Basic Math Examples

$3 \frac{1}{6} - 1 \frac{1}{2}$

Step 1

Convert $3 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{1}{6} - 1 \frac{1}{2}$

Step 1.2

Add $3$ and $\frac{1}{6}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$3 \cdot \frac{6}{6} + \frac{1}{6} - 1 \frac{1}{2}$

Step 1.2.2

Combine $3$ and $\frac{6}{6}$ .

$\frac{3 \cdot 6}{6} + \frac{1}{6} - 1 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 6 + 1}{6} - 1 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $6$ .

$\frac{18 + 1}{6} - 1 \frac{1}{2}$

Step 1.2.4.2

Add $18$ and $1$ .

$\frac{19}{6} - 1 \frac{1}{2}$

Step 2

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

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Step 2.1

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

$\frac{19}{6} - (1 + \frac{1}{2})$

Step 2.2

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

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Step 2.2.1

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

$\frac{19}{6} - (\frac{2}{2} + \frac{1}{2})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{19}{6} - \frac{2 + 1}{2}$

Step 2.2.3

Add $2$ and $1$ .

$\frac{19}{6} - \frac{3}{2}$

Step 3

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{19}{6} - \frac{3}{2} \cdot \frac{3}{3}$

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 $\frac{3}{2}$ by $\frac{3}{3}$ .

$\frac{19}{6} - \frac{3 \cdot 3}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{19}{6} - \frac{3 \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{19 - 3 \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $3$ .

$\frac{19 - 9}{6}$

Step 6.2

Subtract $9$ from $19$ .

$\frac{10}{6}$

Step 7

Cancel the common factor of $10$ and $6$ .

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Step 7.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 7.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 3}$

Step 7.2.3

Rewrite the expression.

$\frac{5}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{3}$

Decimal Form:

$1.\overline{6}$

Mixed Number Form:

$1 \frac{2}{3}$