Algebra Examples

$8 \frac{1}{4} \div d = \frac{2}{11}$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Simplify $8 \frac{1}{4} \div d$ .

Tap for more steps...

Step 1.1.1

Convert $8 \frac{1}{4}$ to an improper fraction.

Tap for more steps...

Step 1.1.1.1

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

$(8 + \frac{1}{4}) \div d = \frac{2}{11}$

Step 1.1.1.2

Add $8$ and $\frac{1}{4}$ .

Tap for more steps...

Step 1.1.1.2.1

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(8 \cdot \frac{4}{4} + \frac{1}{4}) \div d = \frac{2}{11}$

Step 1.1.1.2.2

Combine $8$ and $\frac{4}{4}$ .

$(\frac{8 \cdot 4}{4} + \frac{1}{4}) \div d = \frac{2}{11}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 1}{4} \div d = \frac{2}{11}$

Step 1.1.1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.1.1.2.4.1

Multiply $8$ by $4$ .

$\frac{32 + 1}{4} \div d = \frac{2}{11}$

Step 1.1.1.2.4.2

Add $32$ and $1$ .

$\frac{33}{4} \div d = \frac{2}{11}$

Step 1.1.2

Rewrite the division as a fraction.

$\frac{\frac{33}{4}}{d} = \frac{2}{11}$

Step 1.1.3

Multiply the numerator by the reciprocal of the denominator.

$\frac{33}{4} \cdot \frac{1}{d} = \frac{2}{11}$

Step 1.1.4

Multiply $\frac{33}{4}$ by $\frac{1}{d}$ .

$\frac{33}{4 d} = \frac{2}{11}$

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$33 \cdot 11 = 4 d \cdot 2$

Step 3

Solve the equation for $d$ .

Tap for more steps...

Step 3.1

Rewrite the equation as $4 d \cdot 2 = 33 \cdot 11$ .

$4 d \cdot 2 = 33 \cdot 11$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Multiply $2$ by $4$ .

$8 d = 33 \cdot 11$

Step 3.2.2

Multiply $33$ by $11$ .

$8 d = 363$

Step 3.3

Divide each term in $8 d = 363$ by $8$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $8 d = 363$ by $8$ .

$\frac{8 d}{8} = \frac{363}{8}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{8 d}{8} = \frac{363}{8}$

Step 3.3.2.1.2

Divide $d$ by $1$ .

$d = \frac{363}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = \frac{363}{8}$

Decimal Form:

$d = 45.375$

Mixed Number Form:

$d = 45 \frac{3}{8}$