Basic Math Examples

$3 \frac{2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1

Convert $3 \frac{2}{3}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1.2

Add $3$ and $\frac{2}{3}$ .

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Step 1.2.1

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

$3 \cdot \frac{3}{3} + \frac{2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1.2.2

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

$\frac{3 \cdot 3}{3} + \frac{2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $3$ .

$\frac{9 + 2}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 1.2.4.2

Add $9$ and $2$ .

$\frac{11}{3} - 6 + 2 \div 4 \frac{1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 2

Convert $4 \frac{1}{6}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{3} - 6 + 2 \div (4 + \frac{1}{6}) - 1 + 7 - 2 \frac{1}{2}$

Step 2.2

Add $4$ and $\frac{1}{6}$ .

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Step 2.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{11}{3} - 6 + 2 \div (4 \cdot \frac{6}{6} + \frac{1}{6}) - 1 + 7 - 2 \frac{1}{2}$

Step 2.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{11}{3} - 6 + 2 \div (\frac{4 \cdot 6}{6} + \frac{1}{6}) - 1 + 7 - 2 \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{3} - 6 + 2 \div \frac{4 \cdot 6 + 1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $6$ .

$\frac{11}{3} - 6 + 2 \div \frac{24 + 1}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 2.2.4.2

Add $24$ and $1$ .

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - 2 \frac{1}{2}$

Step 3

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

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Step 3.1

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

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - (2 + \frac{1}{2})$

Step 3.2

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

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Step 3.2.1

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

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - (2 \cdot \frac{2}{2} + \frac{1}{2})$

Step 3.2.2

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

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - (\frac{2 \cdot 2}{2} + \frac{1}{2})$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - \frac{2 \cdot 2 + 1}{2}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $2$ .

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - \frac{4 + 1}{2}$

Step 3.2.4.2

Add $4$ and $1$ .

$\frac{11}{3} - 6 + 2 \div \frac{25}{6} - 1 + 7 - \frac{5}{2}$

Step 4

Simplify each term.

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Step 4.1

To divide by a fraction, multiply by its reciprocal.

$\frac{11}{3} - 6 + 2 (\frac{6}{25}) - 1 + 7 - \frac{5}{2}$

Step 4.2

Multiply $2 (\frac{6}{25})$ .

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Step 4.2.1

Combine $2$ and $\frac{6}{25}$ .

$\frac{11}{3} - 6 + \frac{2 \cdot 6}{25} - 1 + 7 - \frac{5}{2}$

Step 4.2.2

Multiply $2$ by $6$ .

$\frac{11}{3} - 6 + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{11}{3}$ by $\frac{50}{50}$ .

$\frac{11}{3} \cdot \frac{50}{50} - 6 + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5.2

Multiply $\frac{11}{3}$ by $\frac{50}{50}$ .

$\frac{11 \cdot 50}{3 \cdot 50} - 6 + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5.3

Write $- 6$ as a fraction with denominator $1$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6}{1} + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5.4

Multiply $\frac{- 6}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6}{1} \cdot \frac{150}{150} + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5.5

Multiply $\frac{- 6}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12}{25} - 1 + 7 - \frac{5}{2}$

Step 5.6

Multiply $\frac{12}{25}$ by $\frac{6}{6}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12}{25} \cdot \frac{6}{6} - 1 + 7 - \frac{5}{2}$

Step 5.7

Multiply $\frac{12}{25}$ by $\frac{6}{6}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} - 1 + 7 - \frac{5}{2}$

Step 5.8

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

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1}{1} + 7 - \frac{5}{2}$

Step 5.9

Multiply $\frac{- 1}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1}{1} \cdot \frac{150}{150} + 7 - \frac{5}{2}$

Step 5.10

Multiply $\frac{- 1}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + 7 - \frac{5}{2}$

Step 5.11

Write $7$ as a fraction with denominator $1$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7}{1} - \frac{5}{2}$

Step 5.12

Multiply $\frac{7}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7}{1} \cdot \frac{150}{150} - \frac{5}{2}$

Step 5.13

Multiply $\frac{7}{1}$ by $\frac{150}{150}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5}{2}$

Step 5.14

Multiply $\frac{5}{2}$ by $\frac{75}{75}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - (\frac{5}{2} \cdot \frac{75}{75})$

Step 5.15

Multiply $\frac{5}{2}$ by $\frac{75}{75}$ .

$\frac{11 \cdot 50}{3 \cdot 50} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5 \cdot 75}{2 \cdot 75}$

Step 5.16

Multiply $3$ by $50$ .

$\frac{11 \cdot 50}{150} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{25 \cdot 6} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5 \cdot 75}{2 \cdot 75}$

Step 5.17

Reorder the factors of $25 \cdot 6$ .

$\frac{11 \cdot 50}{150} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{6 \cdot 25} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5 \cdot 75}{2 \cdot 75}$

Step 5.18

Multiply $6$ by $25$ .

$\frac{11 \cdot 50}{150} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{150} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5 \cdot 75}{2 \cdot 75}$

Step 5.19

Multiply $2$ by $75$ .

$\frac{11 \cdot 50}{150} + \frac{- 6 \cdot 150}{150} + \frac{12 \cdot 6}{150} + \frac{- 1 \cdot 150}{150} + \frac{7 \cdot 150}{150} - \frac{5 \cdot 75}{150}$

Step 6

Combine the numerators over the common denominator.

$\frac{11 \cdot 50 - 6 \cdot 150 + 12 \cdot 6 - 1 \cdot 150 + 7 \cdot 150 - 5 \cdot 75}{150}$

Step 7

Simplify each term.

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Step 7.1

Multiply $11$ by $50$ .

$\frac{550 - 6 \cdot 150 + 12 \cdot 6 - 1 \cdot 150 + 7 \cdot 150 - 5 \cdot 75}{150}$

Step 7.2

Multiply $- 6$ by $150$ .

$\frac{550 - 900 + 12 \cdot 6 - 1 \cdot 150 + 7 \cdot 150 - 5 \cdot 75}{150}$

Step 7.3

Multiply $12$ by $6$ .

$\frac{550 - 900 + 72 - 1 \cdot 150 + 7 \cdot 150 - 5 \cdot 75}{150}$

Step 7.4

Multiply $- 1$ by $150$ .

$\frac{550 - 900 + 72 - 150 + 7 \cdot 150 - 5 \cdot 75}{150}$

Step 7.5

Multiply $7$ by $150$ .

$\frac{550 - 900 + 72 - 150 + 1050 - 5 \cdot 75}{150}$

Step 7.6

Multiply $- 5$ by $75$ .

$\frac{550 - 900 + 72 - 150 + 1050 - 375}{150}$

Step 8

Simplify by adding and subtracting.

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Step 8.1

Subtract $900$ from $550$ .

$\frac{- 350 + 72 - 150 + 1050 - 375}{150}$

Step 8.2

Add $- 350$ and $72$ .

$\frac{- 278 - 150 + 1050 - 375}{150}$

Step 8.3

Subtract $150$ from $- 278$ .

$\frac{- 428 + 1050 - 375}{150}$

Step 8.4

Add $- 428$ and $1050$ .

$\frac{622 - 375}{150}$

Step 8.5

Subtract $375$ from $622$ .

$\frac{247}{150}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{247}{150}$

Decimal Form:

$1.64\overline{6}$

Mixed Number Form:

$1 \frac{97}{150}$