Basic Math Examples

$4 y - \frac{8}{12} - 3 y = \frac{1}{12} + \frac{6}{12}$

Step 1

Simplify $4 y - \frac{8}{12} - 3 y$ .

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Step 1.1

Cancel the common factor of $8$ and $12$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$4 y - \frac{4 (2)}{12} - 3 y = \frac{1}{12} + \frac{6}{12}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $12$ .

$4 y - \frac{4 \cdot 2}{4 \cdot 3} - 3 y = \frac{1}{12} + \frac{6}{12}$

Step 1.1.2.2

Cancel the common factor.

$4 y - \frac{4 \cdot 2}{4 \cdot 3} - 3 y = \frac{1}{12} + \frac{6}{12}$

Step 1.1.2.3

Rewrite the expression.

$4 y - \frac{2}{3} - 3 y = \frac{1}{12} + \frac{6}{12}$

Step 1.2

Subtract $3 y$ from $4 y$ .

$y - \frac{2}{3} = \frac{1}{12} + \frac{6}{12}$

Step 2

Simplify $\frac{1}{12} + \frac{6}{12}$ .

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Step 2.1

Combine the numerators over the common denominator.

$y - \frac{2}{3} = \frac{1 + 6}{12}$

Step 2.2

Add $1$ and $6$ .

$y - \frac{2}{3} = \frac{7}{12}$

Step 3

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

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Step 3.1

Add $\frac{2}{3}$ to both sides of the equation.

$y = \frac{7}{12} + \frac{2}{3}$

Step 3.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{7}{12} + \frac{2}{3} \cdot \frac{4}{4}$

Step 3.3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$y = \frac{7}{12} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.3.2

Multiply $3$ by $4$ .

$y = \frac{7}{12} + \frac{2 \cdot 4}{12}$

Step 3.4

Combine the numerators over the common denominator.

$y = \frac{7 + 2 \cdot 4}{12}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $4$ .

$y = \frac{7 + 8}{12}$

Step 3.5.2

Add $7$ and $8$ .

$y = \frac{15}{12}$

Step 3.6

Cancel the common factor of $15$ and $12$ .

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Step 3.6.1

Factor $3$ out of $15$ .

$y = \frac{3 (5)}{12}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $3$ out of $12$ .

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

Step 3.6.2.2

Cancel the common factor.

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

Step 3.6.2.3

Rewrite the expression.

$y = \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{4}$

Decimal Form:

$y = 1.25$

Mixed Number Form:

$y = 1 \frac{1}{4}$