Algebra Examples

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

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.

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

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.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $2$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $3$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Combine the numerators over the common denominator.

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

Step 3.2.3

Add $4$ and $1$ .

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

Step 4

Convert $1 \frac{1}{5}$ to an improper fraction.

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Step 4.1

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

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

Step 4.2

Add $1$ and $\frac{1}{5}$ .

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Step 4.2.1

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

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

Step 4.2.2

Combine the numerators over the common denominator.

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

Step 4.2.3

Add $5$ and $1$ .

$\frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{4}{3} \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 5.2

Rewrite the expression.

$\frac{1}{2} \cdot 4 \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $4$ .

$\frac{1}{2} \cdot (2 (2)) \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 6.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 2) \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 6.3

Rewrite the expression.

$2 \cdot \frac{5}{4} \cdot \frac{6}{5}$

Step 7

Cancel the common factor of $2$ .

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Step 7.1

Factor $2$ out of $4$ .

$2 \cdot \frac{5}{2 (2)} \cdot \frac{6}{5}$

Step 7.2

Cancel the common factor.

$2 \cdot \frac{5}{2 \cdot 2} \cdot \frac{6}{5}$

Step 7.3

Rewrite the expression.

$\frac{5}{2} \cdot \frac{6}{5}$

Step 8

Cancel the common factor of $5$ .

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Step 8.1

Cancel the common factor.

$\frac{5}{2} \cdot \frac{6}{5}$

Step 8.2

Rewrite the expression.

$\frac{1}{2} \cdot 6$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $6$ .

$\frac{1}{2} \cdot (2 (3))$

Step 9.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 3)$

Step 9.3

Rewrite the expression.

$3$