Basic Math Examples

${(\frac{1}{3})}^{2} + \frac{1}{3} + 1 \frac{4}{5}$

Step 1

Convert $1 \frac{4}{5}$ to an improper fraction.

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Step 1.1

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

${(\frac{1}{3})}^{2} + \frac{1}{3} + 1 + \frac{4}{5}$

Step 1.2

Add $1$ and $\frac{4}{5}$ .

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Step 1.2.1

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

${(\frac{1}{3})}^{2} + \frac{1}{3} + \frac{5}{5} + \frac{4}{5}$

Step 1.2.2

Combine the numerators over the common denominator.

${(\frac{1}{3})}^{2} + \frac{1}{3} + \frac{5 + 4}{5}$

Step 1.2.3

Add $5$ and $4$ .

${(\frac{1}{3})}^{2} + \frac{1}{3} + \frac{9}{5}$

Step 2

Find the common denominator.

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Step 2.1

Write ${(\frac{1}{3})}^{2}$ as a fraction with denominator $1$ .

$\frac{{(\frac{1}{3})}^{2}}{1} + \frac{1}{3} + \frac{9}{5}$

Step 2.2

Multiply $\frac{{(\frac{1}{3})}^{2}}{1}$ by $\frac{15}{15}$ .

$\frac{{(\frac{1}{3})}^{2}}{1} \cdot \frac{15}{15} + \frac{1}{3} + \frac{9}{5}$

Step 2.3

Multiply $\frac{{(\frac{1}{3})}^{2}}{1}$ by $\frac{15}{15}$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{1}{3} + \frac{9}{5}$

Step 2.4

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{1}{3} \cdot \frac{5}{5} + \frac{9}{5}$

Step 2.5

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{3 \cdot 5} + \frac{9}{5}$

Step 2.6

Multiply $\frac{9}{5}$ by $\frac{3}{3}$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{3 \cdot 5} + \frac{9}{5} \cdot \frac{3}{3}$

Step 2.7

Multiply $\frac{9}{5}$ by $\frac{3}{3}$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{3 \cdot 5} + \frac{9 \cdot 3}{5 \cdot 3}$

Step 2.8

Multiply $3$ by $5$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{15} + \frac{9 \cdot 3}{5 \cdot 3}$

Step 2.9

Reorder the factors of $5 \cdot 3$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{15} + \frac{9 \cdot 3}{3 \cdot 5}$

Step 2.10

Multiply $3$ by $5$ .

$\frac{{(\frac{1}{3})}^{2} \cdot 15}{15} + \frac{5}{15} + \frac{9 \cdot 3}{15}$

Step 3

Combine the numerators over the common denominator.

$\frac{{(\frac{1}{3})}^{2} \cdot 15 + 5 + 9 \cdot 3}{15}$

Step 4

Simplify each term.

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Step 4.1

Apply the product rule to $\frac{1}{3}$ .

$\frac{\frac{1^{2}}{3^{2}} \cdot 15 + 5 + 9 \cdot 3}{15}$

Step 4.2

One to any power is one.

$\frac{\frac{1}{3^{2}} \cdot 15 + 5 + 9 \cdot 3}{15}$

Step 4.3

Raise $3$ to the power of $2$ .

$\frac{\frac{1}{9} \cdot 15 + 5 + 9 \cdot 3}{15}$

Step 4.4

Cancel the common factor of $3$ .

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Step 4.4.1

Factor $3$ out of $9$ .

$\frac{\frac{1}{3 (3)} \cdot 15 + 5 + 9 \cdot 3}{15}$

Step 4.4.2

Factor $3$ out of $15$ .

$\frac{\frac{1}{3 \cdot 3} \cdot (3 \cdot 5) + 5 + 9 \cdot 3}{15}$

Step 4.4.3

Cancel the common factor.

$\frac{\frac{1}{3 \cdot 3} \cdot (3 \cdot 5) + 5 + 9 \cdot 3}{15}$

Step 4.4.4

Rewrite the expression.

$\frac{\frac{1}{3} \cdot 5 + 5 + 9 \cdot 3}{15}$

Step 4.5

Combine $\frac{1}{3}$ and $5$ .

$\frac{\frac{5}{3} + 5 + 9 \cdot 3}{15}$

Step 4.6

Multiply $9$ by $3$ .

$\frac{\frac{5}{3} + 5 + 27}{15}$

Step 5

Find the common denominator.

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Step 5.1

Write $5$ as a fraction with denominator $1$ .

$\frac{\frac{5}{3} + \frac{5}{1} + 27}{15}$

Step 5.2

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{5}{3} + \frac{5}{1} \cdot \frac{3}{3} + 27}{15}$

Step 5.3

Multiply $\frac{5}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{5}{3} + \frac{5 \cdot 3}{3} + 27}{15}$

Step 5.4

Write $27$ as a fraction with denominator $1$ .

$\frac{\frac{5}{3} + \frac{5 \cdot 3}{3} + \frac{27}{1}}{15}$

Step 5.5

Multiply $\frac{27}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{5}{3} + \frac{5 \cdot 3}{3} + \frac{27}{1} \cdot \frac{3}{3}}{15}$

Step 5.6

Multiply $\frac{27}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{5}{3} + \frac{5 \cdot 3}{3} + \frac{27 \cdot 3}{3}}{15}$

Step 6

Combine the numerators over the common denominator.

$\frac{\frac{5 + 5 \cdot 3 + 27 \cdot 3}{3}}{15}$

Step 7

Simplify each term.

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Step 7.1

Multiply $5$ by $3$ .

$\frac{\frac{5 + 15 + 27 \cdot 3}{3}}{15}$

Step 7.2

Multiply $27$ by $3$ .

$\frac{\frac{5 + 15 + 81}{3}}{15}$

Step 8

Simplify by adding numbers.

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Step 8.1

Add $5$ and $15$ .

$\frac{\frac{20 + 81}{3}}{15}$

Step 8.2

Add $20$ and $81$ .

$\frac{\frac{101}{3}}{15}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{101}{3} \cdot \frac{1}{15}$

Step 10

Multiply $\frac{101}{3} \cdot \frac{1}{15}$ .

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Step 10.1

Multiply $\frac{101}{3}$ by $\frac{1}{15}$ .

$\frac{101}{3 \cdot 15}$

Step 10.2

Multiply $3$ by $15$ .

$\frac{101}{45}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{101}{45}$

Decimal Form:

$2.2\overline{4}$

Mixed Number Form:

$2 \frac{11}{45}$