Basic Math Examples

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

Step 1

Convert $1 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{2}{5}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $5$ and $2$ .

${(\frac{7}{5})}^{2} + {(2 \frac{1}{2})}^{2}$

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.

${(\frac{7}{5})}^{2} + {(2 + \frac{1}{2})}^{2}$

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 $\frac{2}{2}$ .

${(\frac{7}{5})}^{2} + {(2 \cdot \frac{2}{2} + \frac{1}{2})}^{2}$

Step 2.2.2

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

${(\frac{7}{5})}^{2} + {(\frac{2 \cdot 2}{2} + \frac{1}{2})}^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

${(\frac{7}{5})}^{2} + {(\frac{2 \cdot 2 + 1}{2})}^{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

${(\frac{7}{5})}^{2} + {(\frac{4 + 1}{2})}^{2}$

Step 2.2.4.2

Add $4$ and $1$ .

${(\frac{7}{5})}^{2} + {(\frac{5}{2})}^{2}$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{7}{5}$ .

$\frac{7^{2}}{5^{2}} + {(\frac{5}{2})}^{2}$

Step 3.2

Raise $7$ to the power of $2$ .

$\frac{49}{5^{2}} + {(\frac{5}{2})}^{2}$

Step 3.3

Raise $5$ to the power of $2$ .

$\frac{49}{25} + {(\frac{5}{2})}^{2}$

Step 3.4

Apply the product rule to $\frac{5}{2}$ .

$\frac{49}{25} + \frac{5^{2}}{2^{2}}$

Step 3.5

Raise $5$ to the power of $2$ .

$\frac{49}{25} + \frac{25}{2^{2}}$

Step 3.6

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

$\frac{49}{25} + \frac{25}{4}$

Step 4

To write $\frac{49}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{49}{25} \cdot \frac{4}{4} + \frac{25}{4}$

Step 5

To write $\frac{25}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{49}{25} \cdot \frac{4}{4} + \frac{25}{4} \cdot \frac{25}{25}$

Step 6

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{49}{25}$ by $\frac{4}{4}$ .

$\frac{49 \cdot 4}{25 \cdot 4} + \frac{25}{4} \cdot \frac{25}{25}$

Step 6.2

Multiply $25$ by $4$ .

$\frac{49 \cdot 4}{100} + \frac{25}{4} \cdot \frac{25}{25}$

Step 6.3

Multiply $\frac{25}{4}$ by $\frac{25}{25}$ .

$\frac{49 \cdot 4}{100} + \frac{25 \cdot 25}{4 \cdot 25}$

Step 6.4

Multiply $4$ by $25$ .

$\frac{49 \cdot 4}{100} + \frac{25 \cdot 25}{100}$

Step 7

Combine the numerators over the common denominator.

$\frac{49 \cdot 4 + 25 \cdot 25}{100}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $49$ by $4$ .

$\frac{196 + 25 \cdot 25}{100}$

Step 8.2

Multiply $25$ by $25$ .

$\frac{196 + 625}{100}$

Step 8.3

Add $196$ and $625$ .

$\frac{821}{100}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{821}{100}$

Decimal Form:

$8.21$

Mixed Number Form:

$8 \frac{21}{100}$