Basic Math Examples

$15 \frac{3}{5} - 3 \frac{2}{7}$

Step 1

Convert

$15 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

$15 + \frac{3}{5} - 3 \frac{2}{7}$

Step 1.2

Add

$15$ and

$\frac{3}{5}$ .

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Step 1.2.1

To write

$15$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$15 \cdot \frac{5}{5} + \frac{3}{5} - 3 \frac{2}{7}$

Step 1.2.2

Combine

$15$ and

$\frac{5}{5}$ .

$\frac{15 \cdot 5}{5} + \frac{3}{5} - 3 \frac{2}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{15 \cdot 5 + 3}{5} - 3 \frac{2}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$15$ by

$5$ .

$\frac{75 + 3}{5} - 3 \frac{2}{7}$

Step 1.2.4.2

Add

$75$ and

$3$ .

$\frac{78}{5} - 3 \frac{2}{7}$

Step 2

Convert

$3 \frac{2}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{78}{5} - (3 + \frac{2}{7})$

Step 2.2

Add

$3$ and

$\frac{2}{7}$ .

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Step 2.2.1

To write

$3$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{78}{5} - (3 \cdot \frac{7}{7} + \frac{2}{7})$

Step 2.2.2

Combine

$3$ and

$\frac{7}{7}$ .

$\frac{78}{5} - (\frac{3 \cdot 7}{7} + \frac{2}{7})$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{78}{5} - \frac{3 \cdot 7 + 2}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$3$ by

$7$ .

$\frac{78}{5} - \frac{21 + 2}{7}$

Step 2.2.4.2

Add

$21$ and

$2$ .

$\frac{78}{5} - \frac{23}{7}$

Step 3

To write

$\frac{78}{5}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{78}{5} \cdot \frac{7}{7} - \frac{23}{7}$

Step 4

To write

$- \frac{23}{7}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{78}{5} \cdot \frac{7}{7} - \frac{23}{7} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

$35$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{78}{5}$ by

$\frac{7}{7}$ .

$\frac{78 \cdot 7}{5 \cdot 7} - \frac{23}{7} \cdot \frac{5}{5}$

Step 5.2

Multiply

$5$ by

$7$ .

$\frac{78 \cdot 7}{35} - \frac{23}{7} \cdot \frac{5}{5}$

Step 5.3

Multiply

$\frac{23}{7}$ by

$\frac{5}{5}$ .

$\frac{78 \cdot 7}{35} - \frac{23 \cdot 5}{7 \cdot 5}$

Step 5.4

Multiply

$7$ by

$5$ .

$\frac{78 \cdot 7}{35} - \frac{23 \cdot 5}{35}$

Step 6

Combine the numerators over the common denominator.

$\frac{78 \cdot 7 - 23 \cdot 5}{35}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$78$ by

$7$ .

$\frac{546 - 23 \cdot 5}{35}$

Step 7.2

Multiply

$- 23$ by

$5$ .

$\frac{546 - 115}{35}$

Step 7.3

Subtract

$115$ from

$546$ .

$\frac{431}{35}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{431}{35}$

Decimal Form:

$12.31428571 \dots$

Mixed Number Form:

$12 \frac{11}{35}$