Algebra Examples

$\frac{1}{2} d - \frac{3}{4} d + 3 f - 2 f$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{2}$ and $d$ .

$\frac{d}{2} - \frac{3}{4} d + 3 f - 2 f$

Step 1.2

Combine $d$ and $\frac{3}{4}$ .

$\frac{d}{2} - \frac{d \cdot 3}{4} + 3 f - 2 f$

Step 1.3

Move $3$ to the left of $d$ .

$\frac{d}{2} - \frac{3 d}{4} + 3 f - 2 f$

Step 2

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

$\frac{d}{2} \cdot \frac{2}{2} - \frac{3 d}{4} + 3 f - 2 f$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{d}{2}$ by $\frac{2}{2}$ .

$\frac{d \cdot 2}{2 \cdot 2} - \frac{3 d}{4} + 3 f - 2 f$

Step 3.2

Multiply $2$ by $2$ .

$\frac{d \cdot 2}{4} - \frac{3 d}{4} + 3 f - 2 f$

Step 4

Combine the numerators over the common denominator.

$\frac{d \cdot 2 - 3 d}{4} + 3 f - 2 f$

Step 5

Subtract $3 d$ from $d \cdot 2$ .

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Step 5.1

Reorder $d$ and $2$ .

$\frac{2 \cdot d - 3 d}{4} + 3 f - 2 f$

Step 5.2

Subtract $3 d$ from $2 \cdot d$ .

$\frac{- d}{4} + 3 f - 2 f$

Step 6

Move the negative in front of the fraction.

$- \frac{d}{4} + 3 f - 2 f$

Step 7

Subtract $2 f$ from $3 f$ .

$- \frac{d}{4} + f$