Basic Math Examples

$\frac{2 y \cdot 10}{3} + \frac{7 y \cdot 7}{3} - \frac{49 y \cdot 4}{3} = 0$

Step 1

Simplify $\frac{2 y \cdot 10}{3} + \frac{7 y \cdot 7}{3} - \frac{49 y \cdot 4}{3}$ .

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Step 1.1

Combine the numerators over the common denominator.

$\frac{2 y \cdot 10 + 7 y \cdot 7 - 49 y \cdot 4}{3} = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $10$ by $2$ .

$\frac{20 y + 7 y \cdot 7 - 49 y \cdot 4}{3} = 0$

Step 1.2.2

Multiply $7$ by $7$ .

$\frac{20 y + 49 y - 49 y \cdot 4}{3} = 0$

Step 1.2.3

Multiply $4$ by $- 49$ .

$\frac{20 y + 49 y - 196 y}{3} = 0$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Add $20 y$ and $49 y$ .

$\frac{69 y - 196 y}{3} = 0$

Step 1.3.2

Subtract $196 y$ from $69 y$ .

$\frac{- 127 y}{3} = 0$

Step 1.3.3

Move the negative in front of the fraction.

$- \frac{127 y}{3} = 0$

Step 2

Set the numerator equal to zero.

$127 y = 0$

Step 3

Divide each term in $127 y = 0$ by $127$ and simplify.

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Step 3.1

Divide each term in $127 y = 0$ by $127$ .

$\frac{127 y}{127} = \frac{0}{127}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $127$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{127 y}{127} = \frac{0}{127}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{0}{127}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0$ by $127$ .

$y = 0$