Finite Math Examples

$\frac{7}{10} y = \frac{1}{10} y + \frac{4}{5}$

Step 1

Simplify $\frac{7}{10} y$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{7}{10} y = \frac{1}{10} y + \frac{4}{5}$

Step 1.2

Simplify by adding zeros.

$\frac{7}{10} y = \frac{1}{10} y + \frac{4}{5}$

Step 1.3

Combine $\frac{7}{10}$ and $y$ .

$\frac{7 y}{10} = \frac{1}{10} y + \frac{4}{5}$

Step 2

Combine $\frac{1}{10}$ and $y$ .

$\frac{7 y}{10} = \frac{y}{10} + \frac{4}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{y}{10}$ from both sides of the equation.

$\frac{7 y}{10} - \frac{y}{10} = \frac{4}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{7 y - y}{10} = \frac{4}{5}$

Step 3.3

Subtract $y$ from $7 y$ .

$\frac{6 y}{10} = \frac{4}{5}$

Step 3.4

Cancel the common factor of $6$ and $10$ .

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Step 3.4.1

Factor $2$ out of $6 y$ .

$\frac{2 (3 y)}{10} = \frac{4}{5}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $2$ out of $10$ .

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

Step 3.4.2.2

Cancel the common factor.

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

Step 3.4.2.3

Rewrite the expression.

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

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 y = 4$

Step 5

Divide each term in $3 y = 4$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 y = 4$ by $3$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $y$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 1.\overline{3}$

Mixed Number Form:

$y = 1 \frac{1}{3}$