Simplify 2 5/8x-5 3/4x+2

$2 \frac{5}{8} x - 5 \frac{3}{4} x + 2$

Step 1

Convert $2 \frac{5}{8}$ to an improper fraction.

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

$(2 + \frac{5}{8}) x - 5 \frac{3}{4} x + 2$

Add $2$ and $\frac{5}{8}$ .

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

$(2 \cdot \frac{8}{8} + \frac{5}{8}) x - 5 \frac{3}{4} x + 2$

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

$(\frac{2 \cdot 8}{8} + \frac{5}{8}) x - 5 \frac{3}{4} x + 2$

Combine the numerators over the common denominator.

$\frac{2 \cdot 8 + 5}{8} x - 5 \frac{3}{4} x + 2$

Simplify the numerator.

Multiply $2$ by $8$ .

$\frac{16 + 5}{8} x - 5 \frac{3}{4} x + 2$

Add $16$ and $5$ .

$\frac{21}{8} x - 5 \frac{3}{4} x + 2$

Step 2

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

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

$\frac{21}{8} x - (5 + \frac{3}{4}) x + 2$

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

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

$\frac{21}{8} x - (5 \cdot \frac{4}{4} + \frac{3}{4}) x + 2$

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

$\frac{21}{8} x - (\frac{5 \cdot 4}{4} + \frac{3}{4}) x + 2$

Combine the numerators over the common denominator.

$\frac{21}{8} x - \frac{5 \cdot 4 + 3}{4} x + 2$

Simplify the numerator.

Multiply $5$ by $4$ .

$\frac{21}{8} x - \frac{20 + 3}{4} x + 2$

Add $20$ and $3$ .

$\frac{21}{8} x - \frac{23}{4} x + 2$

Step 3

Simplify each term.

Combine $\frac{21}{8}$ and $x$ .

$\frac{21 x}{8} - \frac{23}{4} x + 2$

Combine $x$ and $\frac{23}{4}$ .

$\frac{21 x}{8} - \frac{x \cdot 23}{4} + 2$

Move $23$ to the left of $x$ .

$\frac{21 x}{8} - \frac{23 x}{4} + 2$

Step 4

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

$\frac{21 x}{8} - \frac{23 x}{4} \cdot \frac{2}{2} + 2$

Step 5

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

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

$\frac{21 x}{8} - \frac{23 x \cdot 2}{4 \cdot 2} + 2$

Multiply $4$ by $2$ .

$\frac{21 x}{8} - \frac{23 x \cdot 2}{8} + 2$

Step 6

Combine the numerators over the common denominator.

$\frac{21 x - 23 x \cdot 2}{8} + 2$

Step 7

Simplify each term.

Simplify the numerator.

Factor $x$ out of $21 x - 23 x \cdot 2$ .

Factor $x$ out of $21 x$ .

$\frac{x \cdot 21 - 23 x \cdot 2}{8} + 2$

Factor $x$ out of $- 23 x \cdot 2$ .

$\frac{x \cdot 21 + x (- 23 \cdot 2)}{8} + 2$

Factor $x$ out of $x \cdot 21 + x (- 23 \cdot 2)$ .

$\frac{x (21 - 23 \cdot 2)}{8} + 2$

Multiply $- 23$ by $2$ .

$\frac{x (21 - 46)}{8} + 2$

Subtract $46$ from $21$ .

$\frac{x \cdot - 25}{8} + 2$

Move $- 25$ to the left of $x$ .

$\frac{- 25 \cdot x}{8} + 2$

Move the negative in front of the fraction.

$- \frac{25 x}{8} + 2$

Simplify 2 5/8x-5 3/4x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.