Basic Math Examples

$\frac{17}{3} a + \frac{15}{7} b - \frac{3}{4} a - \frac{9}{14} b - 39$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{17}{3}$ and $a$ .

$\frac{17 a}{3} + \frac{15}{7} b - \frac{3}{4} a - \frac{9}{14} b - 39$

Step 1.2

Combine $\frac{15}{7}$ and $b$ .

$\frac{17 a}{3} + \frac{15 b}{7} - \frac{3}{4} a - \frac{9}{14} b - 39$

Step 1.3

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

$\frac{17 a}{3} + \frac{15 b}{7} - \frac{a \cdot 3}{4} - \frac{9}{14} b - 39$

Step 1.4

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

$\frac{17 a}{3} + \frac{15 b}{7} - \frac{3 \cdot a}{4} - \frac{9}{14} b - 39$

Step 1.5

Combine $b$ and $\frac{9}{14}$ .

$\frac{17 a}{3} + \frac{15 b}{7} - \frac{3 a}{4} - \frac{b \cdot 9}{14} - 39$

Step 1.6

Move $9$ to the left of $b$ .

$\frac{17 a}{3} + \frac{15 b}{7} - \frac{3 a}{4} - \frac{9 b}{14} - 39$

Step 2

To write $\frac{17 a}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{15 b}{7} + \frac{17 a}{3} \cdot \frac{4}{4} - \frac{3 a}{4} - \frac{9 b}{14} - 39$

Step 3

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

$\frac{15 b}{7} + \frac{17 a}{3} \cdot \frac{4}{4} - \frac{3 a}{4} \cdot \frac{3}{3} - \frac{9 b}{14} - 39$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{17 a}{3}$ by $\frac{4}{4}$ .

$\frac{15 b}{7} + \frac{17 a \cdot 4}{3 \cdot 4} - \frac{3 a}{4} \cdot \frac{3}{3} - \frac{9 b}{14} - 39$

Step 4.2

Multiply $3$ by $4$ .

$\frac{15 b}{7} + \frac{17 a \cdot 4}{12} - \frac{3 a}{4} \cdot \frac{3}{3} - \frac{9 b}{14} - 39$

Step 4.3

Multiply $\frac{3 a}{4}$ by $\frac{3}{3}$ .

$\frac{15 b}{7} + \frac{17 a \cdot 4}{12} - \frac{3 a \cdot 3}{4 \cdot 3} - \frac{9 b}{14} - 39$

Step 4.4

Multiply $4$ by $3$ .

$\frac{15 b}{7} + \frac{17 a \cdot 4}{12} - \frac{3 a \cdot 3}{12} - \frac{9 b}{14} - 39$

Step 5

Combine the numerators over the common denominator.

$\frac{15 b}{7} + \frac{17 a \cdot 4 - 3 a \cdot 3}{12} - \frac{9 b}{14} - 39$

Step 6

Simplify each term.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Factor $a$ out of $17 a \cdot 4 - 3 a \cdot 3$ .

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Step 6.1.1.1

Factor $a$ out of $17 a \cdot 4$ .

$\frac{15 b}{7} + \frac{a (17 \cdot 4) - 3 a \cdot 3}{12} - \frac{9 b}{14} - 39$

Step 6.1.1.2

Factor $a$ out of $- 3 a \cdot 3$ .

$\frac{15 b}{7} + \frac{a (17 \cdot 4) + a (- 3 \cdot 3)}{12} - \frac{9 b}{14} - 39$

Step 6.1.1.3

Factor $a$ out of $a (17 \cdot 4) + a (- 3 \cdot 3)$ .

$\frac{15 b}{7} + \frac{a (17 \cdot 4 - 3 \cdot 3)}{12} - \frac{9 b}{14} - 39$

Step 6.1.2

Multiply $17$ by $4$ .

$\frac{15 b}{7} + \frac{a (68 - 3 \cdot 3)}{12} - \frac{9 b}{14} - 39$

Step 6.1.3

Multiply $- 3$ by $3$ .

$\frac{15 b}{7} + \frac{a (68 - 9)}{12} - \frac{9 b}{14} - 39$

Step 6.1.4

Subtract $9$ from $68$ .

$\frac{15 b}{7} + \frac{a \cdot 59}{12} - \frac{9 b}{14} - 39$

Step 6.2

Move $59$ to the left of $a$ .

$\frac{15 b}{7} + \frac{59 a}{12} - \frac{9 b}{14} - 39$

Step 7

To write $\frac{15 b}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{59 a}{12} + \frac{15 b}{7} \cdot \frac{2}{2} - \frac{9 b}{14} - 39$

Step 8

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{15 b}{7}$ by $\frac{2}{2}$ .

$\frac{59 a}{12} + \frac{15 b \cdot 2}{7 \cdot 2} - \frac{9 b}{14} - 39$

Step 8.2

Multiply $7$ by $2$ .

$\frac{59 a}{12} + \frac{15 b \cdot 2}{14} - \frac{9 b}{14} - 39$

Step 9

Combine the numerators over the common denominator.

$\frac{59 a}{12} + \frac{15 b \cdot 2 - 9 b}{14} - 39$

Step 10

Simplify each term.

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Step 10.1

Simplify the numerator.

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Step 10.1.1

Factor $3 b$ out of $15 b \cdot 2 - 9 b$ .

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Step 10.1.1.1

Factor $3 b$ out of $15 b \cdot 2$ .

$\frac{59 a}{12} + \frac{3 b (5 \cdot 2) - 9 b}{14} - 39$

Step 10.1.1.2

Factor $3 b$ out of $- 9 b$ .

$\frac{59 a}{12} + \frac{3 b (5 \cdot 2) + 3 b (- 3)}{14} - 39$

Step 10.1.1.3

Factor $3 b$ out of $3 b (5 \cdot 2) + 3 b (- 3)$ .

$\frac{59 a}{12} + \frac{3 b (5 \cdot 2 - 3)}{14} - 39$

Step 10.1.2

Multiply $5$ by $2$ .

$\frac{59 a}{12} + \frac{3 b (10 - 3)}{14} - 39$

Step 10.1.3

Subtract $3$ from $10$ .

$\frac{59 a}{12} + \frac{3 b \cdot 7}{14} - 39$

Step 10.1.4

Multiply $7$ by $3$ .

$\frac{59 a}{12} + \frac{21 b}{14} - 39$

Step 10.2

Cancel the common factor of $21$ and $14$ .

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Step 10.2.1

Factor $7$ out of $21 b$ .

$\frac{59 a}{12} + \frac{7 (3 b)}{14} - 39$

Step 10.2.2

Cancel the common factors.

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Step 10.2.2.1

Factor $7$ out of $14$ .

$\frac{59 a}{12} + \frac{7 (3 b)}{7 (2)} - 39$

Step 10.2.2.2

Cancel the common factor.

$\frac{59 a}{12} + \frac{7 (3 b)}{7 \cdot 2} - 39$

Step 10.2.2.3

Rewrite the expression.

$\frac{59 a}{12} + \frac{3 b}{2} - 39$