Basic Math Examples

$2 \frac{1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

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.

$2 + \frac{1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

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 $\frac{2}{2}$ .

$2 \cdot \frac{2}{2} + \frac{1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 1.2.2

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

$\frac{2 \cdot 2}{2} + \frac{1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $2$ .

$\frac{4 + 1}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 1.2.4.2

Add $4$ and $1$ .

$\frac{5}{2} + 3 \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2

Convert $3 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{5}{2} + 3 + \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2.2

Add $3$ and $\frac{2}{5}$ .

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Step 2.2.1

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

$\frac{5}{2} + 3 \cdot \frac{5}{5} + \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2.2.2

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

$\frac{5}{2} + \frac{3 \cdot 5}{5} + \frac{2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{3 \cdot 5 + 2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $5$ .

$\frac{5}{2} + \frac{15 + 2}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 2.2.4.2

Add $15$ and $2$ .

$\frac{5}{2} + \frac{17}{5} + 2 \frac{3}{4} + 3 \frac{5}{8}$

Step 3

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{5}{2} + \frac{17}{5} + 2 + \frac{3}{4} + 3 \frac{5}{8}$

Step 3.2

Add $2$ and $\frac{3}{4}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5}{2} + \frac{17}{5} + 2 \cdot \frac{4}{4} + \frac{3}{4} + 3 \frac{5}{8}$

Step 3.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{5}{2} + \frac{17}{5} + \frac{2 \cdot 4}{4} + \frac{3}{4} + 3 \frac{5}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{17}{5} + \frac{2 \cdot 4 + 3}{4} + 3 \frac{5}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $4$ .

$\frac{5}{2} + \frac{17}{5} + \frac{8 + 3}{4} + 3 \frac{5}{8}$

Step 3.2.4.2

Add $8$ and $3$ .

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + 3 \frac{5}{8}$

Step 4

Convert $3 \frac{5}{8}$ to an improper fraction.

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Step 4.1

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

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + 3 + \frac{5}{8}$

Step 4.2

Add $3$ and $\frac{5}{8}$ .

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Step 4.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + 3 \cdot \frac{8}{8} + \frac{5}{8}$

Step 4.2.2

Combine $3$ and $\frac{8}{8}$ .

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + \frac{3 \cdot 8}{8} + \frac{5}{8}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + \frac{3 \cdot 8 + 5}{8}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $3$ by $8$ .

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + \frac{24 + 5}{8}$

Step 4.2.4.2

Add $24$ and $5$ .

$\frac{5}{2} + \frac{17}{5} + \frac{11}{4} + \frac{29}{8}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{5}{2}$ by $\frac{20}{20}$ .

$\frac{5}{2} \cdot \frac{20}{20} + \frac{17}{5} + \frac{11}{4} + \frac{29}{8}$

Step 5.2

Multiply $\frac{5}{2}$ by $\frac{20}{20}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17}{5} + \frac{11}{4} + \frac{29}{8}$

Step 5.3

Multiply $\frac{17}{5}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17}{5} \cdot \frac{8}{8} + \frac{11}{4} + \frac{29}{8}$

Step 5.4

Multiply $\frac{17}{5}$ by $\frac{8}{8}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11}{4} + \frac{29}{8}$

Step 5.5

Multiply $\frac{11}{4}$ by $\frac{10}{10}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11}{4} \cdot \frac{10}{10} + \frac{29}{8}$

Step 5.6

Multiply $\frac{11}{4}$ by $\frac{10}{10}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11 \cdot 10}{4 \cdot 10} + \frac{29}{8}$

Step 5.7

Multiply $\frac{29}{8}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11 \cdot 10}{4 \cdot 10} + \frac{29}{8} \cdot \frac{5}{5}$

Step 5.8

Multiply $\frac{29}{8}$ by $\frac{5}{5}$ .

$\frac{5 \cdot 20}{2 \cdot 20} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11 \cdot 10}{4 \cdot 10} + \frac{29 \cdot 5}{8 \cdot 5}$

Step 5.9

Multiply $2$ by $20$ .

$\frac{5 \cdot 20}{40} + \frac{17 \cdot 8}{5 \cdot 8} + \frac{11 \cdot 10}{4 \cdot 10} + \frac{29 \cdot 5}{8 \cdot 5}$

Step 5.10

Multiply $5$ by $8$ .

$\frac{5 \cdot 20}{40} + \frac{17 \cdot 8}{40} + \frac{11 \cdot 10}{4 \cdot 10} + \frac{29 \cdot 5}{8 \cdot 5}$

Step 5.11

Multiply $4$ by $10$ .

$\frac{5 \cdot 20}{40} + \frac{17 \cdot 8}{40} + \frac{11 \cdot 10}{40} + \frac{29 \cdot 5}{8 \cdot 5}$

Step 5.12

Reorder the factors of $8 \cdot 5$ .

$\frac{5 \cdot 20}{40} + \frac{17 \cdot 8}{40} + \frac{11 \cdot 10}{40} + \frac{29 \cdot 5}{5 \cdot 8}$

Step 5.13

Multiply $5$ by $8$ .

$\frac{5 \cdot 20}{40} + \frac{17 \cdot 8}{40} + \frac{11 \cdot 10}{40} + \frac{29 \cdot 5}{40}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 \cdot 20 + 17 \cdot 8 + 11 \cdot 10 + 29 \cdot 5}{40}$

Step 7

Simplify each term.

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Step 7.1

Multiply $5$ by $20$ .

$\frac{100 + 17 \cdot 8 + 11 \cdot 10 + 29 \cdot 5}{40}$

Step 7.2

Multiply $17$ by $8$ .

$\frac{100 + 136 + 11 \cdot 10 + 29 \cdot 5}{40}$

Step 7.3

Multiply $11$ by $10$ .

$\frac{100 + 136 + 110 + 29 \cdot 5}{40}$

Step 7.4

Multiply $29$ by $5$ .

$\frac{100 + 136 + 110 + 145}{40}$

Step 8

Simplify by adding numbers.

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Step 8.1

Add $100$ and $136$ .

$\frac{236 + 110 + 145}{40}$

Step 8.2

Add $236$ and $110$ .

$\frac{346 + 145}{40}$

Step 8.3

Add $346$ and $145$ .

$\frac{491}{40}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{491}{40}$

Decimal Form:

$12.275$

Mixed Number Form:

$12 \frac{11}{40}$