}{128}$

Step 8

Multiply $201$ by $19$ .

$\frac{3819}{128}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{3819}{128}$

Decimal Form:

$29.8359375$

Mixed Number Form:

$29 \frac{107}{128}$