Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.2.4.2

Add $4$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $3$ .

$\frac{5}{2} + \frac{9 + 1}{3} + 1 \frac{5}{6}$

Step 2.2.4.2

Add $9$ and $1$ .

$\frac{5}{2} + \frac{10}{3} + 1 \frac{5}{6}$

Step 3

Convert $1 \frac{5}{6}$ to an improper fraction.

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Step 3.1

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

$\frac{5}{2} + \frac{10}{3} + 1 + \frac{5}{6}$

Step 3.2

Add $1$ and $\frac{5}{6}$ .

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Step 3.2.1

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

$\frac{5}{2} + \frac{10}{3} + \frac{6}{6} + \frac{5}{6}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{10}{3} + \frac{6 + 5}{6}$

Step 3.2.3

Add $6$ and $5$ .

$\frac{5}{2} + \frac{10}{3} + \frac{11}{6}$

Step 4

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{2} \cdot \frac{3}{3} + \frac{10}{3} + \frac{11}{6}$

Step 5

To write $\frac{10}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{2} \cdot \frac{3}{3} + \frac{10}{3} \cdot \frac{2}{2} + \frac{11}{6}$

Step 6

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 \cdot 3} + \frac{10}{3} \cdot \frac{2}{2} + \frac{11}{6}$

Step 6.2

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6} + \frac{10}{3} \cdot \frac{2}{2} + \frac{11}{6}$

Step 6.3

Multiply $\frac{10}{3}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{6} + \frac{10 \cdot 2}{3 \cdot 2} + \frac{11}{6}$

Step 6.4

Multiply $3$ by $2$ .

$\frac{5 \cdot 3}{6} + \frac{10 \cdot 2}{6} + \frac{11}{6}$

Step 7

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 + 10 \cdot 2}{6} + \frac{11}{6}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $5$ by $3$ .

$\frac{15 + 10 \cdot 2}{6} + \frac{11}{6}$

Step 8.2

Multiply $10$ by $2$ .

$\frac{15 + 20}{6} + \frac{11}{6}$

Step 8.3

Add $15$ and $20$ .

$\frac{35}{6} + \frac{11}{6}$

Step 9

Combine the numerators over the common denominator.

$\frac{35 + 11}{6}$

Step 10

Add $35$ and $11$ .

$\frac{46}{6}$

Step 11

Cancel the common factor of $46$ and $6$ .

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Step 11.1

Factor $2$ out of $46$ .

$\frac{2 (23)}{6}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 23}{2 \cdot 3}$

Step 11.2.2

Cancel the common factor.

$\frac{2 \cdot 23}{2 \cdot 3}$

Step 11.2.3

Rewrite the expression.

$\frac{23}{3}$