Algebra Examples

$\frac{3}{4} c - \frac{7}{12} + \frac{7}{24} c + \frac{2}{3} - \frac{1}{6} c$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{3 c}{4} - \frac{7}{12} + \frac{7}{24} c + \frac{2}{3} - \frac{1}{6} c$

Step 1.2

Combine $\frac{7}{24}$ and $c$ .

$\frac{3 c}{4} - \frac{7}{12} + \frac{7 c}{24} + \frac{2}{3} - \frac{1}{6} c$

Step 1.3

Combine $c$ and $\frac{1}{6}$ .

$\frac{3 c}{4} - \frac{7}{12} + \frac{7 c}{24} + \frac{2}{3} - \frac{c}{6}$

Step 2

To write $\frac{3 c}{4}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{3 c}{4} \cdot \frac{6}{6} + \frac{7 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 3

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3 c}{4}$ by $\frac{6}{6}$ .

$\frac{3 c \cdot 6}{4 \cdot 6} + \frac{7 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 3.2

Multiply $4$ by $6$ .

$\frac{3 c \cdot 6}{24} + \frac{7 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 c \cdot 6 + 7 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $c$ out of $3 c \cdot 6 + 7 c$ .

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Step 5.1.1.1

Factor $c$ out of $3 c \cdot 6$ .

$\frac{c (3 \cdot 6) + 7 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5.1.1.2

Factor $c$ out of $7 c$ .

$\frac{c (3 \cdot 6) + c \cdot 7}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5.1.1.3

Factor $c$ out of $c (3 \cdot 6) + c \cdot 7$ .

$\frac{c (3 \cdot 6 + 7)}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5.1.2

Multiply $3$ by $6$ .

$\frac{c (18 + 7)}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5.1.3

Add $18$ and $7$ .

$\frac{c \cdot 25}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 5.2

Move $25$ to the left of $c$ .

$\frac{25 c}{24} - \frac{7}{12} + \frac{2}{3} - \frac{c}{6}$

Step 6

To write $- \frac{c}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25 c}{24} - \frac{c}{6} \cdot \frac{4}{4} - \frac{7}{12} + \frac{2}{3}$

Step 7

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{c}{6}$ by $\frac{4}{4}$ .

$\frac{25 c}{24} - \frac{c \cdot 4}{6 \cdot 4} - \frac{7}{12} + \frac{2}{3}$

Step 7.2

Multiply $6$ by $4$ .

$\frac{25 c}{24} - \frac{c \cdot 4}{24} - \frac{7}{12} + \frac{2}{3}$

Step 8

Combine the numerators over the common denominator.

$\frac{25 c - c \cdot 4}{24} - \frac{7}{12} + \frac{2}{3}$

Step 9

Find the common denominator.

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Step 9.1

Multiply $\frac{7}{12}$ by $\frac{2}{2}$ .

$\frac{25 c - c \cdot 4}{24} - (\frac{7}{12} \cdot \frac{2}{2}) + \frac{2}{3}$

Step 9.2

Multiply $\frac{7}{12}$ by $\frac{2}{2}$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{12 \cdot 2} + \frac{2}{3}$

Step 9.3

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{12 \cdot 2} + \frac{2}{3} \cdot \frac{8}{8}$

Step 9.4

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{12 \cdot 2} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 9.5

Reorder the factors of $12 \cdot 2$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{2 \cdot 12} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 9.6

Multiply $2$ by $12$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{24} + \frac{2 \cdot 8}{3 \cdot 8}$

Step 9.7

Multiply $3$ by $8$ .

$\frac{25 c - c \cdot 4}{24} - \frac{7 \cdot 2}{24} + \frac{2 \cdot 8}{24}$

Step 10

Combine the numerators over the common denominator.

$\frac{25 c - c \cdot 4 - 7 \cdot 2 + 2 \cdot 8}{24}$

Step 11

Simplify each term.

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Step 11.1

Multiply $4$ by $- 1$ .

$\frac{25 c - 4 c - 7 \cdot 2 + 2 \cdot 8}{24}$

Step 11.2

Multiply $- 7$ by $2$ .

$\frac{25 c - 4 c - 14 + 2 \cdot 8}{24}$

Step 11.3

Multiply $2$ by $8$ .

$\frac{25 c - 4 c - 14 + 16}{24}$

Step 12

Simplify by adding terms.

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Step 12.1

Subtract $4 c$ from $25 c$ .

$\frac{21 c - 14 + 16}{24}$

Step 12.2

Add $- 14$ and $16$ .

$\frac{21 c + 2}{24}$