Algebra Examples

$2 \frac{3}{4} c + 3 \frac{1}{8} c + 7$

Step 1

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

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Step 1.1

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

$(2 + \frac{3}{4}) c + 3 \frac{1}{8} c + 7$

Step 1.2

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

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Step 1.2.1

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

$(2 \cdot \frac{4}{4} + \frac{3}{4}) c + 3 \frac{1}{8} c + 7$

Step 1.2.2

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

$(\frac{2 \cdot 4}{4} + \frac{3}{4}) c + 3 \frac{1}{8} c + 7$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} c + 3 \frac{1}{8} c + 7$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 3}{4} c + 3 \frac{1}{8} c + 7$

Step 1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} c + 3 \frac{1}{8} c + 7$

Step 2

Convert $3 \frac{1}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{11}{4} c + (3 + \frac{1}{8}) c + 7$

Step 2.2

Add $3$ and $\frac{1}{8}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{11}{4} c + (3 \cdot \frac{8}{8} + \frac{1}{8}) c + 7$

Step 2.2.2

Combine $3$ and $\frac{8}{8}$ .

$\frac{11}{4} c + (\frac{3 \cdot 8}{8} + \frac{1}{8}) c + 7$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{11}{4} c + \frac{3 \cdot 8 + 1}{8} c + 7$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $8$ .

$\frac{11}{4} c + \frac{24 + 1}{8} c + 7$

Step 2.2.4.2

Add $24$ and $1$ .

$\frac{11}{4} c + \frac{25}{8} c + 7$

Step 3

Simplify each term.

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Step 3.1

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

$\frac{11 c}{4} + \frac{25}{8} c + 7$

Step 3.2

Combine $\frac{25}{8}$ and $c$ .

$\frac{11 c}{4} + \frac{25 c}{8} + 7$

Step 4

To write $\frac{11 c}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 c}{4} \cdot \frac{2}{2} + \frac{25 c}{8} + 7$

Step 5

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

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Step 5.1

Multiply $\frac{11 c}{4}$ by $\frac{2}{2}$ .

$\frac{11 c \cdot 2}{4 \cdot 2} + \frac{25 c}{8} + 7$

Step 5.2

Multiply $4$ by $2$ .

$\frac{11 c \cdot 2}{8} + \frac{25 c}{8} + 7$

Step 6

Combine the numerators over the common denominator.

$\frac{11 c \cdot 2 + 25 c}{8} + 7$

Step 7

Simplify each term.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Factor $c$ out of $11 c \cdot 2 + 25 c$ .

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Step 7.1.1.1

Factor $c$ out of $11 c \cdot 2$ .

$\frac{c (11 \cdot 2) + 25 c}{8} + 7$

Step 7.1.1.2

Factor $c$ out of $25 c$ .

$\frac{c (11 \cdot 2) + c \cdot 25}{8} + 7$

Step 7.1.1.3

Factor $c$ out of $c (11 \cdot 2) + c \cdot 25$ .

$\frac{c (11 \cdot 2 + 25)}{8} + 7$

Step 7.1.2

Multiply $11$ by $2$ .

$\frac{c (22 + 25)}{8} + 7$

Step 7.1.3

Add $22$ and $25$ .

$\frac{c \cdot 47}{8} + 7$

Step 7.2

Move $47$ to the left of $c$ .

$\frac{47 c}{8} + 7$