Combine 11/2a+13/7b-2/3a-5/14b-37

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

Simplify each term.

Tap for more steps…

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tap for more steps…

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

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

Multiply $2$ by $7$ .

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

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

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

Multiply $7$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Tap for more steps…

Multiply $7$ by $11$ .

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

Multiply $2$ by $13$ .

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

To write $\frac{77 a + 26 b}{14}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $- \frac{2 a}{3}$ as a fraction with a common denominator, multiply by $\frac{14}{14}$ .

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

Write each expression with a common denominator of $42$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps…

Multiply $\frac{77 a + 26 b}{14}$ and $\frac{3}{3}$ .

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

Multiply $14$ by $3$ .

$\frac{(77 a + 26 b) \cdot 3}{42} - \frac{2 a}{3} \cdot \frac{14}{14} - \frac{5 b}{14} - 37$

Multiply $\frac{2 a}{3}$ and $\frac{14}{14}$ .

$\frac{(77 a + 26 b) \cdot 3}{42} - \frac{2 a \cdot 14}{3 \cdot 14} - \frac{5 b}{14} - 37$

Multiply $3$ by $14$ .

$\frac{(77 a + 26 b) \cdot 3}{42} - \frac{2 a \cdot 14}{42} - \frac{5 b}{14} - 37$

Combine the numerators over the common denominator.

$\frac{(77 a + 26 b) \cdot 3 - 2 a \cdot 14}{42} - \frac{5 b}{14} - 37$

Simplify each term.

Tap for more steps…

Simplify the numerator.

Tap for more steps…

Apply the distributive property.

$\frac{77 a \cdot 3 + 26 b \cdot 3 - 2 a \cdot 14}{42} - \frac{5 b}{14} - 37$

Multiply $3$ by $77$ .

$\frac{231 a + 26 b \cdot 3 - 2 a \cdot 14}{42} - \frac{5 b}{14} - 37$

Multiply $3$ by $26$ .

$\frac{231 a + 78 b - 2 a \cdot 14}{42} - \frac{5 b}{14} - 37$

Multiply $14$ by $- 2$ .

$\frac{231 a + 78 b - 28 a}{42} - \frac{5 b}{14} - 37$

Subtract $28 a$ from $231 a$ .

$\frac{203 a + 78 b}{42} - \frac{5 b}{14} - 37$

Split the fraction into multiple fractions.

$\frac{203 a}{42} + \frac{78 b}{42} - \frac{5 b}{14} - 37$

Reduce the expression $\frac{203 a}{42}$ by cancelling the common factors.

Tap for more steps…

Factor $7$ out of $203 a$ .

$\frac{7 (29 a)}{42} + \frac{78 b}{42} - \frac{5 b}{14} - 37$

Factor $7$ out of $42$ .

$\frac{7 (29 a)}{7 (6)} + \frac{78 b}{42} - \frac{5 b}{14} - 37$

Cancel the common factor.

$\frac{7 (29 a)}{7 \cdot 6} + \frac{78 b}{42} - \frac{5 b}{14} - 37$

Rewrite the expression.

$\frac{29 a}{6} + \frac{78 b}{42} - \frac{5 b}{14} - 37$

Reduce the expression $\frac{78 b}{42}$ by cancelling the common factors.

Tap for more steps…

Factor $6$ out of $78 b$ .

$\frac{29 a}{6} + \frac{6 (13 b)}{42} - \frac{5 b}{14} - 37$

Factor $6$ out of $42$ .

$\frac{29 a}{6} + \frac{6 (13 b)}{6 (7)} - \frac{5 b}{14} - 37$

Cancel the common factor.

$\frac{29 a}{6} + \frac{6 (13 b)}{6 \cdot 7} - \frac{5 b}{14} - 37$

Rewrite the expression.

$\frac{29 a}{6} + \frac{13 b}{7} - \frac{5 b}{14} - 37$

Combine 11/2a+13/7b-2/3a-5/14b-37

Solving MATH problems