Algebra Examples

$\frac{2}{3} y + \frac{3}{8} y = 5$

Step 1

Simplify $\frac{2}{3} y + \frac{3}{8} y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{2 y}{3} + \frac{3}{8} y = 5$

Step 1.1.2

Combine $\frac{3}{8}$ and $y$ .

$\frac{2 y}{3} + \frac{3 y}{8} = 5$

Step 1.2

To write $\frac{2 y}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{2 y}{3} \cdot \frac{8}{8} + \frac{3 y}{8} = 5$

Step 1.3

To write $\frac{3 y}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 y}{3} \cdot \frac{8}{8} + \frac{3 y}{8} \cdot \frac{3}{3} = 5$

Step 1.4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2 y}{3}$ by $\frac{8}{8}$ .

$\frac{2 y \cdot 8}{3 \cdot 8} + \frac{3 y}{8} \cdot \frac{3}{3} = 5$

Step 1.4.2

Multiply $3$ by $8$ .

$\frac{2 y \cdot 8}{24} + \frac{3 y}{8} \cdot \frac{3}{3} = 5$

Step 1.4.3

Multiply $\frac{3 y}{8}$ by $\frac{3}{3}$ .

$\frac{2 y \cdot 8}{24} + \frac{3 y \cdot 3}{8 \cdot 3} = 5$

Step 1.4.4

Multiply $8$ by $3$ .

$\frac{2 y \cdot 8}{24} + \frac{3 y \cdot 3}{24} = 5$

Step 1.5

Combine the numerators over the common denominator.

$\frac{2 y \cdot 8 + 3 y \cdot 3}{24} = 5$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $y$ out of $2 y \cdot 8 + 3 y \cdot 3$ .

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Step 1.6.1.1

Factor $y$ out of $2 y \cdot 8$ .

$\frac{y (2 \cdot 8) + 3 y \cdot 3}{24} = 5$

Step 1.6.1.2

Factor $y$ out of $3 y \cdot 3$ .

$\frac{y (2 \cdot 8) + y (3 \cdot 3)}{24} = 5$

Step 1.6.1.3

Factor $y$ out of $y (2 \cdot 8) + y (3 \cdot 3)$ .

$\frac{y (2 \cdot 8 + 3 \cdot 3)}{24} = 5$

Step 1.6.2

Multiply $2$ by $8$ .

$\frac{y (16 + 3 \cdot 3)}{24} = 5$

Step 1.6.3

Multiply $3$ by $3$ .

$\frac{y (16 + 9)}{24} = 5$

Step 1.6.4

Add $16$ and $9$ .

$\frac{y \cdot 25}{24} = 5$

Step 1.7

Move $25$ to the left of $y$ .

$\frac{25 y}{24} = 5$

Step 2

Multiply both sides of the equation by $\frac{24}{25}$ .

$\frac{24}{25} \cdot \frac{25 y}{24} = \frac{24}{25} \cdot 5$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{24}{25} \cdot \frac{25 y}{24}$ .

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Step 3.1.1.1

Cancel the common factor of $24$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{24}{25} \cdot \frac{25 y}{24} = \frac{24}{25} \cdot 5$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{25} (25 y) = \frac{24}{25} \cdot 5$

Step 3.1.1.2

Cancel the common factor of $25$ .

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Step 3.1.1.2.1

Factor $25$ out of $25 y$ .

$\frac{1}{25} (25 (y)) = \frac{24}{25} \cdot 5$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{25} (25 y) = \frac{24}{25} \cdot 5$

Step 3.1.1.2.3

Rewrite the expression.

$y = \frac{24}{25} \cdot 5$

Step 3.2

Simplify the right side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Factor $5$ out of $25$ .

$y = \frac{24}{5 (5)} \cdot 5$

Step 3.2.1.2

Cancel the common factor.

$y = \frac{24}{5 \cdot 5} \cdot 5$

Step 3.2.1.3

Rewrite the expression.

$y = \frac{24}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{24}{5}$

Decimal Form:

$y = 4.8$

Mixed Number Form:

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