Basic Math Examples

$5 \frac{1}{3} - 3 \frac{5}{6}$

Step 1

Convert

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

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Step 1.1

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

$5 + \frac{1}{3} - 3 \frac{5}{6}$

Step 1.2

Add

$5$ and

$\frac{1}{3}$ .

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Step 1.2.1

To write

$5$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$5 \cdot \frac{3}{3} + \frac{1}{3} - 3 \frac{5}{6}$

Step 1.2.2

Combine

$5$ and

$\frac{3}{3}$ .

$\frac{5 \cdot 3}{3} + \frac{1}{3} - 3 \frac{5}{6}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 1}{3} - 3 \frac{5}{6}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$5$ by

$3$ .

$\frac{15 + 1}{3} - 3 \frac{5}{6}$

Step 1.2.4.2

Add

$15$ and

$1$ .

$\frac{16}{3} - 3 \frac{5}{6}$

Step 2

Convert

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

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Step 2.1

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

$\frac{16}{3} - (3 + \frac{5}{6})$

Step 2.2

Add

$3$ and

$\frac{5}{6}$ .

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Step 2.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{6}{6}$ .

$\frac{16}{3} - (3 \cdot \frac{6}{6} + \frac{5}{6})$

Step 2.2.2

Combine

$3$ and

$\frac{6}{6}$ .

$\frac{16}{3} - (\frac{3 \cdot 6}{6} + \frac{5}{6})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16}{3} - \frac{3 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$6$ .

$\frac{16}{3} - \frac{18 + 5}{6}$

Step 2.2.4.2

Add

$18$ and

$5$ .

$\frac{16}{3} - \frac{23}{6}$

Step 3

To write

$\frac{16}{3}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$\frac{16}{3} \cdot \frac{2}{2} - \frac{23}{6}$

Step 4

Write each expression with a common denominator of

$6$ , by multiplying each by an appropriate factor of

$1$ .

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Step 4.1

Multiply

$\frac{16}{3}$ by

$\frac{2}{2}$ .

$\frac{16 \cdot 2}{3 \cdot 2} - \frac{23}{6}$

Step 4.2

Multiply

$3$ by

$2$ .

$\frac{16 \cdot 2}{6} - \frac{23}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 - 23}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

$16$ by

$2$ .

$\frac{32 - 23}{6}$

Step 6.2

Subtract

$23$ from

$32$ .

$\frac{9}{6}$

Step 7

Cancel the common factor of

$9$ and

$6$ .

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Step 7.1

Factor

$3$ out of

$9$ .

$\frac{3 (3)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor

$3$ out of

$6$ .

$\frac{3 \cdot 3}{3 \cdot 2}$

Step 7.2.2

Cancel the common factor.

$\frac{3 \cdot 3}{3 \cdot 2}$

Step 7.2.3

Rewrite the expression.

$\frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$