Simplify 4 5/8-1 3/4

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

Step 1

Convert

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

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

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

Add

$4$ and

$\frac{5}{8}$ .

To write

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

$\frac{8}{8}$ .

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

Combine

$4$ and

$\frac{8}{8}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply

$4$ by

$8$ .

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

Add

$32$ and

$5$ .

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

Step 2

Convert

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

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

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

Add

$1$ and

$\frac{3}{4}$ .

Write

$1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add

$4$ and

$3$ .

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

Step 3

To write

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

$\frac{2}{2}$ .

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

Step 4

Write each expression with a common denominator of

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

$1$ .

Multiply

$\frac{7}{4}$ by

$\frac{2}{2}$ .

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

Multiply

$4$ by

$2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Multiply

$- 7$ by

$2$ .

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

Subtract

$14$ from

$37$ .

$\frac{23}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{23}{8}$

Decimal Form:

$2.875$

Mixed Number Form:

$2 \frac{7}{8}$

Simplify 4 5/8-1 3/4

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