Basic Math Examples

$7 \frac{1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

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.

$7 + \frac{1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

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 $\frac{2}{2}$ .

$7 \cdot \frac{2}{2} + \frac{1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

Step 1.2.2

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

$\frac{7 \cdot 2}{2} + \frac{1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $2$ .

$\frac{14 + 1}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

Step 1.2.4.2

Add $14$ and $1$ .

$\frac{15}{2} - 1 \frac{5}{8} - 2 \frac{3}{16}$

Step 2

Convert $1 \frac{5}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{15}{2} - (1 + \frac{5}{8}) - 2 \frac{3}{16}$

Step 2.2

Add $1$ and $\frac{5}{8}$ .

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Step 2.2.1

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

$\frac{15}{2} - (\frac{8}{8} + \frac{5}{8}) - 2 \frac{3}{16}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{15}{2} - \frac{8 + 5}{8} - 2 \frac{3}{16}$

Step 2.2.3

Add $8$ and $5$ .

$\frac{15}{2} - \frac{13}{8} - 2 \frac{3}{16}$

Step 3

Convert $2 \frac{3}{16}$ to an improper fraction.

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Step 3.1

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

$\frac{15}{2} - \frac{13}{8} - (2 + \frac{3}{16})$

Step 3.2

Add $2$ and $\frac{3}{16}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{15}{2} - \frac{13}{8} - (2 \cdot \frac{16}{16} + \frac{3}{16})$

Step 3.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{15}{2} - \frac{13}{8} - (\frac{2 \cdot 16}{16} + \frac{3}{16})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{15}{2} - \frac{13}{8} - \frac{2 \cdot 16 + 3}{16}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $16$ .

$\frac{15}{2} - \frac{13}{8} - \frac{32 + 3}{16}$

Step 3.2.4.2

Add $32$ and $3$ .

$\frac{15}{2} - \frac{13}{8} - \frac{35}{16}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{15}{2}$ by $\frac{8}{8}$ .

$\frac{15}{2} \cdot \frac{8}{8} - \frac{13}{8} - \frac{35}{16}$

Step 4.2

Multiply $\frac{15}{2}$ by $\frac{8}{8}$ .

$\frac{15 \cdot 8}{2 \cdot 8} - \frac{13}{8} - \frac{35}{16}$

Step 4.3

Multiply $\frac{13}{8}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 8}{2 \cdot 8} - (\frac{13}{8} \cdot \frac{2}{2}) - \frac{35}{16}$

Step 4.4

Multiply $\frac{13}{8}$ by $\frac{2}{2}$ .

$\frac{15 \cdot 8}{2 \cdot 8} - \frac{13 \cdot 2}{8 \cdot 2} - \frac{35}{16}$

Step 4.5

Multiply $2$ by $8$ .

$\frac{15 \cdot 8}{16} - \frac{13 \cdot 2}{8 \cdot 2} - \frac{35}{16}$

Step 4.6

Reorder the factors of $8 \cdot 2$ .

$\frac{15 \cdot 8}{16} - \frac{13 \cdot 2}{2 \cdot 8} - \frac{35}{16}$

Step 4.7

Multiply $2$ by $8$ .

$\frac{15 \cdot 8}{16} - \frac{13 \cdot 2}{16} - \frac{35}{16}$

Step 5

Combine the numerators over the common denominator.

$\frac{15 \cdot 8 - 13 \cdot 2 - 35}{16}$

Step 6

Simplify each term.

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Step 6.1

Multiply $15$ by $8$ .

$\frac{120 - 13 \cdot 2 - 35}{16}$

Step 6.2

Multiply $- 13$ by $2$ .

$\frac{120 - 26 - 35}{16}$

Step 7

Simplify by subtracting numbers.

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Step 7.1

Subtract $26$ from $120$ .

$\frac{94 - 35}{16}$

Step 7.2

Subtract $35$ from $94$ .

$\frac{59}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{16}$

Decimal Form:

$3.6875$

Mixed Number Form:

$3 \frac{11}{16}$