Basic Math Examples

$(10 \frac{1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1

Convert $10 \frac{1}{12}$ to an improper fraction.

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Step 1.1

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

$(10 + \frac{1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1.2

Add $10$ and $\frac{1}{12}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$(10 \cdot \frac{12}{12} + \frac{1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1.2.2

Combine $10$ and $\frac{12}{12}$ .

$(\frac{10 \cdot 12}{12} + \frac{1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{10 \cdot 12 + 1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $12$ .

$(\frac{120 + 1}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 1.2.4.2

Add $120$ and $1$ .

$(\frac{121}{12} + 2 \frac{3}{8}) \div 1 \frac{2}{3}$

Step 2

Convert $2 \frac{3}{8}$ to an improper fraction.

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Step 2.1

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

$(\frac{121}{12} + 2 + \frac{3}{8}) \div 1 \frac{2}{3}$

Step 2.2

Add $2$ and $\frac{3}{8}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{121}{12} + 2 \cdot \frac{8}{8} + \frac{3}{8}) \div 1 \frac{2}{3}$

Step 2.2.2

Combine $2$ and $\frac{8}{8}$ .

$(\frac{121}{12} + \frac{2 \cdot 8}{8} + \frac{3}{8}) \div 1 \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{121}{12} + \frac{2 \cdot 8 + 3}{8}) \div 1 \frac{2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $8$ .

$(\frac{121}{12} + \frac{16 + 3}{8}) \div 1 \frac{2}{3}$

Step 2.2.4.2

Add $16$ and $3$ .

$(\frac{121}{12} + \frac{19}{8}) \div 1 \frac{2}{3}$

Step 3

Convert $1 \frac{2}{3}$ to an improper fraction.

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Step 3.1

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

$(\frac{121}{12} + \frac{19}{8}) \div (1 + \frac{2}{3})$

Step 3.2

Add $1$ and $\frac{2}{3}$ .

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Step 3.2.1

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

$(\frac{121}{12} + \frac{19}{8}) \div (\frac{3}{3} + \frac{2}{3})$

Step 3.2.2

Combine the numerators over the common denominator.

$(\frac{121}{12} + \frac{19}{8}) \div \frac{3 + 2}{3}$

Step 3.2.3

Add $3$ and $2$ .

$(\frac{121}{12} + \frac{19}{8}) \div \frac{5}{3}$

Step 4

To divide by a fraction, multiply by its reciprocal.

$(\frac{121}{12} + \frac{19}{8}) \frac{3}{5}$

Step 5

To write $\frac{121}{12}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{121}{12} \cdot \frac{2}{2} + \frac{19}{8}) \frac{3}{5}$

Step 6

To write $\frac{19}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{121}{12} \cdot \frac{2}{2} + \frac{19}{8} \cdot \frac{3}{3}) \frac{3}{5}$

Step 7

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{121}{12}$ by $\frac{2}{2}$ .

$(\frac{121 \cdot 2}{12 \cdot 2} + \frac{19}{8} \cdot \frac{3}{3}) \frac{3}{5}$

Step 7.2

Multiply $12$ by $2$ .

$(\frac{121 \cdot 2}{24} + \frac{19}{8} \cdot \frac{3}{3}) \frac{3}{5}$

Step 7.3

Multiply $\frac{19}{8}$ by $\frac{3}{3}$ .

$(\frac{121 \cdot 2}{24} + \frac{19 \cdot 3}{8 \cdot 3}) \frac{3}{5}$

Step 7.4

Multiply $8$ by $3$ .

$(\frac{121 \cdot 2}{24} + \frac{19 \cdot 3}{24}) \frac{3}{5}$

Step 8

Combine the numerators over the common denominator.

$\frac{121 \cdot 2 + 19 \cdot 3}{24} \cdot \frac{3}{5}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $121$ by $2$ .

$\frac{242 + 19 \cdot 3}{24} \cdot \frac{3}{5}$

Step 9.2

Multiply $19$ by $3$ .

$\frac{242 + 57}{24} \cdot \frac{3}{5}$

Step 9.3

Add $242$ and $57$ .

$\frac{299}{24} \cdot \frac{3}{5}$

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Factor $3$ out of $24$ .

$\frac{299}{3 (8)} \cdot \frac{3}{5}$

Step 10.2

Cancel the common factor.

$\frac{299}{3 \cdot 8} \cdot \frac{3}{5}$

Step 10.3

Rewrite the expression.

$\frac{299}{8} \cdot \frac{1}{5}$

Step 11

Multiply $\frac{299}{8}$ by $\frac{1}{5}$ .

$\frac{299}{8 \cdot 5}$

Step 12

Multiply $8$ by $5$ .

$\frac{299}{40}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{299}{40}$

Decimal Form:

$7.475$

Mixed Number Form:

$7 \frac{19}{40}$