Evaluate (8 5/8-7 4/5)*1 1/3

$(8 \frac{5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Step 1

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

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

$(8 + \frac{5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Add $8$ and $\frac{5}{8}$ .

To write $8$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(8 \cdot \frac{8}{8} + \frac{5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Combine $8$ and $\frac{8}{8}$ .

$(\frac{8 \cdot 8}{8} + \frac{5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Combine the numerators over the common denominator.

$(\frac{8 \cdot 8 + 5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Simplify the numerator.

Multiply $8$ by $8$ .

$(\frac{64 + 5}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Add $64$ and $5$ .

$(\frac{69}{8} - 7 \frac{4}{5}) \cdot 1 \frac{1}{3}$

Step 2

Convert $7 \frac{4}{5}$ to an improper fraction.

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

$(\frac{69}{8} - (7 + \frac{4}{5})) \cdot 1 \frac{1}{3}$

Add $7$ and $\frac{4}{5}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{69}{8} - (7 \cdot \frac{5}{5} + \frac{4}{5})) \cdot 1 \frac{1}{3}$

Combine $7$ and $\frac{5}{5}$ .

$(\frac{69}{8} - (\frac{7 \cdot 5}{5} + \frac{4}{5})) \cdot 1 \frac{1}{3}$

Combine the numerators over the common denominator.

$(\frac{69}{8} - \frac{7 \cdot 5 + 4}{5}) \cdot 1 \frac{1}{3}$

Simplify the numerator.

Multiply $7$ by $5$ .

$(\frac{69}{8} - \frac{35 + 4}{5}) \cdot 1 \frac{1}{3}$

Add $35$ and $4$ .

$(\frac{69}{8} - \frac{39}{5}) \cdot 1 \frac{1}{3}$

Step 3

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

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

$(\frac{69}{8} - \frac{39}{5}) \cdot (1 + \frac{1}{3})$

Add $1$ and $\frac{1}{3}$ .

Write $1$ as a fraction with a common denominator.

$(\frac{69}{8} - \frac{39}{5}) \cdot (\frac{3}{3} + \frac{1}{3})$

Combine the numerators over the common denominator.

$(\frac{69}{8} - \frac{39}{5}) \cdot \frac{3 + 1}{3}$

Add $3$ and $1$ .

$(\frac{69}{8} - \frac{39}{5}) \cdot \frac{4}{3}$

Step 4

To write $\frac{69}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{69}{8} \cdot \frac{5}{5} - \frac{39}{5}) \cdot \frac{4}{3}$

Step 5

To write $- \frac{39}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{69}{8} \cdot \frac{5}{5} - \frac{39}{5} \cdot \frac{8}{8}) \cdot \frac{4}{3}$

Step 6

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{69}{8}$ by $\frac{5}{5}$ .

$(\frac{69 \cdot 5}{8 \cdot 5} - \frac{39}{5} \cdot \frac{8}{8}) \cdot \frac{4}{3}$

Multiply $8$ by $5$ .

$(\frac{69 \cdot 5}{40} - \frac{39}{5} \cdot \frac{8}{8}) \cdot \frac{4}{3}$

Multiply $\frac{39}{5}$ by $\frac{8}{8}$ .

$(\frac{69 \cdot 5}{40} - \frac{39 \cdot 8}{5 \cdot 8}) \cdot \frac{4}{3}$

Multiply $5$ by $8$ .

$(\frac{69 \cdot 5}{40} - \frac{39 \cdot 8}{40}) \cdot \frac{4}{3}$

Step 7

Combine the numerators over the common denominator.

$\frac{69 \cdot 5 - 39 \cdot 8}{40} \cdot \frac{4}{3}$

Step 8

Simplify the numerator.

Multiply $69$ by $5$ .

$\frac{345 - 39 \cdot 8}{40} \cdot \frac{4}{3}$

Multiply $- 39$ by $8$ .

$\frac{345 - 312}{40} \cdot \frac{4}{3}$

Subtract $312$ from $345$ .

$\frac{33}{40} \cdot \frac{4}{3}$

Step 9

Cancel the common factor of $3$ .

Factor $3$ out of $33$ .

$\frac{3 (11)}{40} \cdot \frac{4}{3}$

Cancel the common factor.

$\frac{3 \cdot 11}{40} \cdot \frac{4}{3}$

Rewrite the expression.

$\frac{11}{40} \cdot 4$

Step 10

Cancel the common factor of $4$ .

Factor $4$ out of $40$ .

$\frac{11}{4 (10)} \cdot 4$

Cancel the common factor.

$\frac{11}{4 \cdot 10} \cdot 4$

Rewrite the expression.

$\frac{11}{10}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{10}$

Decimal Form:

$1.1$

Mixed Number Form:

$1 \frac{1}{10}$

Evaluate (8 5/8-7 4/5)*1 1/3

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