Basic Math Examples

$(10 \frac{2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1

Convert $10 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

$(10 + \frac{2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1.2

Add $10$ and $\frac{2}{5}$ .

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Step 1.2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(10 \cdot \frac{5}{5} + \frac{2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1.2.2

Combine $10$ and $\frac{5}{5}$ .

$(\frac{10 \cdot 5}{5} + \frac{2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{10 \cdot 5 + 2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $10$ by $5$ .

$(\frac{50 + 2}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 1.2.4.2

Add $50$ and $2$ .

$(\frac{52}{5} - 5 \frac{1}{3}) \div 3 \frac{2}{3}$

Step 2

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

$(\frac{52}{5} - (5 + \frac{1}{3})) \div 3 \frac{2}{3}$

Step 2.2

Add $5$ and $\frac{1}{3}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{52}{5} - (5 \cdot \frac{3}{3} + \frac{1}{3})) \div 3 \frac{2}{3}$

Step 2.2.2

Combine $5$ and $\frac{3}{3}$ .

$(\frac{52}{5} - (\frac{5 \cdot 3}{3} + \frac{1}{3})) \div 3 \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{52}{5} - \frac{5 \cdot 3 + 1}{3}) \div 3 \frac{2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $3$ .

$(\frac{52}{5} - \frac{15 + 1}{3}) \div 3 \frac{2}{3}$

Step 2.2.4.2

Add $15$ and $1$ .

$(\frac{52}{5} - \frac{16}{3}) \div 3 \frac{2}{3}$

Step 3

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

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Step 3.1

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

$(\frac{52}{5} - \frac{16}{3}) \div (3 + \frac{2}{3})$

Step 3.2

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

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Step 3.2.1

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

$(\frac{52}{5} - \frac{16}{3}) \div (3 \cdot \frac{3}{3} + \frac{2}{3})$

Step 3.2.2

Combine $3$ and $\frac{3}{3}$ .

$(\frac{52}{5} - \frac{16}{3}) \div (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Step 3.2.3

Combine the numerators over the common denominator.

$(\frac{52}{5} - \frac{16}{3}) \div \frac{3 \cdot 3 + 2}{3}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $3$ .

$(\frac{52}{5} - \frac{16}{3}) \div \frac{9 + 2}{3}$

Step 3.2.4.2

Add $9$ and $2$ .

$(\frac{52}{5} - \frac{16}{3}) \div \frac{11}{3}$

Step 4

To divide by a fraction, multiply by its reciprocal.

$(\frac{52}{5} - \frac{16}{3}) \frac{3}{11}$

Step 5

To write $\frac{52}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{52}{5} \cdot \frac{3}{3} - \frac{16}{3}) \frac{3}{11}$

Step 6

To write $- \frac{16}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{52}{5} \cdot \frac{3}{3} - \frac{16}{3} \cdot \frac{5}{5}) \frac{3}{11}$

Step 7

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{52}{5}$ by $\frac{3}{3}$ .

$(\frac{52 \cdot 3}{5 \cdot 3} - \frac{16}{3} \cdot \frac{5}{5}) \frac{3}{11}$

Step 7.2

Multiply $5$ by $3$ .

$(\frac{52 \cdot 3}{15} - \frac{16}{3} \cdot \frac{5}{5}) \frac{3}{11}$

Step 7.3

Multiply $\frac{16}{3}$ by $\frac{5}{5}$ .

$(\frac{52 \cdot 3}{15} - \frac{16 \cdot 5}{3 \cdot 5}) \frac{3}{11}$

Step 7.4

Multiply $3$ by $5$ .

$(\frac{52 \cdot 3}{15} - \frac{16 \cdot 5}{15}) \frac{3}{11}$

Step 8

Combine the numerators over the common denominator.

$\frac{52 \cdot 3 - 16 \cdot 5}{15} \cdot \frac{3}{11}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $52$ by $3$ .

$\frac{156 - 16 \cdot 5}{15} \cdot \frac{3}{11}$

Step 9.2

Multiply $- 16$ by $5$ .

$\frac{156 - 80}{15} \cdot \frac{3}{11}$

Step 9.3

Subtract $80$ from $156$ .

$\frac{76}{15} \cdot \frac{3}{11}$

Step 10

Cancel the common factor of $3$ .

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Step 10.1

Factor $3$ out of $15$ .

$\frac{76}{3 (5)} \cdot \frac{3}{11}$

Step 10.2

Cancel the common factor.

$\frac{76}{3 \cdot 5} \cdot \frac{3}{11}$

Step 10.3

Rewrite the expression.

$\frac{76}{5} \cdot \frac{1}{11}$

Step 11

Multiply $\frac{76}{5}$ by $\frac{1}{11}$ .

$\frac{76}{5 \cdot 11}$

Step 12

Multiply $5$ by $11$ .

$\frac{76}{55}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{76}{55}$

Decimal Form:

$1.3\overline{81}$

Mixed Number Form:

$1 \frac{21}{55}$