Basic Math Examples

$17 \frac{1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1

Convert $17 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$17 + \frac{1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1.2

Add $17$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $17$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$17 \cdot \frac{2}{2} + \frac{1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1.2.2

Combine $17$ and $\frac{2}{2}$ .

$\frac{17 \cdot 2}{2} + \frac{1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{17 \cdot 2 + 1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $17$ by $2$ .

$\frac{34 + 1}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 1.2.4.2

Add $34$ and $1$ .

$\frac{35}{2} - 2 \frac{1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2

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

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Step 2.1

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

$\frac{35}{2} - (2 + \frac{1}{2}) - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2.2

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

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Step 2.2.1

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

$\frac{35}{2} - (2 \cdot \frac{2}{2} + \frac{1}{2}) - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2.2.2

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

$\frac{35}{2} - (\frac{2 \cdot 2}{2} + \frac{1}{2}) - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{35}{2} - \frac{2 \cdot 2 + 1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$\frac{35}{2} - \frac{4 + 1}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 2.2.4.2

Add $4$ and $1$ .

$\frac{35}{2} - \frac{5}{2} - 3 \frac{1}{4} - 1 \frac{4}{7}$

Step 3

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{35}{2} - \frac{5}{2} - (3 + \frac{1}{4}) - 1 \frac{4}{7}$

Step 3.2

Add $3$ and $\frac{1}{4}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{35}{2} - \frac{5}{2} - (3 \cdot \frac{4}{4} + \frac{1}{4}) - 1 \frac{4}{7}$

Step 3.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{35}{2} - \frac{5}{2} - (\frac{3 \cdot 4}{4} + \frac{1}{4}) - 1 \frac{4}{7}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{35}{2} - \frac{5}{2} - \frac{3 \cdot 4 + 1}{4} - 1 \frac{4}{7}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $4$ .

$\frac{35}{2} - \frac{5}{2} - \frac{12 + 1}{4} - 1 \frac{4}{7}$

Step 3.2.4.2

Add $12$ and $1$ .

$\frac{35}{2} - \frac{5}{2} - \frac{13}{4} - 1 \frac{4}{7}$

Step 4

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

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Step 4.1

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

$\frac{35}{2} - \frac{5}{2} - \frac{13}{4} - (1 + \frac{4}{7})$

Step 4.2

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

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Step 4.2.1

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

$\frac{35}{2} - \frac{5}{2} - \frac{13}{4} - (\frac{7}{7} + \frac{4}{7})$

Step 4.2.2

Combine the numerators over the common denominator.

$\frac{35}{2} - \frac{5}{2} - \frac{13}{4} - \frac{7 + 4}{7}$

Step 4.2.3

Add $7$ and $4$ .

$\frac{35}{2} - \frac{5}{2} - \frac{13}{4} - \frac{11}{7}$

Step 5

Combine the numerators over the common denominator.

$\frac{35 - 5}{2} + \frac{- 13}{4} + \frac{- 11}{7}$

Step 6

Subtract $5$ from $35$ .

$\frac{30}{2} + \frac{- 13}{4} + \frac{- 11}{7}$

Step 7

Find the common denominator.

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Step 7.1

Multiply $\frac{30}{2}$ by $\frac{14}{14}$ .

$\frac{30}{2} \cdot \frac{14}{14} + \frac{- 13}{4} + \frac{- 11}{7}$

Step 7.2

Multiply $\frac{30}{2}$ by $\frac{14}{14}$ .

$\frac{30 \cdot 14}{2 \cdot 14} + \frac{- 13}{4} + \frac{- 11}{7}$

Step 7.3

Multiply $\frac{- 13}{4}$ by $\frac{7}{7}$ .

$\frac{30 \cdot 14}{2 \cdot 14} + \frac{- 13}{4} \cdot \frac{7}{7} + \frac{- 11}{7}$

Step 7.4

Multiply $\frac{- 13}{4}$ by $\frac{7}{7}$ .

$\frac{30 \cdot 14}{2 \cdot 14} + \frac{- 13 \cdot 7}{4 \cdot 7} + \frac{- 11}{7}$

Step 7.5

Multiply $\frac{- 11}{7}$ by $\frac{4}{4}$ .

$\frac{30 \cdot 14}{2 \cdot 14} + \frac{- 13 \cdot 7}{4 \cdot 7} + \frac{- 11}{7} \cdot \frac{4}{4}$

Step 7.6

Multiply $\frac{- 11}{7}$ by $\frac{4}{4}$ .

$\frac{30 \cdot 14}{2 \cdot 14} + \frac{- 13 \cdot 7}{4 \cdot 7} + \frac{- 11 \cdot 4}{7 \cdot 4}$

Step 7.7

Multiply $2$ by $14$ .

$\frac{30 \cdot 14}{28} + \frac{- 13 \cdot 7}{4 \cdot 7} + \frac{- 11 \cdot 4}{7 \cdot 4}$

Step 7.8

Multiply $4$ by $7$ .

$\frac{30 \cdot 14}{28} + \frac{- 13 \cdot 7}{28} + \frac{- 11 \cdot 4}{7 \cdot 4}$

Step 7.9

Reorder the factors of $7 \cdot 4$ .

$\frac{30 \cdot 14}{28} + \frac{- 13 \cdot 7}{28} + \frac{- 11 \cdot 4}{4 \cdot 7}$

Step 7.10

Multiply $4$ by $7$ .

$\frac{30 \cdot 14}{28} + \frac{- 13 \cdot 7}{28} + \frac{- 11 \cdot 4}{28}$

Step 8

Combine the numerators over the common denominator.

$\frac{30 \cdot 14 - 13 \cdot 7 - 11 \cdot 4}{28}$

Step 9

Simplify each term.

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Step 9.1

Multiply $30$ by $14$ .

$\frac{420 - 13 \cdot 7 - 11 \cdot 4}{28}$

Step 9.2

Multiply $- 13$ by $7$ .

$\frac{420 - 91 - 11 \cdot 4}{28}$

Step 9.3

Multiply $- 11$ by $4$ .

$\frac{420 - 91 - 44}{28}$

Step 10

Simplify by subtracting numbers.

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Step 10.1

Subtract $91$ from $420$ .

$\frac{329 - 44}{28}$

Step 10.2

Subtract $44$ from $329$ .

$\frac{285}{28}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{285}{28}$

Decimal Form:

$10.17857142 \dots$

Mixed Number Form:

$10 \frac{5}{28}$