Basic Math Examples

$\frac{11}{2} a + \frac{13}{7} b - \frac{2}{3} a - \frac{5}{14} b - 37$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{11}{2}$ and $a$ .

$\frac{11 a}{2} + \frac{13}{7} b - \frac{2}{3} a - \frac{5}{14} b - 37$

Step 1.2

Combine $\frac{13}{7}$ and $b$ .

$\frac{11 a}{2} + \frac{13 b}{7} - \frac{2}{3} a - \frac{5}{14} b - 37$

Step 1.3

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

$\frac{11 a}{2} + \frac{13 b}{7} - \frac{a \cdot 2}{3} - \frac{5}{14} b - 37$

Step 1.4

Move $2$ to the left of $a$ .

$\frac{11 a}{2} + \frac{13 b}{7} - \frac{2 \cdot a}{3} - \frac{5}{14} b - 37$

Step 1.5

Combine $b$ and $\frac{5}{14}$ .

$\frac{11 a}{2} + \frac{13 b}{7} - \frac{2 a}{3} - \frac{b \cdot 5}{14} - 37$

Step 1.6

Move $5$ to the left of $b$ .

$\frac{11 a}{2} + \frac{13 b}{7} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 2

To write $\frac{11 a}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{11 a}{2} \cdot \frac{7}{7} + \frac{13 b}{7} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 3

To write $\frac{13 b}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 a}{2} \cdot \frac{7}{7} + \frac{13 b}{7} \cdot \frac{2}{2} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 4

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

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Step 4.1

Multiply $\frac{11 a}{2}$ by $\frac{7}{7}$ .

$\frac{11 a \cdot 7}{2 \cdot 7} + \frac{13 b}{7} \cdot \frac{2}{2} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 4.2

Multiply $2$ by $7$ .

$\frac{11 a \cdot 7}{14} + \frac{13 b}{7} \cdot \frac{2}{2} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 4.3

Multiply $\frac{13 b}{7}$ by $\frac{2}{2}$ .

$\frac{11 a \cdot 7}{14} + \frac{13 b \cdot 2}{7 \cdot 2} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 4.4

Multiply $7$ by $2$ .

$\frac{11 a \cdot 7}{14} + \frac{13 b \cdot 2}{14} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 5

Simplify terms.

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Step 5.1

Combine the numerators over the common denominator.

$\frac{11 a \cdot 7 + 13 b \cdot 2}{14} - \frac{2 a}{3} - \frac{5 b}{14} - 37$

Step 5.2

Combine the numerators over the common denominator.

$- 37 + \frac{11 a \cdot 7 + 13 b \cdot 2 - 5 b}{14} + \frac{- 2 a}{3}$

Step 6

Simplify each term.

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Step 6.1

Multiply $7$ by $11$ .

$- 37 + \frac{77 a + 13 b \cdot 2 - 5 b}{14} + \frac{- 2 a}{3}$

Step 6.2

Multiply $2$ by $13$ .

$- 37 + \frac{77 a + 26 b - 5 b}{14} + \frac{- 2 a}{3}$

Step 7

Subtract $5 b$ from $26 b$ .

$- 37 + \frac{77 a + 21 b}{14} + \frac{- 2 a}{3}$

Step 8

Simplify each term.

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Step 8.1

Cancel the common factor of $77 a + 21 b$ and $14$ .

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Step 8.1.1

Factor $7$ out of $77 a$ .

$- 37 + \frac{7 (11 a) + 21 b}{14} + \frac{- 2 a}{3}$

Step 8.1.2

Factor $7$ out of $21 b$ .

$- 37 + \frac{7 (11 a) + 7 (3 b)}{14} + \frac{- 2 a}{3}$

Step 8.1.3

Factor $7$ out of $7 (11 a) + 7 (3 b)$ .

$- 37 + \frac{7 (11 a + 3 b)}{14} + \frac{- 2 a}{3}$

Step 8.1.4

Cancel the common factors.

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Step 8.1.4.1

Factor $7$ out of $14$ .

$- 37 + \frac{7 (11 a + 3 b)}{7 (2)} + \frac{- 2 a}{3}$

Step 8.1.4.2

Cancel the common factor.

$- 37 + \frac{7 (11 a + 3 b)}{7 \cdot 2} + \frac{- 2 a}{3}$

Step 8.1.4.3

Rewrite the expression.

$- 37 + \frac{11 a + 3 b}{2} + \frac{- 2 a}{3}$

Step 8.2

Move the negative in front of the fraction.

$- 37 + \frac{11 a + 3 b}{2} - \frac{2 a}{3}$

Step 9

To write $- 37$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 37 \cdot \frac{2}{2} + \frac{11 a + 3 b}{2} - \frac{2 a}{3}$

Step 10

Combine $- 37$ and $\frac{2}{2}$ .

$\frac{- 37 \cdot 2}{2} + \frac{11 a + 3 b}{2} - \frac{2 a}{3}$

Step 11

Combine the numerators over the common denominator.

$\frac{- 37 \cdot 2 + 11 a + 3 b}{2} - \frac{2 a}{3}$

Step 12

Multiply $- 37$ by $2$ .

$\frac{- 74 + 11 a + 3 b}{2} - \frac{2 a}{3}$

Step 13

To write $\frac{- 74 + 11 a + 3 b}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{- 74 + 11 a + 3 b}{2} \cdot \frac{3}{3} - \frac{2 a}{3}$

Step 14

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

$\frac{- 74 + 11 a + 3 b}{2} \cdot \frac{3}{3} - \frac{2 a}{3} \cdot \frac{2}{2}$

Step 15

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

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Step 15.1

Multiply $\frac{- 74 + 11 a + 3 b}{2}$ by $\frac{3}{3}$ .

$\frac{(- 74 + 11 a + 3 b) \cdot 3}{2 \cdot 3} - \frac{2 a}{3} \cdot \frac{2}{2}$

Step 15.2

Multiply $2$ by $3$ .

$\frac{(- 74 + 11 a + 3 b) \cdot 3}{6} - \frac{2 a}{3} \cdot \frac{2}{2}$

Step 15.3

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

$\frac{(- 74 + 11 a + 3 b) \cdot 3}{6} - \frac{2 a \cdot 2}{3 \cdot 2}$

Step 15.4

Multiply $3$ by $2$ .

$\frac{(- 74 + 11 a + 3 b) \cdot 3}{6} - \frac{2 a \cdot 2}{6}$

Step 16

Combine the numerators over the common denominator.

$\frac{(- 74 + 11 a + 3 b) \cdot 3 - 2 a \cdot 2}{6}$

Step 17

Simplify the numerator.

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Step 17.1

Apply the distributive property.

$\frac{- 74 \cdot 3 + 11 a \cdot 3 + 3 b \cdot 3 - 2 a \cdot 2}{6}$

Step 17.2

Simplify.

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Step 17.2.1

Multiply $- 74$ by $3$ .

$\frac{- 222 + 11 a \cdot 3 + 3 b \cdot 3 - 2 a \cdot 2}{6}$

Step 17.2.2

Multiply $3$ by $11$ .

$\frac{- 222 + 33 a + 3 b \cdot 3 - 2 a \cdot 2}{6}$

Step 17.2.3

Multiply $3$ by $3$ .

$\frac{- 222 + 33 a + 9 b - 2 a \cdot 2}{6}$

Step 17.3

Multiply $2$ by $- 2$ .

$\frac{- 222 + 33 a + 9 b - 4 a}{6}$

Step 17.4

Subtract $4 a$ from $33 a$ .

$\frac{- 222 + 29 a + 9 b}{6}$

Step 18

Simplify with factoring out.

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Step 18.1

Rewrite $- 222$ as $- 1 (222)$ .

$\frac{- 1 (222) + 29 a + 9 b}{6}$

Step 18.2

Factor $- 1$ out of $29 a$ .

$\frac{- 1 (222) - (- 29 a) + 9 b}{6}$

Step 18.3

Factor $- 1$ out of $- 1 (222) - (- 29 a)$ .

$\frac{- 1 (222 - 29 a) + 9 b}{6}$

Step 18.4

Factor $- 1$ out of $9 b$ .

$\frac{- 1 (222 - 29 a) - (- 9 b)}{6}$

Step 18.5

Factor $- 1$ out of $- 1 (222 - 29 a) - (- 9 b)$ .

$\frac{- 1 (222 - 29 a - 9 b)}{6}$

Step 18.6

Move the negative in front of the fraction.

$- \frac{222 - 29 a - 9 b}{6}$