Basic Math Examples

$3 \frac{1}{5} - 1 \frac{3}{4}$

Step 1

Convert

$3 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{1}{5} - 1 \frac{3}{4}$

Step 1.2

Add

$3$ and

$\frac{1}{5}$ .

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Step 1.2.1

To write

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

$\frac{5}{5}$ .

$3 \cdot \frac{5}{5} + \frac{1}{5} - 1 \frac{3}{4}$

Step 1.2.2

Combine

$3$ and

$\frac{5}{5}$ .

$\frac{3 \cdot 5}{5} + \frac{1}{5} - 1 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 5 + 1}{5} - 1 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$3$ by

$5$ .

$\frac{15 + 1}{5} - 1 \frac{3}{4}$

Step 1.2.4.2

Add

$15$ and

$1$ .

$\frac{16}{5} - 1 \frac{3}{4}$

Step 2

Convert

$1 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{16}{5} - (1 + \frac{3}{4})$

Step 2.2

Add

$1$ and

$\frac{3}{4}$ .

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Step 2.2.1

Write

$1$ as a fraction with a common denominator.

$\frac{16}{5} - (\frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{16}{5} - \frac{4 + 3}{4}$

Step 2.2.3

Add

$4$ and

$3$ .

$\frac{16}{5} - \frac{7}{4}$

Step 3

To write

$\frac{16}{5}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{16}{5} \cdot \frac{4}{4} - \frac{7}{4}$

Step 4

To write

$- \frac{7}{4}$ as a fraction with a common denominator, multiply by

$\frac{5}{5}$ .

$\frac{16}{5} \cdot \frac{4}{4} - \frac{7}{4} \cdot \frac{5}{5}$

Step 5

Write each expression with a common denominator of

$20$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{16}{5}$ by

$\frac{4}{4}$ .

$\frac{16 \cdot 4}{5 \cdot 4} - \frac{7}{4} \cdot \frac{5}{5}$

Step 5.2

Multiply

$5$ by

$4$ .

$\frac{16 \cdot 4}{20} - \frac{7}{4} \cdot \frac{5}{5}$

Step 5.3

Multiply

$\frac{7}{4}$ by

$\frac{5}{5}$ .

$\frac{16 \cdot 4}{20} - \frac{7 \cdot 5}{4 \cdot 5}$

Step 5.4

Multiply

$4$ by

$5$ .

$\frac{16 \cdot 4}{20} - \frac{7 \cdot 5}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{16 \cdot 4 - 7 \cdot 5}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$16$ by

$4$ .

$\frac{64 - 7 \cdot 5}{20}$

Step 7.2

Multiply

$- 7$ by

$5$ .

$\frac{64 - 35}{20}$

Step 7.3

Subtract

$35$ from

$64$ .

$\frac{29}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{20}$

Decimal Form:

$1.45$

Mixed Number Form:

$1 \frac{9}{20}$