Basic Math Examples

$2 \frac{5}{32}$ , $2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1

Convert $2 \frac{5}{32}$ to an improper fraction.

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Step 1.1

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

$2 + \frac{5}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1.2

Add $2$ and $\frac{5}{32}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$2 \cdot \frac{32}{32} + \frac{5}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1.2.2

Combine $2$ and $\frac{32}{32}$ .

$\frac{2 \cdot 32}{32} + \frac{5}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 32 + 5}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $32$ .

$\frac{64 + 5}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 1.2.4.2

Add $64$ and $5$ .

$\frac{69}{32}, 2 \frac{7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2

Convert $2 \frac{7}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{69}{32}, (2 + \frac{7}{8}) \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2.2

Add $2$ and $\frac{7}{8}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{69}{32}, (2 \cdot \frac{8}{8} + \frac{7}{8}) \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{69}{32}, (\frac{2 \cdot 8}{8} + \frac{7}{8}) \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{69}{32}, \frac{2 \cdot 8 + 7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $8$ .

$\frac{69}{32}, \frac{16 + 7}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 2.2.4.2

Add $16$ and $7$ .

$\frac{69}{32}, \frac{23}{8} \cdot 2 \frac{9}{16} \cdot 2 \frac{7}{16}$

Step 3

Convert $2 \frac{9}{16}$ to an improper fraction.

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Step 3.1

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

$\frac{69}{32}, \frac{23}{8} \cdot (2 + \frac{9}{16}) \cdot 2 \frac{7}{16}$

Step 3.2

Add $2$ and $\frac{9}{16}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{69}{32}, \frac{23}{8} \cdot (2 \cdot \frac{16}{16} + \frac{9}{16}) \cdot 2 \frac{7}{16}$

Step 3.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{69}{32}, \frac{23}{8} \cdot (\frac{2 \cdot 16}{16} + \frac{9}{16}) \cdot 2 \frac{7}{16}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{69}{32}, \frac{23}{8} \cdot \frac{2 \cdot 16 + 9}{16} \cdot 2 \frac{7}{16}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $16$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{32 + 9}{16} \cdot 2 \frac{7}{16}$

Step 3.2.4.2

Add $32$ and $9$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot 2 \frac{7}{16}$

Step 4

Convert $2 \frac{7}{16}$ to an improper fraction.

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Step 4.1

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

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot (2 + \frac{7}{16})$

Step 4.2

Add $2$ and $\frac{7}{16}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot (2 \cdot \frac{16}{16} + \frac{7}{16})$

Step 4.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot (\frac{2 \cdot 16}{16} + \frac{7}{16})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot \frac{2 \cdot 16 + 7}{16}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $16$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot \frac{32 + 7}{16}$

Step 4.2.4.2

Add $32$ and $7$ .

$\frac{69}{32}, \frac{23}{8} \cdot \frac{41}{16} \cdot \frac{39}{16}$

Step 5

Multiply $\frac{23}{8} \cdot \frac{41}{16}$ .

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Step 5.1

Multiply $\frac{23}{8}$ by $\frac{41}{16}$ .

$\frac{69}{32}, \frac{23 \cdot 41}{8 \cdot 16} \cdot \frac{39}{16}$

Step 5.2

Multiply $23$ by $41$ .

$\frac{69}{32}, \frac{943}{8 \cdot 16} \cdot \frac{39}{16}$

Step 5.3

Multiply $8$ by $16$ .

$\frac{69}{32}, \frac{943}{128} \cdot \frac{39}{16}$

Step 6

Multiply $\frac{943}{128} \cdot \frac{39}{16}$ .

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Step 6.1

Multiply $\frac{943}{128}$ by $\frac{39}{16}$ .

$\frac{69}{32}, \frac{943 \cdot 39}{128 \cdot 16}$

Step 6.2

Multiply $943$ by $39$ .

$\frac{69}{32}, \frac{36777}{128 \cdot 16}$

Step 6.3

Multiply $128$ by $16$ .

$\frac{69}{32}, \frac{36777}{2048}$

Step 7

The mean of a set of numbers is the sum divided by the number of terms.

$\frac{\frac{69}{32} + \frac{36777}{2048}}{2}$

Step 8

Simplify the numerator.

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Step 8.1

To write $\frac{69}{32}$ as a fraction with a common denominator, multiply by $\frac{64}{64}$ .

$\frac{\frac{69}{32} \cdot \frac{64}{64} + \frac{36777}{2048}}{2}$

Step 8.2

Write each expression with a common denominator of $2048$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.2.1

Multiply $\frac{69}{32}$ by $\frac{64}{64}$ .

$\frac{\frac{69 \cdot 64}{32 \cdot 64} + \frac{36777}{2048}}{2}$

Step 8.2.2

Multiply $32$ by $64$ .

$\frac{\frac{69 \cdot 64}{2048} + \frac{36777}{2048}}{2}$

Step 8.3

Combine the numerators over the common denominator.

$\frac{\frac{69 \cdot 64 + 36777}{2048}}{2}$

Step 8.4

Simplify the numerator.

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Step 8.4.1

Multiply $69$ by $64$ .

$\frac{\frac{4416 + 36777}{2048}}{2}$

Step 8.4.2

Add $4416$ and $36777$ .

$\frac{\frac{41193}{2048}}{2}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{41193}{2048} \cdot \frac{1}{2}$

Step 10

Multiply $\frac{41193}{2048} \cdot \frac{1}{2}$ .

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Step 10.1

Multiply $\frac{41193}{2048}$ by $\frac{1}{2}$ .

$\frac{41193}{2048 \cdot 2}$

Step 10.2

Multiply $2048$ by $2$ .

$\frac{41193}{4096}$

Step 11

Divide.

$10.05688476$

Step 12

The mean should be rounded to one more decimal place than the original data. If the original data were mixed, round to one decimal place more than the least precise.

$10.1$