Basic Math Examples

$\frac{2 y + 1}{14} + \frac{3}{2} = \frac{24}{7}$

Step 1

Simplify $\frac{2 y + 1}{14} + \frac{3}{2}$ .

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Step 1.1

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{2 y + 1}{14} + \frac{3}{2} \cdot \frac{7}{7} = \frac{24}{7}$

Step 1.2

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{3}{2}$ by $\frac{7}{7}$ .

$\frac{2 y + 1}{14} + \frac{3 \cdot 7}{2 \cdot 7} = \frac{24}{7}$

Step 1.2.2

Multiply $2$ by $7$ .

$\frac{2 y + 1}{14} + \frac{3 \cdot 7}{14} = \frac{24}{7}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{2 y + 1 + 3 \cdot 7}{14} = \frac{24}{7}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $3$ by $7$ .

$\frac{2 y + 1 + 21}{14} = \frac{24}{7}$

Step 1.4.2

Add $1$ and $21$ .

$\frac{2 y + 22}{14} = \frac{24}{7}$

Step 1.4.3

Factor $2$ out of $2 y + 22$ .

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Step 1.4.3.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) + 22}{14} = \frac{24}{7}$

Step 1.4.3.2

Factor $2$ out of $22$ .

$\frac{2 y + 2 \cdot 11}{14} = \frac{24}{7}$

Step 1.4.3.3

Factor $2$ out of $2 y + 2 \cdot 11$ .

$\frac{2 (y + 11)}{14} = \frac{24}{7}$

Step 1.5

Cancel the common factors.

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Step 1.5.1

Factor $2$ out of $14$ .

$\frac{2 (y + 11)}{2 \cdot 7} = \frac{24}{7}$

Step 1.5.2

Cancel the common factor.

$\frac{2 (y + 11)}{2 \cdot 7} = \frac{24}{7}$

Step 1.5.3

Rewrite the expression.

$\frac{y + 11}{7} = \frac{24}{7}$

Step 2

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

$y + 11 = 24$

Step 3

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

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Step 3.1

Subtract $11$ from both sides of the equation.

$y = 24 - 11$

Step 3.2

Subtract $11$ from $24$ .

$y = 13$