Evaluate (7/4-1/3)÷(5/3)

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

To write $\frac{7}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

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

Multiply $4$ by $3$ .

$(\frac{7 \cdot 3}{12} - \frac{1}{3} \cdot \frac{4}{4}) \frac{3}{5}$

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$(\frac{7 \cdot 3}{12} - \frac{4}{3 \cdot 4}) \frac{3}{5}$

Multiply $3$ by $4$ .

$(\frac{7 \cdot 3}{12} - \frac{4}{12}) \frac{3}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 3 - 4}{12} \cdot \frac{3}{5}$

Step 6

Simplify the numerator.

Multiply $7$ by $3$ .

$\frac{21 - 4}{12} \cdot \frac{3}{5}$

Subtract $4$ from $21$ .

$\frac{17}{12} \cdot \frac{3}{5}$

Step 7

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$\frac{17}{3 (4)} \cdot \frac{3}{5}$

Cancel the common factor.

$\frac{17}{3 \cdot 4} \cdot \frac{3}{5}$

Rewrite the expression.

$\frac{17}{4} \cdot \frac{1}{5}$

Step 8

Multiply $\frac{17}{4}$ by $\frac{1}{5}$ .

$\frac{17}{4 \cdot 5}$

Step 9

Multiply $4$ by $5$ .

$\frac{17}{20}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{20}$

Decimal Form:

$0.85$

Evaluate (7/4-1/3)÷(5/3)

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