Basic Math Examples

4 \frac{5}{8} - 1 \frac{3}{4}

$4 \frac{5}{8} - 1 \frac{3}{4}$

Step 1

Convert

4 \frac{5}{8}

$4 \frac{5}{8}$ to an improper fraction.

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Step 1.1

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

4 + \frac{5}{8} - 1 \frac{3}{4}

$4 + \frac{5}{8} - 1 \frac{3}{4}$

Step 1.2

Add

4

$4$ and

\frac{5}{8}

$\frac{5}{8}$ .

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Step 1.2.1

To write

4

$4$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

4 \cdot \frac{8}{8} + \frac{5}{8} - 1 \frac{3}{4}

$4 \cdot \frac{8}{8} + \frac{5}{8} - 1 \frac{3}{4}$

Step 1.2.2

Combine

4

$4$ and

\frac{8}{8}

$\frac{8}{8}$ .

\frac{4 \cdot 8}{8} + \frac{5}{8} - 1 \frac{3}{4}

$\frac{4 \cdot 8}{8} + \frac{5}{8} - 1 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{4 \cdot 8 + 5}{8} - 1 \frac{3}{4}

$\frac{4 \cdot 8 + 5}{8} - 1 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

4

$4$ by

8

$8$ .

\frac{32 + 5}{8} - 1 \frac{3}{4}

$\frac{32 + 5}{8} - 1 \frac{3}{4}$

Step 1.2.4.2

Add

32

$32$ and

5

$5$ .

\frac{37}{8} - 1 \frac{3}{4}

$\frac{37}{8} - 1 \frac{3}{4}$

\frac{37}{8} - 1 \frac{3}{4}

$\frac{37}{8} - 1 \frac{3}{4}$

\frac{37}{8} - 1 \frac{3}{4}

$\frac{37}{8} - 1 \frac{3}{4}$

\frac{37}{8} - 1 \frac{3}{4}

$\frac{37}{8} - 1 \frac{3}{4}$

Step 2

Convert

1 \frac{3}{4}

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

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Step 2.1

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

\frac{37}{8} - (1 + \frac{3}{4})

$\frac{37}{8} - (1 + \frac{3}{4})$

Step 2.2

Add

1

$1$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{37}{8} - (\frac{4}{4} + \frac{3}{4})

$\frac{37}{8} - (\frac{4}{4} + \frac{3}{4})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{37}{8} - \frac{4 + 3}{4}

$\frac{37}{8} - \frac{4 + 3}{4}$

Step 2.2.3

Add

4

$4$ and

3

$3$ .

\frac{37}{8} - \frac{7}{4}

$\frac{37}{8} - \frac{7}{4}$

\frac{37}{8} - \frac{7}{4}

$\frac{37}{8} - \frac{7}{4}$

\frac{37}{8} - \frac{7}{4}

$\frac{37}{8} - \frac{7}{4}$

Step 3

To write

- \frac{7}{4}

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

\frac{2}{2}

$\frac{2}{2}$ .

\frac{37}{8} - \frac{7}{4} \cdot \frac{2}{2}

$\frac{37}{8} - \frac{7}{4} \cdot \frac{2}{2}$

Step 4

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 4.1

Multiply

\frac{7}{4}

$\frac{7}{4}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{37}{8} - \frac{7 \cdot 2}{4 \cdot 2}

$\frac{37}{8} - \frac{7 \cdot 2}{4 \cdot 2}$

Step 4.2

Multiply

4

$4$ by

2

$2$ .

\frac{37}{8} - \frac{7 \cdot 2}{8}

$\frac{37}{8} - \frac{7 \cdot 2}{8}$

\frac{37}{8} - \frac{7 \cdot 2}{8}

$\frac{37}{8} - \frac{7 \cdot 2}{8}$

Step 5

Combine the numerators over the common denominator.

\frac{37 - 7 \cdot 2}{8}

$\frac{37 - 7 \cdot 2}{8}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply

- 7

$- 7$ by

2

$2$ .

\frac{37 - 14}{8}

$\frac{37 - 14}{8}$

Step 6.2

Subtract

14

$14$ from

37

$37$ .

\frac{23}{8}

$\frac{23}{8}$

\frac{23}{8}

$\frac{23}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

\frac{23}{8}

$\frac{23}{8}$

Decimal Form:

2.875

$2.875$

Mixed Number Form:

2 \frac{7}{8}

$2 \frac{7}{8}$