Basic Math Examples

$\frac{a}{3} + \frac{y}{6} = 1 - a$

Step 1

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

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Step 1.1

Add $a$ to both sides of the equation.

$\frac{a}{3} + \frac{y}{6} + a = 1$

Step 1.2

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

$\frac{y}{6} + \frac{a}{3} + a \cdot \frac{3}{3} = 1$

Step 1.3

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

$\frac{y}{6} + \frac{a}{3} + \frac{a \cdot 3}{3} = 1$

Step 1.4

Combine the numerators over the common denominator.

$\frac{y}{6} + \frac{a + a \cdot 3}{3} = 1$

Step 1.5

Add $a$ and $a \cdot 3$ .

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Step 1.5.1

Reorder $a$ and $3$ .

$\frac{y}{6} + \frac{a + 3 \cdot a}{3} = 1$

Step 1.5.2

Add $a$ and $3 \cdot a$ .

$\frac{y}{6} + \frac{4 a}{3} = 1$

Step 2

Subtract $\frac{y}{6}$ from both sides of the equation.

$\frac{4 a}{3} = 1 - \frac{y}{6}$

Step 3

Multiply both sides of the equation by $\frac{3}{4}$ .

$\frac{3}{4} \cdot \frac{4 a}{3} = \frac{3}{4} (1 - \frac{y}{6})$

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 $\frac{3}{4} \cdot \frac{4 a}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{4} \cdot \frac{4 a}{3} = \frac{3}{4} (1 - \frac{y}{6})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 a) = \frac{3}{4} (1 - \frac{y}{6})$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 a$ .

$\frac{1}{4} (4 (a)) = \frac{3}{4} (1 - \frac{y}{6})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 a) = \frac{3}{4} (1 - \frac{y}{6})$

Step 4.1.1.2.3

Rewrite the expression.

$a = \frac{3}{4} (1 - \frac{y}{6})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{4} (1 - \frac{y}{6})$ .

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Step 4.2.1.1

Apply the distributive property.

$a = \frac{3}{4} \cdot 1 + \frac{3}{4} (- \frac{y}{6})$

Step 4.2.1.2

Multiply $\frac{3}{4}$ by $1$ .

$a = \frac{3}{4} + \frac{3}{4} (- \frac{y}{6})$

Step 4.2.1.3

Cancel the common factor of $3$ .

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Step 4.2.1.3.1

Move the leading negative in $- \frac{y}{6}$ into the numerator.

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

Step 4.2.1.3.2

Factor $3$ out of $6$ .

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

Step 4.2.1.3.3

Cancel the common factor.

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

Step 4.2.1.3.4

Rewrite the expression.

$a = \frac{3}{4} + \frac{1}{4} \cdot \frac{- y}{2}$

Step 4.2.1.4

Multiply $\frac{1}{4}$ by $\frac{- y}{2}$ .

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

Step 4.2.1.5

Simplify the expression.

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Step 4.2.1.5.1

Multiply $4$ by $2$ .

$a = \frac{3}{4} + \frac{- y}{8}$

Step 4.2.1.5.2

Move the negative in front of the fraction.

$a = \frac{3}{4} - \frac{y}{8}$

Step 5

Reorder $\frac{3}{4}$ and $- \frac{y}{8}$ .

$a = - \frac{y}{8} + \frac{3}{4}$