Basic Math Examples

$3 \frac{5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1

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

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Step 1.1

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

$3 + \frac{5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2

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

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Step 1.2.1

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

$3 \cdot \frac{6}{6} + \frac{5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.2

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

$\frac{3 \cdot 6}{6} + \frac{5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 6 + 5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $6$ .

$\frac{18 + 5}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 1.2.4.2

Add $18$ and $5$ .

$\frac{23}{6} - 1 \frac{3}{4} + 2 \frac{1}{2}$

Step 2

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{23}{6} - (1 + \frac{3}{4}) + 2 \frac{1}{2}$

Step 2.2

Add $1$ and $\frac{3}{4}$ .

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Step 2.2.1

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

$\frac{23}{6} - (\frac{4}{4} + \frac{3}{4}) + 2 \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{23}{6} - \frac{4 + 3}{4} + 2 \frac{1}{2}$

Step 2.2.3

Add $4$ and $3$ .

$\frac{23}{6} - \frac{7}{4} + 2 \frac{1}{2}$

Step 3

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

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Step 3.1

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

$\frac{23}{6} - \frac{7}{4} + 2 + \frac{1}{2}$

Step 3.2

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

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Step 3.2.1

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

$\frac{23}{6} - \frac{7}{4} + 2 \cdot \frac{2}{2} + \frac{1}{2}$

Step 3.2.2

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

$\frac{23}{6} - \frac{7}{4} + \frac{2 \cdot 2}{2} + \frac{1}{2}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{23}{6} - \frac{7}{4} + \frac{2 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $2$ .

$\frac{23}{6} - \frac{7}{4} + \frac{4 + 1}{2}$

Step 3.2.4.2

Add $4$ and $1$ .

$\frac{23}{6} - \frac{7}{4} + \frac{5}{2}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{23}{6}$ by $\frac{2}{2}$ .

$\frac{23}{6} \cdot \frac{2}{2} - \frac{7}{4} + \frac{5}{2}$

Step 4.2

Multiply $\frac{23}{6}$ by $\frac{2}{2}$ .

$\frac{23 \cdot 2}{6 \cdot 2} - \frac{7}{4} + \frac{5}{2}$

Step 4.3

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{23 \cdot 2}{6 \cdot 2} - (\frac{7}{4} \cdot \frac{3}{3}) + \frac{5}{2}$

Step 4.4

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{23 \cdot 2}{6 \cdot 2} - \frac{7 \cdot 3}{4 \cdot 3} + \frac{5}{2}$

Step 4.5

Multiply $\frac{5}{2}$ by $\frac{6}{6}$ .

$\frac{23 \cdot 2}{6 \cdot 2} - \frac{7 \cdot 3}{4 \cdot 3} + \frac{5}{2} \cdot \frac{6}{6}$

Step 4.6

Multiply $\frac{5}{2}$ by $\frac{6}{6}$ .

$\frac{23 \cdot 2}{6 \cdot 2} - \frac{7 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 6}{2 \cdot 6}$

Step 4.7

Reorder the factors of $6 \cdot 2$ .

$\frac{23 \cdot 2}{2 \cdot 6} - \frac{7 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 6}{2 \cdot 6}$

Step 4.8

Multiply $2$ by $6$ .

$\frac{23 \cdot 2}{12} - \frac{7 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 6}{2 \cdot 6}$

Step 4.9

Reorder the factors of $4 \cdot 3$ .

$\frac{23 \cdot 2}{12} - \frac{7 \cdot 3}{3 \cdot 4} + \frac{5 \cdot 6}{2 \cdot 6}$

Step 4.10

Multiply $3$ by $4$ .

$\frac{23 \cdot 2}{12} - \frac{7 \cdot 3}{12} + \frac{5 \cdot 6}{2 \cdot 6}$

Step 4.11

Multiply $2$ by $6$ .

$\frac{23 \cdot 2}{12} - \frac{7 \cdot 3}{12} + \frac{5 \cdot 6}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{23 \cdot 2 - 7 \cdot 3 + 5 \cdot 6}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $23$ by $2$ .

$\frac{46 - 7 \cdot 3 + 5 \cdot 6}{12}$

Step 6.2

Multiply $- 7$ by $3$ .

$\frac{46 - 21 + 5 \cdot 6}{12}$

Step 6.3

Multiply $5$ by $6$ .

$\frac{46 - 21 + 30}{12}$

Step 7

Simplify by adding and subtracting.

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Step 7.1

Subtract $21$ from $46$ .

$\frac{25 + 30}{12}$

Step 7.2

Add $25$ and $30$ .

$\frac{55}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{12}$

Decimal Form:

$4.58\overline{3}$

Mixed Number Form:

$4 \frac{7}{12}$