Basic Math Examples

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

Step 1

Convert $6 \frac{3}{7}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $6$ and $\frac{3}{7}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine $6$ and $\frac{7}{7}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $7$ .

$\frac{42 + 3}{7} + 2 \frac{2}{5} - 11$

Step 1.2.4.2

Add $42$ and $3$ .

$\frac{45}{7} + 2 \frac{2}{5} - 11$

Step 2

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

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Step 2.1

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

$\frac{45}{7} + 2 + \frac{2}{5} - 11$

Step 2.2

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

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{45}{7} + 2 \cdot \frac{5}{5} + \frac{2}{5} - 11$

Step 2.2.2

Combine $2$ and $\frac{5}{5}$ .

$\frac{45}{7} + \frac{2 \cdot 5}{5} + \frac{2}{5} - 11$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{45}{7} + \frac{2 \cdot 5 + 2}{5} - 11$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $5$ .

$\frac{45}{7} + \frac{10 + 2}{5} - 11$

Step 2.2.4.2

Add $10$ and $2$ .

$\frac{45}{7} + \frac{12}{5} - 11$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{45}{7}$ by $\frac{5}{5}$ .

$\frac{45}{7} \cdot \frac{5}{5} + \frac{12}{5} - 11$

Step 3.2

Multiply $\frac{45}{7}$ by $\frac{5}{5}$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12}{5} - 11$

Step 3.3

Multiply $\frac{12}{5}$ by $\frac{7}{7}$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12}{5} \cdot \frac{7}{7} - 11$

Step 3.4

Multiply $\frac{12}{5}$ by $\frac{7}{7}$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12 \cdot 7}{5 \cdot 7} - 11$

Step 3.5

Write $- 11$ as a fraction with denominator $1$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12 \cdot 7}{5 \cdot 7} + \frac{- 11}{1}$

Step 3.6

Multiply $\frac{- 11}{1}$ by $\frac{35}{35}$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12 \cdot 7}{5 \cdot 7} + \frac{- 11}{1} \cdot \frac{35}{35}$

Step 3.7

Multiply $\frac{- 11}{1}$ by $\frac{35}{35}$ .

$\frac{45 \cdot 5}{7 \cdot 5} + \frac{12 \cdot 7}{5 \cdot 7} + \frac{- 11 \cdot 35}{35}$

Step 3.8

Reorder the factors of $7 \cdot 5$ .

$\frac{45 \cdot 5}{5 \cdot 7} + \frac{12 \cdot 7}{5 \cdot 7} + \frac{- 11 \cdot 35}{35}$

Step 3.9

Multiply $5$ by $7$ .

$\frac{45 \cdot 5}{35} + \frac{12 \cdot 7}{5 \cdot 7} + \frac{- 11 \cdot 35}{35}$

Step 3.10

Multiply $5$ by $7$ .

$\frac{45 \cdot 5}{35} + \frac{12 \cdot 7}{35} + \frac{- 11 \cdot 35}{35}$

Step 4

Combine the numerators over the common denominator.

$\frac{45 \cdot 5 + 12 \cdot 7 - 11 \cdot 35}{35}$

Step 5

Simplify each term.

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Step 5.1

Multiply $45$ by $5$ .

$\frac{225 + 12 \cdot 7 - 11 \cdot 35}{35}$

Step 5.2

Multiply $12$ by $7$ .

$\frac{225 + 84 - 11 \cdot 35}{35}$

Step 5.3

Multiply $- 11$ by $35$ .

$\frac{225 + 84 - 385}{35}$

Step 6

Simplify the expression.

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Step 6.1

Add $225$ and $84$ .

$\frac{309 - 385}{35}$

Step 6.2

Subtract $385$ from $309$ .

$\frac{- 76}{35}$

Step 6.3

Move the negative in front of the fraction.

$- \frac{76}{35}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{76}{35}$

Decimal Form:

$- 2.17142857 \dots$

Mixed Number Form:

$- 2 \frac{6}{35}$