Basic Math Examples

2 \frac{5}{8} - \frac{3}{4}

$2 \frac{5}{8} - \frac{3}{4}$

Step 1

Convert

2 \frac{5}{8}

$2 \frac{5}{8}$ to an improper fraction.

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Step 1.1

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

2 + \frac{5}{8} - \frac{3}{4}

$2 + \frac{5}{8} - \frac{3}{4}$

Step 1.2

Add

2

$2$ and

\frac{5}{8}

$\frac{5}{8}$ .

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Step 1.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

2 \cdot \frac{8}{8} + \frac{5}{8} - \frac{3}{4}

$2 \cdot \frac{8}{8} + \frac{5}{8} - \frac{3}{4}$

Step 1.2.2

Combine

2

$2$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{2 \cdot 8}{8} + \frac{5}{8} - \frac{3}{4}

$\frac{2 \cdot 8}{8} + \frac{5}{8} - \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 8 + 5}{8} - \frac{3}{4}

$\frac{2 \cdot 8 + 5}{8} - \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

8

$8$ .

\frac{16 + 5}{8} - \frac{3}{4}

$\frac{16 + 5}{8} - \frac{3}{4}$

Step 1.2.4.2

Add

16

$16$ and

5

$5$ .

\frac{21}{8} - \frac{3}{4}

$\frac{21}{8} - \frac{3}{4}$

\frac{21}{8} - \frac{3}{4}

$\frac{21}{8} - \frac{3}{4}$

\frac{21}{8} - \frac{3}{4}

$\frac{21}{8} - \frac{3}{4}$

\frac{21}{8} - \frac{3}{4}

$\frac{21}{8} - \frac{3}{4}$

Step 2

To write

- \frac{3}{4}

$- \frac{3}{4}$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{21}{8} - \frac{3}{4} \cdot \frac{2}{2}

$\frac{21}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of

8

$8$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{3}{4}

$\frac{3}{4}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{21}{8} - \frac{3 \cdot 2}{4 \cdot 2}

$\frac{21}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Step 3.2

Multiply

4

$4$ by

2

$2$ .

\frac{21}{8} - \frac{3 \cdot 2}{8}

$\frac{21}{8} - \frac{3 \cdot 2}{8}$

\frac{21}{8} - \frac{3 \cdot 2}{8}

$\frac{21}{8} - \frac{3 \cdot 2}{8}$

Step 4

Combine the numerators over the common denominator.

\frac{21 - 3 \cdot 2}{8}

$\frac{21 - 3 \cdot 2}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

- 3

$- 3$ by

2

$2$ .

\frac{21 - 6}{8}

$\frac{21 - 6}{8}$

Step 5.2

Subtract

6

$6$ from

21

$21$ .

\frac{15}{8}

$\frac{15}{8}$

\frac{15}{8}

$\frac{15}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{15}{8}

$\frac{15}{8}$

Decimal Form:

1.875

$1.875$

Mixed Number Form:

1 \frac{7}{8}

$1 \frac{7}{8}$