Basic Math Examples

$- \frac{1}{10} - 4 \frac{3}{5} - 5 \frac{3}{10}$

Step 1

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

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Step 1.1

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

$- \frac{1}{10} - (4 + \frac{3}{5}) - 5 \frac{3}{10}$

Step 1.2

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

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{1}{10} - (4 \cdot \frac{5}{5} + \frac{3}{5}) - 5 \frac{3}{10}$

Step 1.2.2

Combine $4$ and $\frac{5}{5}$ .

$- \frac{1}{10} - (\frac{4 \cdot 5}{5} + \frac{3}{5}) - 5 \frac{3}{10}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{1}{10} - \frac{4 \cdot 5 + 3}{5} - 5 \frac{3}{10}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $5$ .

$- \frac{1}{10} - \frac{20 + 3}{5} - 5 \frac{3}{10}$

Step 1.2.4.2

Add $20$ and $3$ .

$- \frac{1}{10} - \frac{23}{5} - 5 \frac{3}{10}$

Step 2

Convert $5 \frac{3}{10}$ to an improper fraction.

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Step 2.1

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

$- \frac{1}{10} - \frac{23}{5} - (5 + \frac{3}{10})$

Step 2.2

Add $5$ and $\frac{3}{10}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{1}{10} - \frac{23}{5} - (5 \cdot \frac{10}{10} + \frac{3}{10})$

Step 2.2.2

Combine $5$ and $\frac{10}{10}$ .

$- \frac{1}{10} - \frac{23}{5} - (\frac{5 \cdot 10}{10} + \frac{3}{10})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{1}{10} - \frac{23}{5} - \frac{5 \cdot 10 + 3}{10}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $10$ .

$- \frac{1}{10} - \frac{23}{5} - \frac{50 + 3}{10}$

Step 2.2.4.2

Add $50$ and $3$ .

$- \frac{1}{10} - \frac{23}{5} - \frac{53}{10}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$\frac{- 1 - 53}{10} + \frac{- 23}{5}$

Step 3.2

Subtract $53$ from $- 1$ .

$\frac{- 54}{10} + \frac{- 23}{5}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $- 54$ and $10$ .

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Step 4.1.1

Factor $2$ out of $- 54$ .

$\frac{2 (- 27)}{10} + \frac{- 23}{5}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot - 27}{2 \cdot 5} + \frac{- 23}{5}$

Step 4.1.2.2

Cancel the common factor.

$\frac{2 \cdot - 27}{2 \cdot 5} + \frac{- 23}{5}$

Step 4.1.2.3

Rewrite the expression.

$\frac{- 27}{5} + \frac{- 23}{5}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{27}{5} + \frac{- 23}{5}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{27}{5} - \frac{23}{5}$

Step 5

Combine fractions.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{- 27 - 23}{5}$

Step 5.2

Simplify the expression.

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Step 5.2.1

Subtract $23$ from $- 27$ .

$\frac{- 50}{5}$

Step 5.2.2

Divide $- 50$ by $5$ .

$- 10$