Basic Math Examples

$15 - (7 - (2 \frac{1}{4} + 1 \frac{7}{8}))$

Step 1

Convert $2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$15 - (7 - (2 + \frac{1}{4} + 1 \frac{7}{8}))$

Step 1.2

Add $2$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$15 - (7 - (2 \cdot \frac{4}{4} + \frac{1}{4} + 1 \frac{7}{8}))$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$15 - (7 - (\frac{2 \cdot 4}{4} + \frac{1}{4} + 1 \frac{7}{8}))$

Step 1.2.3

Combine the numerators over the common denominator.

$15 - (7 - (\frac{2 \cdot 4 + 1}{4} + 1 \frac{7}{8}))$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$15 - (7 - (\frac{8 + 1}{4} + 1 \frac{7}{8}))$

Step 1.2.4.2

Add $8$ and $1$ .

$15 - (7 - (\frac{9}{4} + 1 \frac{7}{8}))$

Step 2

Convert $1 \frac{7}{8}$ to an improper fraction.

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Step 2.1

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

$15 - (7 - (\frac{9}{4} + 1 + \frac{7}{8}))$

Step 2.2

Add $1$ and $\frac{7}{8}$ .

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Step 2.2.1

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

$15 - (7 - (\frac{9}{4} + \frac{8}{8} + \frac{7}{8}))$

Step 2.2.2

Combine the numerators over the common denominator.

$15 - (7 - (\frac{9}{4} + \frac{8 + 7}{8}))$

Step 2.2.3

Add $8$ and $7$ .

$15 - (7 - (\frac{9}{4} + \frac{15}{8}))$

Step 3

Simplify each term.

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Step 3.1

Simplify each term.

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Step 3.1.1

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$15 - (7 - (\frac{9}{4} \cdot \frac{2}{2} + \frac{15}{8}))$

Step 3.1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1.2.1

Multiply $\frac{9}{4}$ by $\frac{2}{2}$ .

$15 - (7 - (\frac{9 \cdot 2}{4 \cdot 2} + \frac{15}{8}))$

Step 3.1.2.2

Multiply $4$ by $2$ .

$15 - (7 - (\frac{9 \cdot 2}{8} + \frac{15}{8}))$

Step 3.1.3

Combine the numerators over the common denominator.

$15 - (7 - \frac{9 \cdot 2 + 15}{8})$

Step 3.1.4

Simplify the numerator.

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Step 3.1.4.1

Multiply $9$ by $2$ .

$15 - (7 - \frac{18 + 15}{8})$

Step 3.1.4.2

Add $18$ and $15$ .

$15 - (7 - \frac{33}{8})$

Step 3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$15 - (7 \cdot \frac{8}{8} - \frac{33}{8})$

Step 3.3

Combine $7$ and $\frac{8}{8}$ .

$15 - (\frac{7 \cdot 8}{8} - \frac{33}{8})$

Step 3.4

Combine the numerators over the common denominator.

$15 - \frac{7 \cdot 8 - 33}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $7$ by $8$ .

$15 - \frac{56 - 33}{8}$

Step 3.5.2

Subtract $33$ from $56$ .

$15 - \frac{23}{8}$

Step 4

To write $15$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$15 \cdot \frac{8}{8} - \frac{23}{8}$

Step 5

Combine $15$ and $\frac{8}{8}$ .

$\frac{15 \cdot 8}{8} - \frac{23}{8}$

Step 6

Combine the numerators over the common denominator.

$\frac{15 \cdot 8 - 23}{8}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $15$ by $8$ .

$\frac{120 - 23}{8}$

Step 7.2

Subtract $23$ from $120$ .

$\frac{97}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{97}{8}$

Decimal Form:

$12.125$

Mixed Number Form:

$12 \frac{1}{8}$