Basic Math Examples

$4 \frac{7}{20}$ , $3 \frac{3}{20}$ , $3 \frac{9}{10}$ , $3 \frac{4}{5}$

Step 1

Convert $4 \frac{7}{20}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{7}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 1.2

Add $4$ and $\frac{7}{20}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$4 \cdot \frac{20}{20} + \frac{7}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 1.2.2

Combine $4$ and $\frac{20}{20}$ .

$\frac{4 \cdot 20}{20} + \frac{7}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 20 + 7}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $20$ .

$\frac{80 + 7}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 1.2.4.2

Add $80$ and $7$ .

$\frac{87}{20}, 3 \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2

Convert $3 \frac{3}{20}$ to an improper fraction.

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Step 2.1

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

$\frac{87}{20}, 3 + \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2.2

Add $3$ and $\frac{3}{20}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{87}{20}, 3 \cdot \frac{20}{20} + \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2.2.2

Combine $3$ and $\frac{20}{20}$ .

$\frac{87}{20}, \frac{3 \cdot 20}{20} + \frac{3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{87}{20}, \frac{3 \cdot 20 + 3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $20$ .

$\frac{87}{20}, \frac{60 + 3}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 2.2.4.2

Add $60$ and $3$ .

$\frac{87}{20}, \frac{63}{20}, 3 \frac{9}{10}, 3 \frac{4}{5}$

Step 3

Convert $3 \frac{9}{10}$ to an improper fraction.

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Step 3.1

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

$\frac{87}{20}, \frac{63}{20}, 3 + \frac{9}{10}, 3 \frac{4}{5}$

Step 3.2

Add $3$ and $\frac{9}{10}$ .

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Step 3.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{87}{20}, \frac{63}{20}, 3 \cdot \frac{10}{10} + \frac{9}{10}, 3 \frac{4}{5}$

Step 3.2.2

Combine $3$ and $\frac{10}{10}$ .

$\frac{87}{20}, \frac{63}{20}, \frac{3 \cdot 10}{10} + \frac{9}{10}, 3 \frac{4}{5}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{87}{20}, \frac{63}{20}, \frac{3 \cdot 10 + 9}{10}, 3 \frac{4}{5}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $3$ by $10$ .

$\frac{87}{20}, \frac{63}{20}, \frac{30 + 9}{10}, 3 \frac{4}{5}$

Step 3.2.4.2

Add $30$ and $9$ .

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, 3 \frac{4}{5}$

Step 4

Convert $3 \frac{4}{5}$ to an improper fraction.

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Step 4.1

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

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, 3 + \frac{4}{5}$

Step 4.2

Add $3$ and $\frac{4}{5}$ .

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Step 4.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, 3 \cdot \frac{5}{5} + \frac{4}{5}$

Step 4.2.2

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

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, \frac{3 \cdot 5}{5} + \frac{4}{5}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, \frac{3 \cdot 5 + 4}{5}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $3$ by $5$ .

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, \frac{15 + 4}{5}$

Step 4.2.4.2

Add $15$ and $4$ .

$\frac{87}{20}, \frac{63}{20}, \frac{39}{10}, \frac{19}{5}$

Step 5

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

$\frac{\frac{87}{20} + \frac{63}{20} + \frac{39}{10} + \frac{19}{5}}{4}$

Step 6

Simplify the numerator.

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Step 6.1

Combine the numerators over the common denominator.

$\frac{\frac{87 + 63}{20} + \frac{39}{10} + \frac{19}{5}}{4}$

Step 6.2

Add $87$ and $63$ .

$\frac{\frac{150}{20} + \frac{39}{10} + \frac{19}{5}}{4}$

Step 6.3

To write $\frac{39}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\frac{150}{20} + \frac{39}{10} \cdot \frac{2}{2} + \frac{19}{5}}{4}$

Step 6.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.4.1

Multiply $\frac{39}{10}$ by $\frac{2}{2}$ .

$\frac{\frac{150}{20} + \frac{39 \cdot 2}{10 \cdot 2} + \frac{19}{5}}{4}$

Step 6.4.2

Multiply $10$ by $2$ .

$\frac{\frac{150}{20} + \frac{39 \cdot 2}{20} + \frac{19}{5}}{4}$

Step 6.5

Combine the numerators over the common denominator.

$\frac{\frac{150 + 39 \cdot 2}{20} + \frac{19}{5}}{4}$

Step 6.6

Simplify the numerator.

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Step 6.6.1

Multiply $39$ by $2$ .

$\frac{\frac{150 + 78}{20} + \frac{19}{5}}{4}$

Step 6.6.2

Add $150$ and $78$ .

$\frac{\frac{228}{20} + \frac{19}{5}}{4}$

Step 6.7

To write $\frac{19}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\frac{228}{20} + \frac{19}{5} \cdot \frac{4}{4}}{4}$

Step 6.8

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.8.1

Multiply $\frac{19}{5}$ by $\frac{4}{4}$ .

$\frac{\frac{228}{20} + \frac{19 \cdot 4}{5 \cdot 4}}{4}$

Step 6.8.2

Multiply $5$ by $4$ .

$\frac{\frac{228}{20} + \frac{19 \cdot 4}{20}}{4}$

Step 6.9

Combine the numerators over the common denominator.

$\frac{\frac{228 + 19 \cdot 4}{20}}{4}$

Step 6.10

Simplify the numerator.

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Step 6.10.1

Multiply $19$ by $4$ .

$\frac{\frac{228 + 76}{20}}{4}$

Step 6.10.2

Add $228$ and $76$ .

$\frac{\frac{304}{20}}{4}$

Step 6.11

Cancel the common factor of $304$ and $20$ .

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Step 6.11.1

Factor $4$ out of $304$ .

$\frac{\frac{4 (76)}{20}}{4}$

Step 6.11.2

Cancel the common factors.

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Step 6.11.2.1

Factor $4$ out of $20$ .

$\frac{\frac{4 \cdot 76}{4 \cdot 5}}{4}$

Step 6.11.2.2

Cancel the common factor.

$\frac{\frac{4 \cdot 76}{4 \cdot 5}}{4}$

Step 6.11.2.3

Rewrite the expression.

$\frac{\frac{76}{5}}{4}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{76}{5} \cdot \frac{1}{4}$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Factor $4$ out of $76$ .

$\frac{4 (19)}{5} \cdot \frac{1}{4}$

Step 8.2

Cancel the common factor.

$\frac{4 \cdot 19}{5} \cdot \frac{1}{4}$

Step 8.3

Rewrite the expression.

$\frac{19}{5}$

Step 9

Divide.

$3.8$