Basic Math Examples

$7 \frac{1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $7 \frac{1}{2} + 6 \frac{3}{4} + n$ .

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Step 1.1.1

Convert $7 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

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

$7 + \frac{1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.1.2

Add $7$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$7 \cdot \frac{2}{2} + \frac{1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.1.2.2

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

$\frac{7 \cdot 2}{2} + \frac{1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 2 + 1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $7$ by $2$ .

$\frac{14 + 1}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.1.2.4.2

Add $14$ and $1$ .

$\frac{15}{2} + 6 \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2

Convert $6 \frac{3}{4}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{15}{2} + 6 + \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2.2

Add $6$ and $\frac{3}{4}$ .

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Step 1.1.2.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{15}{2} + 6 \cdot \frac{4}{4} + \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2.2.2

Combine $6$ and $\frac{4}{4}$ .

$\frac{15}{2} + \frac{6 \cdot 4}{4} + \frac{3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{15}{2} + \frac{6 \cdot 4 + 3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $6$ by $4$ .

$\frac{15}{2} + \frac{24 + 3}{4} + n = 15 \frac{3}{8}$

Step 1.1.2.2.4.2

Add $24$ and $3$ .

$\frac{15}{2} + \frac{27}{4} + n = 15 \frac{3}{8}$

Step 1.1.3

To write $\frac{15}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{15}{2} \cdot \frac{2}{2} + \frac{27}{4} + n = 15 \frac{3}{8}$

Step 1.1.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.4.1

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

$\frac{15 \cdot 2}{2 \cdot 2} + \frac{27}{4} + n = 15 \frac{3}{8}$

Step 1.1.4.2

Multiply $2$ by $2$ .

$\frac{15 \cdot 2}{4} + \frac{27}{4} + n = 15 \frac{3}{8}$

Step 1.1.5

Combine the numerators over the common denominator.

$\frac{15 \cdot 2 + 27}{4} + n = 15 \frac{3}{8}$

Step 1.1.6

Simplify the numerator.

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Step 1.1.6.1

Multiply $15$ by $2$ .

$\frac{30 + 27}{4} + n = 15 \frac{3}{8}$

Step 1.1.6.2

Add $30$ and $27$ .

$\frac{57}{4} + n = 15 \frac{3}{8}$

Step 2

Simplify the right side.

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Step 2.1

Convert $15 \frac{3}{8}$ to an improper fraction.

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Step 2.1.1

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

$\frac{57}{4} + n = 15 + \frac{3}{8}$

Step 2.1.2

Add $15$ and $\frac{3}{8}$ .

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Step 2.1.2.1

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

$\frac{57}{4} + n = 15 \cdot \frac{8}{8} + \frac{3}{8}$

Step 2.1.2.2

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

$\frac{57}{4} + n = \frac{15 \cdot 8}{8} + \frac{3}{8}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{57}{4} + n = \frac{15 \cdot 8 + 3}{8}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $15$ by $8$ .

$\frac{57}{4} + n = \frac{120 + 3}{8}$

Step 2.1.2.4.2

Add $120$ and $3$ .

$\frac{57}{4} + n = \frac{123}{8}$

Step 3

Move all terms not containing $n$ to the right side of the equation.

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Step 3.1

Subtract $\frac{57}{4}$ from both sides of the equation.

$n = \frac{123}{8} - \frac{57}{4}$

Step 3.2

To write $- \frac{57}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$n = \frac{123}{8} - \frac{57}{4} \cdot \frac{2}{2}$

Step 3.3

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

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Step 3.3.1

Multiply $\frac{57}{4}$ by $\frac{2}{2}$ .

$n = \frac{123}{8} - \frac{57 \cdot 2}{4 \cdot 2}$

Step 3.3.2

Multiply $4$ by $2$ .

$n = \frac{123}{8} - \frac{57 \cdot 2}{8}$

Step 3.4

Combine the numerators over the common denominator.

$n = \frac{123 - 57 \cdot 2}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 57$ by $2$ .

$n = \frac{123 - 114}{8}$

Step 3.5.2

Subtract $114$ from $123$ .

$n = \frac{9}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{9}{8}$

Decimal Form:

$n = 1.125$

Mixed Number Form:

$n = 1 \frac{1}{8}$