Basic Math Examples

$6 \frac{9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1

Convert $6 \frac{9}{20}$ to an improper fraction.

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Step 1.1

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

$6 + \frac{9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1.2

Add $6$ and $\frac{9}{20}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$6 \cdot \frac{20}{20} + \frac{9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1.2.2

Combine $6$ and $\frac{20}{20}$ .

$\frac{6 \cdot 20}{20} + \frac{9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 20 + 9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $20$ .

$\frac{120 + 9}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 1.2.4.2

Add $120$ and $9$ .

$\frac{129}{20} + 2 \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2

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

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Step 2.1

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

$\frac{129}{20} + 2 + \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2.2

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

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Step 2.2.1

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

$\frac{129}{20} + 2 \cdot \frac{2}{2} + \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2.2.2

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

$\frac{129}{20} + \frac{2 \cdot 2}{2} + \frac{1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{129}{20} + \frac{2 \cdot 2 + 1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$\frac{129}{20} + \frac{4 + 1}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 2.2.4.2

Add $4$ and $1$ .

$\frac{129}{20} + \frac{5}{2} + 3 \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 3

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

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Step 3.1

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

$\frac{129}{20} + \frac{5}{2} + 3 + \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 3.2

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

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{129}{20} + \frac{5}{2} + 3 \cdot \frac{4}{4} + \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 3.2.2

Combine $3$ and $\frac{4}{4}$ .

$\frac{129}{20} + \frac{5}{2} + \frac{3 \cdot 4}{4} + \frac{3}{4} + 4 \frac{1}{4} + 8$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{129}{20} + \frac{5}{2} + \frac{3 \cdot 4 + 3}{4} + 4 \frac{1}{4} + 8$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $4$ .

$\frac{129}{20} + \frac{5}{2} + \frac{12 + 3}{4} + 4 \frac{1}{4} + 8$

Step 3.2.4.2

Add $12$ and $3$ .

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + 4 \frac{1}{4} + 8$

Step 4

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

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Step 4.1

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

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + 4 + \frac{1}{4} + 8$

Step 4.2

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

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Step 4.2.1

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

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + 4 \cdot \frac{4}{4} + \frac{1}{4} + 8$

Step 4.2.2

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

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + \frac{4 \cdot 4}{4} + \frac{1}{4} + 8$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + \frac{4 \cdot 4 + 1}{4} + 8$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $4$ by $4$ .

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + \frac{16 + 1}{4} + 8$

Step 4.2.4.2

Add $16$ and $1$ .

$\frac{129}{20} + \frac{5}{2} + \frac{15}{4} + \frac{17}{4} + 8$

Step 5

Combine the numerators over the common denominator.

$8 + \frac{129}{20} + \frac{5}{2} + \frac{15 + 17}{4}$

Step 6

Add $15$ and $17$ .

$8 + \frac{129}{20} + \frac{5}{2} + \frac{32}{4}$

Step 7

Find the common denominator.

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Step 7.1

Write $8$ as a fraction with denominator $1$ .

$\frac{8}{1} + \frac{129}{20} + \frac{5}{2} + \frac{32}{4}$

Step 7.2

Multiply $\frac{8}{1}$ by $\frac{20}{20}$ .

$\frac{8}{1} \cdot \frac{20}{20} + \frac{129}{20} + \frac{5}{2} + \frac{32}{4}$

Step 7.3

Multiply $\frac{8}{1}$ by $\frac{20}{20}$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5}{2} + \frac{32}{4}$

Step 7.4

Multiply $\frac{5}{2}$ by $\frac{10}{10}$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5}{2} \cdot \frac{10}{10} + \frac{32}{4}$

Step 7.5

Multiply $\frac{5}{2}$ by $\frac{10}{10}$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5 \cdot 10}{2 \cdot 10} + \frac{32}{4}$

Step 7.6

Multiply $\frac{32}{4}$ by $\frac{5}{5}$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5 \cdot 10}{2 \cdot 10} + \frac{32}{4} \cdot \frac{5}{5}$

Step 7.7

Multiply $\frac{32}{4}$ by $\frac{5}{5}$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5 \cdot 10}{2 \cdot 10} + \frac{32 \cdot 5}{4 \cdot 5}$

Step 7.8

Multiply $2$ by $10$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5 \cdot 10}{20} + \frac{32 \cdot 5}{4 \cdot 5}$

Step 7.9

Multiply $4$ by $5$ .

$\frac{8 \cdot 20}{20} + \frac{129}{20} + \frac{5 \cdot 10}{20} + \frac{32 \cdot 5}{20}$

Step 8

Combine the numerators over the common denominator.

$\frac{8 \cdot 20 + 129 + 5 \cdot 10 + 32 \cdot 5}{20}$

Step 9

Simplify each term.

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Step 9.1

Multiply $8$ by $20$ .

$\frac{160 + 129 + 5 \cdot 10 + 32 \cdot 5}{20}$

Step 9.2

Multiply $5$ by $10$ .

$\frac{160 + 129 + 50 + 32 \cdot 5}{20}$

Step 9.3

Multiply $32$ by $5$ .

$\frac{160 + 129 + 50 + 160}{20}$

Step 10

Simplify by adding numbers.

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Step 10.1

Add $160$ and $129$ .

$\frac{289 + 50 + 160}{20}$

Step 10.2

Add $289$ and $50$ .

$\frac{339 + 160}{20}$

Step 10.3

Add $339$ and $160$ .

$\frac{499}{20}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{499}{20}$

Decimal Form:

$24.95$

Mixed Number Form:

$24 \frac{19}{20}$