Algebra Examples

$2 \frac{1}{7} - 1 \frac{2}{5}$

Step 1

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

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Step 1.1

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

$2 + \frac{1}{7} - 1 \frac{2}{5}$

Step 1.2

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

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Step 1.2.1

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

$2 \cdot \frac{7}{7} + \frac{1}{7} - 1 \frac{2}{5}$

Step 1.2.2

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

$\frac{2 \cdot 7}{7} + \frac{1}{7} - 1 \frac{2}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 7 + 1}{7} - 1 \frac{2}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $7$ .

$\frac{14 + 1}{7} - 1 \frac{2}{5}$

Step 1.2.4.2

Add $14$ and $1$ .

$\frac{15}{7} - 1 \frac{2}{5}$

Step 2

Convert $1 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{15}{7} - (1 + \frac{2}{5})$

Step 2.2

Add $1$ and $\frac{2}{5}$ .

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Step 2.2.1

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

$\frac{15}{7} - (\frac{5}{5} + \frac{2}{5})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{15}{7} - \frac{5 + 2}{5}$

Step 2.2.3

Add $5$ and $2$ .

$\frac{15}{7} - \frac{7}{5}$

Step 3

To write $\frac{15}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{15}{7} \cdot \frac{5}{5} - \frac{7}{5}$

Step 4

To write $- \frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{15}{7} \cdot \frac{5}{5} - \frac{7}{5} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{15}{7}$ by $\frac{5}{5}$ .

$\frac{15 \cdot 5}{7 \cdot 5} - \frac{7}{5} \cdot \frac{7}{7}$

Step 5.2

Multiply $7$ by $5$ .

$\frac{15 \cdot 5}{35} - \frac{7}{5} \cdot \frac{7}{7}$

Step 5.3

Multiply $\frac{7}{5}$ by $\frac{7}{7}$ .

$\frac{15 \cdot 5}{35} - \frac{7 \cdot 7}{5 \cdot 7}$

Step 5.4

Multiply $5$ by $7$ .

$\frac{15 \cdot 5}{35} - \frac{7 \cdot 7}{35}$

Step 6

Combine the numerators over the common denominator.

$\frac{15 \cdot 5 - 7 \cdot 7}{35}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $15$ by $5$ .

$\frac{75 - 7 \cdot 7}{35}$

Step 7.2

Multiply $- 7$ by $7$ .

$\frac{75 - 49}{35}$

Step 7.3

Subtract $49$ from $75$ .

$\frac{26}{35}$

Step 8

Since $\frac{26}{35}$ is a proper fraction, it cannot be written as a mixed number.

Cannot be written as a mixed number