Solve for d 5 3/4=d-2 1/8

$5 \frac{3}{4} = d - 2 \frac{1}{8}$

Step 1

Simplify the left side.

Convert $5 \frac{3}{4}$ to an improper fraction.

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

$5 + \frac{3}{4} = d - 2 \frac{1}{8}$

Add $5$ and $\frac{3}{4}$ .

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

$5 \cdot \frac{4}{4} + \frac{3}{4} = d - 2 \frac{1}{8}$

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

$\frac{5 \cdot 4}{4} + \frac{3}{4} = d - 2 \frac{1}{8}$

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 3}{4} = d - 2 \frac{1}{8}$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{20 + 3}{4} = d - 2 \frac{1}{8}$

Add $20$ and $3$ .

$\frac{23}{4} = d - 2 \frac{1}{8}$

Step 2

Simplify the right side.

Convert $2 \frac{1}{8}$ to an improper fraction.

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

$\frac{23}{4} = d - (2 + \frac{1}{8})$

Add $2$ and $\frac{1}{8}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{23}{4} = d - (2 \cdot \frac{8}{8} + \frac{1}{8})$

Combine $2$ and $\frac{8}{8}$ .

$\frac{23}{4} = d - (\frac{2 \cdot 8}{8} + \frac{1}{8})$

Combine the numerators over the common denominator.

$\frac{23}{4} = d - \frac{2 \cdot 8 + 1}{8}$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{23}{4} = d - \frac{16 + 1}{8}$

Add $16$ and $1$ .

$\frac{23}{4} = d - \frac{17}{8}$

Step 3

Rewrite the equation as $d - \frac{17}{8} = \frac{23}{4}$ .

$d - \frac{17}{8} = \frac{23}{4}$

Step 4

Move all terms not containing $d$ to the right side of the equation.

Add $\frac{17}{8}$ to both sides of the equation.

$d = \frac{23}{4} + \frac{17}{8}$

To write $\frac{23}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$d = \frac{23}{4} \cdot \frac{2}{2} + \frac{17}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{23}{4}$ by $\frac{2}{2}$ .

$d = \frac{23 \cdot 2}{4 \cdot 2} + \frac{17}{8}$

Multiply $4$ by $2$ .

$d = \frac{23 \cdot 2}{8} + \frac{17}{8}$

Combine the numerators over the common denominator.

$d = \frac{23 \cdot 2 + 17}{8}$

Simplify the numerator.

Multiply $23$ by $2$ .

$d = \frac{46 + 17}{8}$

Add $46$ and $17$ .

$d = \frac{63}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{63}{8}$

Decimal Form:

$d = 7.875$

Mixed Number Form:

$d = 7 \frac{7}{8}$

Solve for d 5 3/4=d-2 1/8

Related Questions

Support LCMGCF.com by disabling your adblocker.