Simplify 8 3/4-3/7

$8 \frac{3}{4} - \frac{3}{7}$

Step 1

Convert

$8 \frac{3}{4}$ to an improper fraction.

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

$8 + \frac{3}{4} - \frac{3}{7}$

Add

$8$ and

$\frac{3}{4}$ .

To write

$8$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} - \frac{3}{7}$

Combine

$8$ and

$\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} - \frac{3}{7}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} - \frac{3}{7}$

Simplify the numerator.

Multiply

$8$ by

$4$ .

$\frac{32 + 3}{4} - \frac{3}{7}$

Add

$32$ and

$3$ .

$\frac{35}{4} - \frac{3}{7}$

Step 2

To write

$\frac{35}{4}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$\frac{35}{4} \cdot \frac{7}{7} - \frac{3}{7}$

Step 3

To write

$- \frac{3}{7}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{35}{4} \cdot \frac{7}{7} - \frac{3}{7} \cdot \frac{4}{4}$

Step 4

Write each expression with a common denominator of

$28$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{35}{4}$ by

$\frac{7}{7}$ .

$\frac{35 \cdot 7}{4 \cdot 7} - \frac{3}{7} \cdot \frac{4}{4}$

Multiply

$4$ by

$7$ .

$\frac{35 \cdot 7}{28} - \frac{3}{7} \cdot \frac{4}{4}$

Multiply

$\frac{3}{7}$ by

$\frac{4}{4}$ .

$\frac{35 \cdot 7}{28} - \frac{3 \cdot 4}{7 \cdot 4}$

Multiply

$7$ by

$4$ .

$\frac{35 \cdot 7}{28} - \frac{3 \cdot 4}{28}$

Step 5

Combine the numerators over the common denominator.

$\frac{35 \cdot 7 - 3 \cdot 4}{28}$

Step 6

Simplify the numerator.

Multiply

$35$ by

$7$ .

$\frac{245 - 3 \cdot 4}{28}$

Multiply

$- 3$ by

$4$ .

$\frac{245 - 12}{28}$

Subtract

$12$ from

$245$ .

$\frac{233}{28}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{233}{28}$

Decimal Form:

$8.32142857 \dots$

Mixed Number Form:

$8 \frac{9}{28}$

Simplify 8 3/4-3/7

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