Basic Math Examples

$\frac{0.5 + \frac{1}{18}}{(1 \frac{1}{6} - \frac{7}{18}) \div 2.8}$

Step 1

Convert $1 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

$\frac{0.5 + \frac{1}{18}}{(1 + \frac{1}{6} - \frac{7}{18}) \div 2.8}$

Step 1.2

Add $1$ and $\frac{1}{6}$ .

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Step 1.2.1

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

$\frac{0.5 + \frac{1}{18}}{(\frac{6}{6} + \frac{1}{6} - \frac{7}{18}) \div 2.8}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{0.5 + \frac{1}{18}}{(\frac{6 + 1}{6} - \frac{7}{18}) \div 2.8}$

Step 1.2.3

Add $6$ and $1$ .

$\frac{0.5 + \frac{1}{18}}{(\frac{7}{6} - \frac{7}{18}) \div 2.8}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7}{6} - \frac{7}{18}}$

Step 3

Simplify the denominator.

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Step 3.1

To write $\frac{7}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7}{6} \cdot \frac{3}{3} - \frac{7}{18}}$

Step 3.2

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

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Step 3.2.1

Multiply $\frac{7}{6}$ by $\frac{3}{3}$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7 \cdot 3}{6 \cdot 3} - \frac{7}{18}}$

Step 3.2.2

Multiply $6$ by $3$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7 \cdot 3}{18} - \frac{7}{18}}$

Step 3.3

Combine the numerators over the common denominator.

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7 \cdot 3 - 7}{18}}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $7$ by $3$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{21 - 7}{18}}$

Step 3.4.2

Subtract $7$ from $21$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{14}{18}}$

Step 3.5

Cancel the common factor of $14$ and $18$ .

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Step 3.5.1

Factor $2$ out of $14$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{2 (7)}{18}}$

Step 3.5.2

Cancel the common factors.

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Step 3.5.2.1

Factor $2$ out of $18$ .

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{2 \cdot 7}{2 \cdot 9}}$

Step 3.5.2.2

Cancel the common factor.

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{2 \cdot 7}{2 \cdot 9}}$

Step 3.5.2.3

Rewrite the expression.

$(0.5 + \frac{1}{18}) \frac{2.8}{\frac{7}{9}}$

Step 4

To write $0.5$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$(0.5 \cdot \frac{18}{18} + \frac{1}{18}) \frac{2.8}{\frac{7}{9}}$

Step 5

Combine $0.5$ and $\frac{18}{18}$ .

$(\frac{0.5 \cdot 18}{18} + \frac{1}{18}) \frac{2.8}{\frac{7}{9}}$

Step 6

Combine the numerators over the common denominator.

$\frac{0.5 \cdot 18 + 1}{18} \cdot \frac{2.8}{\frac{7}{9}}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $0.5$ by $18$ .

$\frac{9 + 1}{18} \cdot \frac{2.8}{\frac{7}{9}}$

Step 7.2

Add $9$ and $1$ .

$\frac{10}{18} \cdot \frac{2.8}{\frac{7}{9}}$

Step 8

Cancel the common factor of $10$ and $18$ .

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Step 8.1

Factor $2$ out of $10$ .

$\frac{2 (5)}{18} \cdot \frac{2.8}{\frac{7}{9}}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 5}{2 \cdot 9} \cdot \frac{2.8}{\frac{7}{9}}$

Step 8.2.2

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 9} \cdot \frac{2.8}{\frac{7}{9}}$

Step 8.2.3

Rewrite the expression.

$\frac{5}{9} \cdot \frac{2.8}{\frac{7}{9}}$

Step 9

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} (2.8 (\frac{9}{7}))$

Step 10

Multiply $2.8 (\frac{9}{7})$ .

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Step 10.1

Combine $2.8$ and $\frac{9}{7}$ .

$\frac{5}{9} \cdot \frac{2.8 \cdot 9}{7}$

Step 10.2

Multiply $2.8$ by $9$ .

$\frac{5}{9} \cdot \frac{25.2}{7}$

Step 11

Divide $25.2$ by $7$ .

$\frac{5}{9} \cdot 3.6$

Step 12

Multiply $\frac{5}{9} \cdot 3.6$ .

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Step 12.1

Combine $\frac{5}{9}$ and $3.6$ .

$\frac{5 \cdot 3.6}{9}$

Step 12.2

Multiply $5$ by $3.6$ .

$\frac{18}{9}$

Step 13

Divide $18$ by $9$ .

$2$