Algebra Examples

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

Step 1

Convert $7 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $7$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2.2

Combine $7$ and $\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $2$ .

$\frac{\frac{14 + 1}{2} \cdot 7 \frac{5}{2}}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 1.2.4.2

Add $14$ and $1$ .

$\frac{\frac{15}{2} \cdot 7 \frac{5}{2}}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2

Convert $7 \frac{5}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{\frac{15}{2} \cdot (7 + \frac{5}{2})}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2.2

Add $7$ and $\frac{5}{2}$ .

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Step 2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{15}{2} \cdot (7 \cdot \frac{2}{2} + \frac{5}{2})}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2.2.2

Combine $7$ and $\frac{2}{2}$ .

$\frac{\frac{15}{2} \cdot (\frac{7 \cdot 2}{2} + \frac{5}{2})}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{15}{2} \cdot \frac{7 \cdot 2 + 5}{2}}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $2$ .

$\frac{\frac{15}{2} \cdot \frac{14 + 5}{2}}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 2.2.4.2

Add $14$ and $5$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{7 \frac{1}{4} \cdot 7 \frac{3}{4}}$

Step 3

Convert $7 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{(7 + \frac{1}{4}) \cdot 7 \frac{3}{4}}$

Step 3.2

Add $7$ and $\frac{1}{4}$ .

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Step 3.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{(7 \cdot \frac{4}{4} + \frac{1}{4}) \cdot 7 \frac{3}{4}}$

Step 3.2.2

Combine $7$ and $\frac{4}{4}$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{(\frac{7 \cdot 4}{4} + \frac{1}{4}) \cdot 7 \frac{3}{4}}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{7 \cdot 4 + 1}{4} \cdot 7 \frac{3}{4}}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $7$ by $4$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{28 + 1}{4} \cdot 7 \frac{3}{4}}$

Step 3.2.4.2

Add $28$ and $1$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot 7 \frac{3}{4}}$

Step 4

Convert $7 \frac{3}{4}$ to an improper fraction.

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Step 4.1

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

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot (7 + \frac{3}{4})}$

Step 4.2

Add $7$ and $\frac{3}{4}$ .

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Step 4.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot (7 \cdot \frac{4}{4} + \frac{3}{4})}$

Step 4.2.2

Combine $7$ and $\frac{4}{4}$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot (\frac{7 \cdot 4}{4} + \frac{3}{4})}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot \frac{7 \cdot 4 + 3}{4}}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $7$ by $4$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot \frac{28 + 3}{4}}$

Step 4.2.4.2

Add $28$ and $3$ .

$\frac{\frac{15}{2} \cdot \frac{19}{2}}{\frac{29}{4} \cdot \frac{31}{4}}$

Step 5

Multiply $\frac{15}{2}$ by $\frac{19}{2}$ .

$\frac{\frac{15 \cdot 19}{2 \cdot 2}}{\frac{29}{4} \cdot \frac{31}{4}}$

Step 6

Multiply $\frac{29}{4}$ by $\frac{31}{4}$ .

$\frac{\frac{15 \cdot 19}{2 \cdot 2}}{\frac{29 \cdot 31}{4 \cdot 4}}$

Step 7

Multiply $15$ by $19$ .

$\frac{\frac{285}{2 \cdot 2}}{\frac{29 \cdot 31}{4 \cdot 4}}$

Step 8

Multiply $2$ by $2$ .

$\frac{\frac{285}{4}}{\frac{29 \cdot 31}{4 \cdot 4}}$

Step 9

Multiply $29$ by $31$ .

$\frac{\frac{285}{4}}{\frac{899}{4 \cdot 4}}$

Step 10

Multiply $4$ by $4$ .

$\frac{\frac{285}{4}}{\frac{899}{16}}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{285}{4} \cdot \frac{16}{899}$

Step 12

Cancel the common factor of $4$ .

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Step 12.1

Factor $4$ out of $16$ .

$\frac{285}{4} \cdot \frac{4 (4)}{899}$

Step 12.2

Cancel the common factor.

$\frac{285}{4} \cdot \frac{4 \cdot 4}{899}$

Step 12.3

Rewrite the expression.

$285 (\frac{4}{899})$

Step 13

Combine $285$ and $\frac{4}{899}$ .

$\frac{285 \cdot 4}{899}$

Step 14

Multiply $285$ by $4$ .

$\frac{1140}{899}$