Algebra Examples

$1 \frac{1}{5} f + 2 \frac{3}{4} f - 6 f$

Step 1

Convert $1 \frac{1}{5}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{1}{5}) f + 2 \frac{3}{4} f - 6 f$

Step 1.2

Add $1$ and $\frac{1}{5}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$(\frac{5}{5} + \frac{1}{5}) f + 2 \frac{3}{4} f - 6 f$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{5 + 1}{5} f + 2 \frac{3}{4} f - 6 f$

Step 1.2.3

Add $5$ and $1$ .

$\frac{6}{5} f + 2 \frac{3}{4} f - 6 f$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{6}{5} f + (2 + \frac{3}{4}) f - 6 f$

Step 2.2

Add $2$ and $\frac{3}{4}$ .

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Step 2.2.1

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

$\frac{6}{5} f + (2 \cdot \frac{4}{4} + \frac{3}{4}) f - 6 f$

Step 2.2.2

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

$\frac{6}{5} f + (\frac{2 \cdot 4}{4} + \frac{3}{4}) f - 6 f$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{6}{5} f + \frac{2 \cdot 4 + 3}{4} f - 6 f$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{6}{5} f + \frac{8 + 3}{4} f - 6 f$

Step 2.2.4.2

Add $8$ and $3$ .

$\frac{6}{5} f + \frac{11}{4} f - 6 f$

Step 3

Simplify each term.

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Step 3.1

Combine $\frac{6}{5}$ and $f$ .

$\frac{6 f}{5} + \frac{11}{4} f - 6 f$

Step 3.2

Combine $\frac{11}{4}$ and $f$ .

$\frac{6 f}{5} + \frac{11 f}{4} - 6 f$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{6 f}{5}$ by $\frac{4}{4}$ .

$\frac{6 f}{5} \cdot \frac{4}{4} + \frac{11 f}{4} - 6 f$

Step 4.2

Multiply $\frac{6 f}{5}$ by $\frac{4}{4}$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f}{4} - 6 f$

Step 4.3

Multiply $\frac{11 f}{4}$ by $\frac{5}{5}$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f}{4} \cdot \frac{5}{5} - 6 f$

Step 4.4

Multiply $\frac{11 f}{4}$ by $\frac{5}{5}$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f \cdot 5}{4 \cdot 5} - 6 f$

Step 4.5

Write $- 6 f$ as a fraction with denominator $1$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f \cdot 5}{4 \cdot 5} + \frac{- 6 f}{1}$

Step 4.6

Multiply $\frac{- 6 f}{1}$ by $\frac{20}{20}$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f \cdot 5}{4 \cdot 5} + \frac{- 6 f}{1} \cdot \frac{20}{20}$

Step 4.7

Multiply $\frac{- 6 f}{1}$ by $\frac{20}{20}$ .

$\frac{6 f \cdot 4}{5 \cdot 4} + \frac{11 f \cdot 5}{4 \cdot 5} + \frac{- 6 f \cdot 20}{20}$

Step 4.8

Reorder the factors of $5 \cdot 4$ .

$\frac{6 f \cdot 4}{4 \cdot 5} + \frac{11 f \cdot 5}{4 \cdot 5} + \frac{- 6 f \cdot 20}{20}$

Step 4.9

Multiply $4$ by $5$ .

$\frac{6 f \cdot 4}{20} + \frac{11 f \cdot 5}{4 \cdot 5} + \frac{- 6 f \cdot 20}{20}$

Step 4.10

Multiply $4$ by $5$ .

$\frac{6 f \cdot 4}{20} + \frac{11 f \cdot 5}{20} + \frac{- 6 f \cdot 20}{20}$

Step 5

Combine the numerators over the common denominator.

$\frac{6 f \cdot 4 + 11 f \cdot 5 - 6 f \cdot 20}{20}$

Step 6

Simplify each term.

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Step 6.1

Multiply $4$ by $6$ .

$\frac{24 f + 11 f \cdot 5 - 6 f \cdot 20}{20}$

Step 6.2

Multiply $5$ by $11$ .

$\frac{24 f + 55 f - 6 f \cdot 20}{20}$

Step 6.3

Multiply $20$ by $- 6$ .

$\frac{24 f + 55 f - 120 f}{20}$

Step 7

Simplify by adding terms.

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Step 7.1

Add $24 f$ and $55 f$ .

$\frac{79 f - 120 f}{20}$

Step 7.2

Subtract $120 f$ from $79 f$ .

$\frac{- 41 f}{20}$

Step 7.3

Move the negative in front of the fraction.

$- \frac{41 f}{20}$