Basic Math Examples

$7 y - \frac{5}{3} = - \frac{4}{5} y - \frac{3}{5}$

Step 1

Simplify each term.

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Step 1.1

Combine $y$ and $\frac{4}{5}$ .

$7 y - \frac{5}{3} = - \frac{y \cdot 4}{5} - \frac{3}{5}$

Step 1.2

Move $4$ to the left of $y$ .

$7 y - \frac{5}{3} = - \frac{4 y}{5} - \frac{3}{5}$

Step 2

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

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Step 2.1

Add $\frac{4 y}{5}$ to both sides of the equation.

$7 y - \frac{5}{3} + \frac{4 y}{5} = - \frac{3}{5}$

Step 2.2

To write $7 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$7 y \cdot \frac{5}{5} + \frac{4 y}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.3

Combine $7 y$ and $\frac{5}{5}$ .

$\frac{7 y \cdot 5}{5} + \frac{4 y}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 y \cdot 5 + 4 y}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $y$ out of $7 y \cdot 5 + 4 y$ .

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Step 2.5.1.1.1

Factor $y$ out of $7 y \cdot 5$ .

$\frac{y (7 \cdot 5) + 4 y}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5.1.1.2

Factor $y$ out of $4 y$ .

$\frac{y (7 \cdot 5) + y \cdot 4}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5.1.1.3

Factor $y$ out of $y (7 \cdot 5) + y \cdot 4$ .

$\frac{y (7 \cdot 5 + 4)}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5.1.2

Multiply $7$ by $5$ .

$\frac{y (35 + 4)}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5.1.3

Add $35$ and $4$ .

$\frac{y \cdot 39}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 2.5.2

Move $39$ to the left of $y$ .

$\frac{39 y}{5} - \frac{5}{3} = - \frac{3}{5}$

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Add $\frac{5}{3}$ to both sides of the equation.

$\frac{39 y}{5} = - \frac{3}{5} + \frac{5}{3}$

Step 3.2

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

$\frac{39 y}{5} = - \frac{3}{5} \cdot \frac{3}{3} + \frac{5}{3}$

Step 3.3

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

$\frac{39 y}{5} = - \frac{3}{5} \cdot \frac{3}{3} + \frac{5}{3} \cdot \frac{5}{5}$

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$\frac{39 y}{5} = - \frac{3 \cdot 3}{5 \cdot 3} + \frac{5}{3} \cdot \frac{5}{5}$

Step 3.4.2

Multiply $5$ by $3$ .

$\frac{39 y}{5} = - \frac{3 \cdot 3}{15} + \frac{5}{3} \cdot \frac{5}{5}$

Step 3.4.3

Multiply $\frac{5}{3}$ by $\frac{5}{5}$ .

$\frac{39 y}{5} = - \frac{3 \cdot 3}{15} + \frac{5 \cdot 5}{3 \cdot 5}$

Step 3.4.4

Multiply $3$ by $5$ .

$\frac{39 y}{5} = - \frac{3 \cdot 3}{15} + \frac{5 \cdot 5}{15}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{39 y}{5} = \frac{- 3 \cdot 3 + 5 \cdot 5}{15}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 3$ by $3$ .

$\frac{39 y}{5} = \frac{- 9 + 5 \cdot 5}{15}$

Step 3.6.2

Multiply $5$ by $5$ .

$\frac{39 y}{5} = \frac{- 9 + 25}{15}$

Step 3.6.3

Add $- 9$ and $25$ .

$\frac{39 y}{5} = \frac{16}{15}$

Step 4

Multiply both sides of the equation by $\frac{5}{39}$ .

$\frac{5}{39} \cdot \frac{39 y}{5} = \frac{5}{39} \cdot \frac{16}{15}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{5}{39} \cdot \frac{39 y}{5}$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{5}{39} \cdot \frac{39 y}{5} = \frac{5}{39} \cdot \frac{16}{15}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{39} (39 y) = \frac{5}{39} \cdot \frac{16}{15}$

Step 5.1.1.2

Cancel the common factor of $39$ .

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Step 5.1.1.2.1

Factor $39$ out of $39 y$ .

$\frac{1}{39} (39 (y)) = \frac{5}{39} \cdot \frac{16}{15}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{39} (39 y) = \frac{5}{39} \cdot \frac{16}{15}$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{5}{39} \cdot \frac{16}{15}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{5}{39} \cdot \frac{16}{15}$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $15$ .

$y = \frac{5}{39} \cdot \frac{16}{5 (3)}$

Step 5.2.1.1.2

Cancel the common factor.

$y = \frac{5}{39} \cdot \frac{16}{5 \cdot 3}$

Step 5.2.1.1.3

Rewrite the expression.

$y = \frac{1}{39} \cdot \frac{16}{3}$

Step 5.2.1.2

Multiply $\frac{1}{39}$ by $\frac{16}{3}$ .

$y = \frac{16}{39 \cdot 3}$

Step 5.2.1.3

Multiply $39$ by $3$ .

$y = \frac{16}{117}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{16}{117}$

Decimal Form:

$y = 0.\overline{136752}$