Basic Math Examples

$1 \frac{7}{9} + 2 \frac{5}{6}$

Step 1

Convert $1 \frac{7}{9}$ to an improper fraction.

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Step 1.1

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

$1 + \frac{7}{9} + 2 \frac{5}{6}$

Step 1.2

Add $1$ and $\frac{7}{9}$ .

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Step 1.2.1

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

$\frac{9}{9} + \frac{7}{9} + 2 \frac{5}{6}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{9 + 7}{9} + 2 \frac{5}{6}$

Step 1.2.3

Add $9$ and $7$ .

$\frac{16}{9} + 2 \frac{5}{6}$

Step 2

Convert $2 \frac{5}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{16}{9} + 2 + \frac{5}{6}$

Step 2.2

Add $2$ and $\frac{5}{6}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{16}{9} + 2 \cdot \frac{6}{6} + \frac{5}{6}$

Step 2.2.2

Combine $2$ and $\frac{6}{6}$ .

$\frac{16}{9} + \frac{2 \cdot 6}{6} + \frac{5}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{16}{9} + \frac{2 \cdot 6 + 5}{6}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $6$ .

$\frac{16}{9} + \frac{12 + 5}{6}$

Step 2.2.4.2

Add $12$ and $5$ .

$\frac{16}{9} + \frac{17}{6}$

Step 3

To write $\frac{16}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{16}{9} \cdot \frac{2}{2} + \frac{17}{6}$

Step 4

To write $\frac{17}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{16}{9} \cdot \frac{2}{2} + \frac{17}{6} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{16}{9}$ by $\frac{2}{2}$ .

$\frac{16 \cdot 2}{9 \cdot 2} + \frac{17}{6} \cdot \frac{3}{3}$

Step 5.2

Multiply $9$ by $2$ .

$\frac{16 \cdot 2}{18} + \frac{17}{6} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{17}{6}$ by $\frac{3}{3}$ .

$\frac{16 \cdot 2}{18} + \frac{17 \cdot 3}{6 \cdot 3}$

Step 5.4

Multiply $6$ by $3$ .

$\frac{16 \cdot 2}{18} + \frac{17 \cdot 3}{18}$

Step 6

Combine the numerators over the common denominator.

$\frac{16 \cdot 2 + 17 \cdot 3}{18}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $16$ by $2$ .

$\frac{32 + 17 \cdot 3}{18}$

Step 7.2

Multiply $17$ by $3$ .

$\frac{32 + 51}{18}$

Step 7.3

Add $32$ and $51$ .

$\frac{83}{18}$

Step 8

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

$\frac{\frac{83}{18}}{1}$

Step 9

Divide $\frac{83}{18}$ by $1$ .

$\frac{83}{18}$

Step 10

Divide.

$4.6\overline{1}$

Step 11

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.

$4.6$