Basic Math Examples

$52 \frac{7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1

Convert $52 \frac{7}{8}$ to an improper fraction.

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Step 1.1

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

$52 + \frac{7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1.2

Add $52$ and $\frac{7}{8}$ .

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Step 1.2.1

To write $52$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$52 \cdot \frac{8}{8} + \frac{7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1.2.2

Combine $52$ and $\frac{8}{8}$ .

$\frac{52 \cdot 8}{8} + \frac{7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{52 \cdot 8 + 7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $52$ by $8$ .

$\frac{416 + 7}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 1.2.4.2

Add $416$ and $7$ .

$\frac{423}{8} - 12 \frac{1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2

Convert $12 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{423}{8} - (12 + \frac{1}{2}) - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2.2

Add $12$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{423}{8} - (12 \cdot \frac{2}{2} + \frac{1}{2}) - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2.2.2

Combine $12$ and $\frac{2}{2}$ .

$\frac{423}{8} - (\frac{12 \cdot 2}{2} + \frac{1}{2}) - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{423}{8} - \frac{12 \cdot 2 + 1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $12$ by $2$ .

$\frac{423}{8} - \frac{24 + 1}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 2.2.4.2

Add $24$ and $1$ .

$\frac{423}{8} - \frac{25}{2} - 10 \frac{1}{4} - 19 \frac{1}{8}$

Step 3

Convert $10 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{423}{8} - \frac{25}{2} - (10 + \frac{1}{4}) - 19 \frac{1}{8}$

Step 3.2

Add $10$ and $\frac{1}{4}$ .

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Step 3.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{423}{8} - \frac{25}{2} - (10 \cdot \frac{4}{4} + \frac{1}{4}) - 19 \frac{1}{8}$

Step 3.2.2

Combine $10$ and $\frac{4}{4}$ .

$\frac{423}{8} - \frac{25}{2} - (\frac{10 \cdot 4}{4} + \frac{1}{4}) - 19 \frac{1}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{423}{8} - \frac{25}{2} - \frac{10 \cdot 4 + 1}{4} - 19 \frac{1}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $10$ by $4$ .

$\frac{423}{8} - \frac{25}{2} - \frac{40 + 1}{4} - 19 \frac{1}{8}$

Step 3.2.4.2

Add $40$ and $1$ .

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - 19 \frac{1}{8}$

Step 4

Convert $19 \frac{1}{8}$ to an improper fraction.

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Step 4.1

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

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - (19 + \frac{1}{8})$

Step 4.2

Add $19$ and $\frac{1}{8}$ .

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Step 4.2.1

To write $19$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - (19 \cdot \frac{8}{8} + \frac{1}{8})$

Step 4.2.2

Combine $19$ and $\frac{8}{8}$ .

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - (\frac{19 \cdot 8}{8} + \frac{1}{8})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - \frac{19 \cdot 8 + 1}{8}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $19$ by $8$ .

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - \frac{152 + 1}{8}$

Step 4.2.4.2

Add $152$ and $1$ .

$\frac{423}{8} - \frac{25}{2} - \frac{41}{4} - \frac{153}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{423 - 153}{8} + \frac{- 25}{2} + \frac{- 41}{4}$

Step 6

Subtract $153$ from $423$ .

$\frac{270}{8} + \frac{- 25}{2} + \frac{- 41}{4}$

Step 7

Find the common denominator.

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Step 7.1

Multiply $\frac{- 25}{2}$ by $\frac{4}{4}$ .

$\frac{270}{8} + \frac{- 25}{2} \cdot \frac{4}{4} + \frac{- 41}{4}$

Step 7.2

Multiply $\frac{- 25}{2}$ by $\frac{4}{4}$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{2 \cdot 4} + \frac{- 41}{4}$

Step 7.3

Multiply $\frac{- 41}{4}$ by $\frac{2}{2}$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{2 \cdot 4} + \frac{- 41}{4} \cdot \frac{2}{2}$

Step 7.4

Multiply $\frac{- 41}{4}$ by $\frac{2}{2}$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{2 \cdot 4} + \frac{- 41 \cdot 2}{4 \cdot 2}$

Step 7.5

Multiply $2$ by $4$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{8} + \frac{- 41 \cdot 2}{4 \cdot 2}$

Step 7.6

Reorder the factors of $4 \cdot 2$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{8} + \frac{- 41 \cdot 2}{2 \cdot 4}$

Step 7.7

Multiply $2$ by $4$ .

$\frac{270}{8} + \frac{- 25 \cdot 4}{8} + \frac{- 41 \cdot 2}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{270 - 25 \cdot 4 - 41 \cdot 2}{8}$

Step 9

Simplify each term.

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Step 9.1

Multiply $- 25$ by $4$ .

$\frac{270 - 100 - 41 \cdot 2}{8}$

Step 9.2

Multiply $- 41$ by $2$ .

$\frac{270 - 100 - 82}{8}$

Step 10

Simplify the expression.

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Step 10.1

Subtract $100$ from $270$ .

$\frac{170 - 82}{8}$

Step 10.2

Subtract $82$ from $170$ .

$\frac{88}{8}$

Step 10.3

Divide $88$ by $8$ .

$11$