Basic Math Examples

$3 - \frac{5}{4} \cdot (2 y - 6) = 5 y - \frac{2}{3}$

Step 1

Simplify $3 - \frac{5}{4} \cdot (2 y - 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 - \frac{5}{4} (2 y) - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$3 + \frac{- 5}{4} (2 y) - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.2.2

Factor $2$ out of $4$ .

$3 + \frac{- 5}{2 (2)} (2 y) - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.2.3

Factor $2$ out of $2 y$ .

$3 + \frac{- 5}{2 (2)} (2 (y)) - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.2.4

Cancel the common factor.

$3 + \frac{- 5}{2 \cdot 2} (2 y) - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.2.5

Rewrite the expression.

$3 + \frac{- 5}{2} y - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.3

Combine $\frac{- 5}{2}$ and $y$ .

$3 + \frac{- 5 y}{2} - \frac{5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$3 + \frac{- 5 y}{2} + \frac{- 5}{4} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.4.2

Factor $2$ out of $4$ .

$3 + \frac{- 5 y}{2} + \frac{- 5}{2 (2)} \cdot - 6 = 5 y - \frac{2}{3}$

Step 1.1.4.3

Factor $2$ out of $- 6$ .

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

Step 1.1.4.4

Cancel the common factor.

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

Step 1.1.4.5

Rewrite the expression.

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

Step 1.1.5

Combine $\frac{- 5}{2}$ and $- 3$ .

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

Step 1.1.6

Multiply $- 5$ by $- 3$ .

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

Step 1.1.7

Move the negative in front of the fraction.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $3$ by $2$ .

$- \frac{5 y}{2} + \frac{6 + 15}{2} = 5 y - \frac{2}{3}$

Step 1.5.2

Add $6$ and $15$ .

$- \frac{5 y}{2} + \frac{21}{2} = 5 y - \frac{2}{3}$

Step 2

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

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Step 2.1

Subtract $5 y$ from both sides of the equation.

$- \frac{5 y}{2} + \frac{21}{2} - 5 y = - \frac{2}{3}$

Step 2.2

To write $- 5 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 y}{2} - 5 y \cdot \frac{2}{2} + \frac{21}{2} = - \frac{2}{3}$

Step 2.3

Combine $- 5 y$ and $\frac{2}{2}$ .

$- \frac{5 y}{2} + \frac{- 5 y \cdot 2}{2} + \frac{21}{2} = - \frac{2}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 5 y - 5 y \cdot 2}{2} + \frac{21}{2} = - \frac{2}{3}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 5 y - 5 y \cdot 2 + 21}{2} = - \frac{2}{3}$

Step 2.6

Multiply $2$ by $- 5$ .

$\frac{- 5 y - 10 y + 21}{2} = - \frac{2}{3}$

Step 2.7

Subtract $10 y$ from $- 5 y$ .

$\frac{- 15 y + 21}{2} = - \frac{2}{3}$

Step 2.8

Factor $3$ out of $- 15 y + 21$ .

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Step 2.8.1

Factor $3$ out of $- 15 y$ .

$\frac{3 (- 5 y) + 21}{2} = - \frac{2}{3}$

Step 2.8.2

Factor $3$ out of $21$ .

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

Step 2.8.3

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

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

Step 2.9

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

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

Step 2.10

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{3 (- (5 y) - 1 (- 7))}{2} = - \frac{2}{3}$

Step 2.11

Factor $- 1$ out of $- (5 y) - 1 (- 7)$ .

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

Step 2.12

Rewrite $- (5 y - 7)$ as $- 1 (5 y - 7)$ .

$\frac{3 (- 1 (5 y - 7))}{2} = - \frac{2}{3}$

Step 2.13

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by $- \frac{2}{3}$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{2}{3} (- \frac{3 (5 y - 7)}{2})$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 4.1.1.1.2

Move the leading negative in $- \frac{3 (5 y - 7)}{2}$ into the numerator.

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

Step 4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 (5 y - 7)}{2} = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 (5 y - 7)}{2} = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 (5 y - 7)) = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $- 3 (5 y - 7)$ .

$\frac{- 1}{3} (3 (- (5 y - 7))) = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- (5 y - 7))) = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (5 y - 7) = - \frac{2}{3} (- \frac{2}{3})$

Step 4.1.1.3.2

Multiply $5 y - 7$ by $1$ .

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{2}{3} (- \frac{2}{3})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$5 y - 7 = 1 (\frac{2}{3}) \frac{2}{3}$

Step 4.2.1.2

Multiply $\frac{2}{3}$ by $1$ .

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

Step 4.2.1.3

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

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

Step 4.2.1.4

Multiply $2$ by $2$ .

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

Step 4.2.1.5

Multiply $3$ by $3$ .

$5 y - 7 = \frac{4}{9}$

Step 5

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

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Step 5.1

Add $7$ to both sides of the equation.

$5 y = \frac{4}{9} + 7$

Step 5.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$5 y = \frac{4}{9} + 7 \cdot \frac{9}{9}$

Step 5.3

Combine $7$ and $\frac{9}{9}$ .

$5 y = \frac{4}{9} + \frac{7 \cdot 9}{9}$

Step 5.4

Combine the numerators over the common denominator.

$5 y = \frac{4 + 7 \cdot 9}{9}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $7$ by $9$ .

$5 y = \frac{4 + 63}{9}$

Step 5.5.2

Add $4$ and $63$ .

$5 y = \frac{67}{9}$

Step 6

Divide each term in $5 y = \frac{67}{9}$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 y = \frac{67}{9}$ by $5$ .

$\frac{5 y}{5} = \frac{\frac{67}{9}}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{\frac{67}{9}}{5}$

Step 6.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{67}{9}}{5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{67}{9} \cdot \frac{1}{5}$

Step 6.3.2

Multiply $\frac{67}{9} \cdot \frac{1}{5}$ .

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Step 6.3.2.1

Multiply $\frac{67}{9}$ by $\frac{1}{5}$ .

$y = \frac{67}{9 \cdot 5}$

Step 6.3.2.2

Multiply $9$ by $5$ .

$y = \frac{67}{45}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{67}{45}$

Decimal Form:

$y = 1.4\overline{8}$

Mixed Number Form:

$y = 1 \frac{22}{45}$