Basic Math Examples

$\frac{7}{3 c} - 6 \div \frac{4}{c} + 3$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{7}{3 c} - (6 \frac{c}{4}) + 3$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $6$ .

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

Step 1.2.2

Factor $2$ out of $4$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

$\frac{7}{3 c} - (3 \frac{c}{2}) + 3$

Step 1.3

Combine $3$ and $\frac{c}{2}$ .

$\frac{7}{3 c} - \frac{3 c}{2} + 3$

Step 2

To write $\frac{7}{3 c}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

To write $- \frac{3 c}{2}$ as a fraction with a common denominator, multiply by $\frac{3 c}{3 c}$ .

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

Step 4

Write each expression with a common denominator of $6 c$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{7}{3 c}$ by $\frac{2}{2}$ .

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

Step 4.2

Multiply $2$ by $3$ .

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

Step 4.3

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

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

Step 4.4

Multiply $3$ by $2$ .

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

Step 5

Combine into one fraction.

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Step 5.1

Combine the numerators over the common denominator.

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

Step 5.2

Multiply $7$ by $2$ .

$\frac{14 - 3 c (3 c)}{6 c} + 3$

Step 6

Simplify the numerator.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{14 - 3 \cdot 3 c \cdot c}{6 c} + 3$

Step 6.2

Multiply $c$ by $c$ by adding the exponents.

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Step 6.2.1

Move $c$ .

$\frac{14 - 3 \cdot 3 (c \cdot c)}{6 c} + 3$

Step 6.2.2

Multiply $c$ by $c$ .

$\frac{14 - 3 \cdot 3 c^{2}}{6 c} + 3$

Step 6.3

Multiply $- 3$ by $3$ .

$\frac{14 - 9 c^{2}}{6 c} + 3$

Step 7

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

$\frac{14 - 9 c^{2}}{6 c} + 3 \cdot \frac{6 c}{6 c}$

Step 8

Simplify terms.

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Step 8.1

Combine $3$ and $\frac{6 c}{6 c}$ .

$\frac{14 - 9 c^{2}}{6 c} + \frac{3 (6 c)}{6 c}$

Step 8.2

Combine the numerators over the common denominator.

$\frac{14 - 9 c^{2} + 3 (6 c)}{6 c}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $3$ by $6$ .

$\frac{14 - 9 c^{2} + 18 c}{6 c}$

Step 9.2

Reorder terms.

$\frac{- 9 c^{2} + 18 c + 14}{6 c}$

Step 10

Simplify with factoring out.

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Step 10.1

Factor $- 1$ out of $- 9 c^{2}$ .

$\frac{- (9 c^{2}) + 18 c + 14}{6 c}$

Step 10.2

Factor $- 1$ out of $18 c$ .

$\frac{- (9 c^{2}) - (- 18 c) + 14}{6 c}$

Step 10.3

Factor $- 1$ out of $- (9 c^{2}) - (- 18 c)$ .

$\frac{- (9 c^{2} - 18 c) + 14}{6 c}$

Step 10.4

Rewrite $14$ as $- 1 (- 14)$ .

$\frac{- (9 c^{2} - 18 c) - 1 (- 14)}{6 c}$

Step 10.5

Factor $- 1$ out of $- (9 c^{2} - 18 c) - 1 (- 14)$ .

$\frac{- (9 c^{2} - 18 c - 14)}{6 c}$

Step 10.6

Simplify the expression.

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Step 10.6.1

Rewrite $- (9 c^{2} - 18 c - 14)$ as $- 1 (9 c^{2} - 18 c - 14)$ .

$\frac{- 1 (9 c^{2} - 18 c - 14)}{6 c}$

Step 10.6.2

Move the negative in front of the fraction.

$- \frac{9 c^{2} - 18 c - 14}{6 c}$