Basic Math Examples

$\frac{5}{3} y + \frac{1}{3} y = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1

Simplify $\frac{5}{3} y + \frac{1}{3} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{3}$ and $y$ .

$\frac{5 y}{3} + \frac{1}{3} y = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.1.2

Combine $\frac{1}{3}$ and $y$ .

$\frac{5 y}{3} + \frac{y}{3} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$\frac{5 y + y}{3} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.2

Add $5 y$ and $y$ .

$\frac{6 y}{3} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.3

Cancel the common factor of $6$ and $3$ .

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Step 1.2.3.1

Factor $3$ out of $6 y$ .

$\frac{3 (2 y)}{3} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 y)}{3 (1)} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.3.2.2

Cancel the common factor.

$\frac{3 (2 y)}{3 \cdot 1} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.3.2.3

Rewrite the expression.

$\frac{2 y}{1} = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 1.2.3.2.4

Divide $2 y$ by $1$ .

$2 y = 5 y + \frac{70}{3} + \frac{5}{3} y$

Step 2

Simplify $5 y + \frac{70}{3} + \frac{5}{3} y$ .

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Step 2.1

Combine $\frac{5}{3}$ and $y$ .

$2 y = 5 y + \frac{70}{3} + \frac{5 y}{3}$

Step 2.2

To write $5 y$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$2 y = 5 y \cdot \frac{3}{3} + \frac{5 y}{3} + \frac{70}{3}$

Step 2.3

Combine $5 y$ and $\frac{3}{3}$ .

$2 y = \frac{5 y \cdot 3}{3} + \frac{5 y}{3} + \frac{70}{3}$

Step 2.4

Combine the numerators over the common denominator.

$2 y = \frac{5 y \cdot 3 + 5 y}{3} + \frac{70}{3}$

Step 2.5

Combine the numerators over the common denominator.

$2 y = \frac{5 y \cdot 3 + 5 y + 70}{3}$

Step 2.6

Multiply $3$ by $5$ .

$2 y = \frac{15 y + 5 y + 70}{3}$

Step 2.7

Add $15 y$ and $5 y$ .

$2 y = \frac{20 y + 70}{3}$

Step 2.8

Factor $10$ out of $20 y + 70$ .

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Step 2.8.1

Factor $10$ out of $20 y$ .

$2 y = \frac{10 (2 y) + 70}{3}$

Step 2.8.2

Factor $10$ out of $70$ .

$2 y = \frac{10 (2 y) + 10 (7)}{3}$

Step 2.8.3

Factor $10$ out of $10 (2 y) + 10 (7)$ .

$2 y = \frac{10 (2 y + 7)}{3}$

Step 3

Move all terms containing $y$ to the left side of the equation.

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Step 3.1

Subtract $\frac{10 (2 y + 7)}{3}$ from both sides of the equation.

$2 y - \frac{10 (2 y + 7)}{3} = 0$

Step 3.2

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

$2 y \cdot \frac{3}{3} - \frac{10 (2 y + 7)}{3} = 0$

Step 3.3

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

$\frac{2 y \cdot 3}{3} - \frac{10 (2 y + 7)}{3} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{2 y \cdot 3 - 10 (2 y + 7)}{3} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $2$ out of $2 y \cdot 3 - 10 (2 y + 7)$ .

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Step 3.5.1.1

Factor $2$ out of $2 y \cdot 3$ .

$\frac{2 (y \cdot 3) - 10 (2 y + 7)}{3} = 0$

Step 3.5.1.2

Factor $2$ out of $- 10 (2 y + 7)$ .

$\frac{2 (y \cdot 3) + 2 (- 5 (2 y + 7))}{3} = 0$

Step 3.5.1.3

Factor $2$ out of $2 (y \cdot 3) + 2 (- 5 (2 y + 7))$ .

$\frac{2 (y \cdot 3 - 5 (2 y + 7))}{3} = 0$

Step 3.5.2

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

$\frac{2 (3 \cdot y - 5 (2 y + 7))}{3} = 0$

Step 3.5.3

Apply the distributive property.

$\frac{2 (3 y - 5 (2 y) - 5 \cdot 7)}{3} = 0$

Step 3.5.4

Multiply $2$ by $- 5$ .

$\frac{2 (3 y - 10 y - 5 \cdot 7)}{3} = 0$

Step 3.5.5

Multiply $- 5$ by $7$ .

$\frac{2 (3 y - 10 y - 35)}{3} = 0$

Step 3.5.6

Subtract $10 y$ from $3 y$ .

$\frac{2 (- 7 y - 35)}{3} = 0$

Step 3.5.7

Factor $7$ out of $- 7 y - 35$ .

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Step 3.5.7.1

Factor $7$ out of $- 7 y$ .

$\frac{2 (7 (- y) - 35)}{3} = 0$

Step 3.5.7.2

Factor $7$ out of $- 35$ .

$\frac{2 (7 (- y) + 7 (- 5))}{3} = 0$

Step 3.5.7.3

Factor $7$ out of $7 (- y) + 7 (- 5)$ .

$\frac{2 (7 (- y - 5))}{3} = 0$

$\frac{2 \cdot 7 (- y - 5)}{3} = 0$

Step 3.5.8

Multiply $2$ by $7$ .

$\frac{14 (- y - 5)}{3} = 0$

Step 3.6

Factor $- 1$ out of $- y$ .

$\frac{14 (- (y) - 5)}{3} = 0$

Step 3.7

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{14 (- (y) - 1 (5))}{3} = 0$

Step 3.8

Factor $- 1$ out of $- (y) - 1 (5)$ .

$\frac{14 (- (y + 5))}{3} = 0$

Step 3.9

Rewrite $- (y + 5)$ as $- 1 (y + 5)$ .

$\frac{14 (- 1 (y + 5))}{3} = 0$

Step 3.10

Move the negative in front of the fraction.

$- \frac{14 (y + 5)}{3} = 0$

Step 4

Set the numerator equal to zero.

$14 (y + 5) = 0$

Step 5

Solve the equation for $y$ .

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Step 5.1

Divide each term in $14 (y + 5) = 0$ by $14$ and simplify.

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Step 5.1.1

Divide each term in $14 (y + 5) = 0$ by $14$ .

$\frac{14 (y + 5)}{14} = \frac{0}{14}$

Step 5.1.2

Simplify the left side.

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Step 5.1.2.1

Cancel the common factor of $14$ .

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Step 5.1.2.1.1

Cancel the common factor.

$\frac{14 (y + 5)}{14} = \frac{0}{14}$

Step 5.1.2.1.2

Divide $y + 5$ by $1$ .

$y + 5 = \frac{0}{14}$

Step 5.1.3

Simplify the right side.

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Step 5.1.3.1

Divide $0$ by $14$ .

$y + 5 = 0$

Step 5.2

Subtract $5$ from both sides of the equation.

$y = - 5$