Basic Math Examples

$(8 \frac{3}{4} + 7 \frac{2}{5}) + 6 \frac{3}{5} = n + 14$

Step 1

Simplify the left side.

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Step 1.1

Simplify $8 \frac{3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5}$ .

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Step 1.1.1

Convert $8 \frac{3}{4}$ 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.

$8 + \frac{3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.1.2

Add $8$ and $\frac{3}{4}$ .

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Step 1.1.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.1.2.2

Combine $8$ and $\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $8$ by $4$ .

$\frac{32 + 3}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.1.2.4.2

Add $32$ and $3$ .

$\frac{35}{4} + 7 \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2

Convert $7 \frac{2}{5}$ 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.

$\frac{35}{4} + 7 + \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2.2

Add $7$ and $\frac{2}{5}$ .

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Step 1.1.2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{35}{4} + 7 \cdot \frac{5}{5} + \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2.2.2

Combine $7$ and $\frac{5}{5}$ .

$\frac{35}{4} + \frac{7 \cdot 5}{5} + \frac{2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{7 \cdot 5 + 2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $7$ by $5$ .

$\frac{35}{4} + \frac{35 + 2}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.2.2.4.2

Add $35$ and $2$ .

$\frac{35}{4} + \frac{37}{5} + 6 \frac{3}{5} = n + 14$

Step 1.1.3

Convert $6 \frac{3}{5}$ to an improper fraction.

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Step 1.1.3.1

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

$\frac{35}{4} + \frac{37}{5} + 6 + \frac{3}{5} = n + 14$

Step 1.1.3.2

Add $6$ and $\frac{3}{5}$ .

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Step 1.1.3.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{35}{4} + \frac{37}{5} + 6 \cdot \frac{5}{5} + \frac{3}{5} = n + 14$

Step 1.1.3.2.2

Combine $6$ and $\frac{5}{5}$ .

$\frac{35}{4} + \frac{37}{5} + \frac{6 \cdot 5}{5} + \frac{3}{5} = n + 14$

Step 1.1.3.2.3

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{37}{5} + \frac{6 \cdot 5 + 3}{5} = n + 14$

Step 1.1.3.2.4

Simplify the numerator.

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Step 1.1.3.2.4.1

Multiply $6$ by $5$ .

$\frac{35}{4} + \frac{37}{5} + \frac{30 + 3}{5} = n + 14$

Step 1.1.3.2.4.2

Add $30$ and $3$ .

$\frac{35}{4} + \frac{37}{5} + \frac{33}{5} = n + 14$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{37 + 33}{5} = n + 14$

Step 1.1.5

Simplify the expression.

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Step 1.1.5.1

Add $37$ and $33$ .

$\frac{35}{4} + \frac{70}{5} = n + 14$

Step 1.1.5.2

Divide $70$ by $5$ .

$\frac{35}{4} + 14 = n + 14$

Step 1.1.6

To write $14$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{35}{4} + 14 \cdot \frac{4}{4} = n + 14$

Step 1.1.7

Combine $14$ and $\frac{4}{4}$ .

$\frac{35}{4} + \frac{14 \cdot 4}{4} = n + 14$

Step 1.1.8

Combine the numerators over the common denominator.

$\frac{35 + 14 \cdot 4}{4} = n + 14$

Step 1.1.9

Simplify the numerator.

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Step 1.1.9.1

Multiply $14$ by $4$ .

$\frac{35 + 56}{4} = n + 14$

Step 1.1.9.2

Add $35$ and $56$ .

$\frac{91}{4} = n + 14$

Step 2

Rewrite the equation as $n + 14 = \frac{91}{4}$ .

$n + 14 = \frac{91}{4}$

Step 3

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

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Step 3.1

Subtract $14$ from both sides of the equation.

$n = \frac{91}{4} - 14$

Step 3.2

To write $- 14$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$n = \frac{91}{4} - 14 \cdot \frac{4}{4}$

Step 3.3

Combine $- 14$ and $\frac{4}{4}$ .

$n = \frac{91}{4} + \frac{- 14 \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$n = \frac{91 - 14 \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 14$ by $4$ .

$n = \frac{91 - 56}{4}$

Step 3.5.2

Subtract $56$ from $91$ .

$n = \frac{35}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{35}{4}$

Decimal Form:

$n = 8.75$

Mixed Number Form:

$n = 8 \frac{3}{4}$