Evaluate (7/20+3/4)÷(11/25)

$(\frac{7}{20} + \frac{3}{4}) \div \frac{11}{25}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$(\frac{7}{20} + \frac{3}{4}) \frac{25}{11}$

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{7}{20} + \frac{3}{4} \cdot \frac{5}{5}) \frac{25}{11}$

Step 3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{4}$ by $\frac{5}{5}$ .

$(\frac{7}{20} + \frac{3 \cdot 5}{4 \cdot 5}) \frac{25}{11}$

Multiply $4$ by $5$ .

$(\frac{7}{20} + \frac{3 \cdot 5}{20}) \frac{25}{11}$

Step 4

Combine the numerators over the common denominator.

$\frac{7 + 3 \cdot 5}{20} \cdot \frac{25}{11}$

Step 5

Simplify the numerator.

Multiply $3$ by $5$ .

$\frac{7 + 15}{20} \cdot \frac{25}{11}$

Add $7$ and $15$ .

$\frac{22}{20} \cdot \frac{25}{11}$

Step 6

Cancel the common factor of $11$ .

Factor $11$ out of $22$ .

$\frac{11 (2)}{20} \cdot \frac{25}{11}$

Cancel the common factor.

$\frac{11 \cdot 2}{20} \cdot \frac{25}{11}$

Rewrite the expression.

$\frac{2}{20} \cdot 25$

Step 7

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$\frac{2}{5 (4)} \cdot 25$

Factor $5$ out of $25$ .

$\frac{2}{5 \cdot 4} \cdot (5 \cdot 5)$

Cancel the common factor.

$\frac{2}{5 \cdot 4} \cdot (5 \cdot 5)$

Rewrite the expression.

$\frac{2}{4} \cdot 5$

Step 8

Combine $\frac{2}{4}$ and $5$ .

$\frac{2 \cdot 5}{4}$

Step 9

Multiply $2$ by $5$ .

$\frac{10}{4}$

Step 10

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$\frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$\frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$\frac{5}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

Evaluate (7/20+3/4)÷(11/25)

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