Basic Math Examples

$7 \frac{6}{10} - 3 \frac{2}{3}$

Step 1

Convert $7 \frac{6}{10}$ to an improper fraction.

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Step 1.1

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

$7 + \frac{6}{10} - 3 \frac{2}{3}$

Step 1.2

Add $7$ and $\frac{6}{10}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$7 \cdot \frac{10}{10} + \frac{6}{10} - 3 \frac{2}{3}$

Step 1.2.2

Combine $7$ and $\frac{10}{10}$ .

$\frac{7 \cdot 10}{10} + \frac{6}{10} - 3 \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{7 \cdot 10 + 6}{10} - 3 \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $10$ .

$\frac{70 + 6}{10} - 3 \frac{2}{3}$

Step 1.2.4.2

Add $70$ and $6$ .

$\frac{76}{10} - 3 \frac{2}{3}$

Step 2

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

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Step 2.1

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

$\frac{76}{10} - (3 + \frac{2}{3})$

Step 2.2

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

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Step 2.2.1

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

$\frac{76}{10} - (3 \cdot \frac{3}{3} + \frac{2}{3})$

Step 2.2.2

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

$\frac{76}{10} - (\frac{3 \cdot 3}{3} + \frac{2}{3})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{76}{10} - \frac{3 \cdot 3 + 2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $3$ .

$\frac{76}{10} - \frac{9 + 2}{3}$

Step 2.2.4.2

Add $9$ and $2$ .

$\frac{76}{10} - \frac{11}{3}$

Step 3

Cancel the common factor of $76$ and $10$ .

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Step 3.1

Factor $2$ out of $76$ .

$\frac{2 (38)}{10} - \frac{11}{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $10$ .

$\frac{2 \cdot 38}{2 \cdot 5} - \frac{11}{3}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \cdot 38}{2 \cdot 5} - \frac{11}{3}$

Step 3.2.3

Rewrite the expression.

$\frac{38}{5} - \frac{11}{3}$

Step 4

To write $\frac{38}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{38}{5} \cdot \frac{3}{3} - \frac{11}{3}$

Step 5

To write $- \frac{11}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{38}{5} \cdot \frac{3}{3} - \frac{11}{3} \cdot \frac{5}{5}$

Step 6

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{38}{5}$ by $\frac{3}{3}$ .

$\frac{38 \cdot 3}{5 \cdot 3} - \frac{11}{3} \cdot \frac{5}{5}$

Step 6.2

Multiply $5$ by $3$ .

$\frac{38 \cdot 3}{15} - \frac{11}{3} \cdot \frac{5}{5}$

Step 6.3

Multiply $\frac{11}{3}$ by $\frac{5}{5}$ .

$\frac{38 \cdot 3}{15} - \frac{11 \cdot 5}{3 \cdot 5}$

Step 6.4

Multiply $3$ by $5$ .

$\frac{38 \cdot 3}{15} - \frac{11 \cdot 5}{15}$

Step 7

Combine the numerators over the common denominator.

$\frac{38 \cdot 3 - 11 \cdot 5}{15}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $38$ by $3$ .

$\frac{114 - 11 \cdot 5}{15}$

Step 8.2

Multiply $- 11$ by $5$ .

$\frac{114 - 55}{15}$

Step 8.3

Subtract $55$ from $114$ .

$\frac{59}{15}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{59}{15}$

Decimal Form:

$3.9\overline{3}$

Mixed Number Form:

$3 \frac{14}{15}$