Basic Math Examples

$\frac{2}{3} y + \frac{1}{4} = \frac{1}{3} y + \frac{7}{5}$

Step 1

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

$\frac{2 y}{3} + \frac{1}{4} = \frac{1}{3} y + \frac{7}{5}$

Step 2

Combine $\frac{1}{3}$ and $y$ .

$\frac{2 y}{3} + \frac{1}{4} = \frac{y}{3} + \frac{7}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{y}{3}$ from both sides of the equation.

$\frac{2 y}{3} + \frac{1}{4} - \frac{y}{3} = \frac{7}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 y - y}{3} + \frac{1}{4} = \frac{7}{5}$

Step 3.3

Subtract $y$ from $2 y$ .

$\frac{y}{3} + \frac{1}{4} = \frac{7}{5}$

Step 4

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

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Step 4.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$\frac{y}{3} = \frac{7}{5} - \frac{1}{4}$

Step 4.2

To write $\frac{7}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{y}{3} = \frac{7}{5} \cdot \frac{4}{4} - \frac{1}{4}$

Step 4.3

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{3} = \frac{7}{5} \cdot \frac{4}{4} - \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.4.1

Multiply $\frac{7}{5}$ by $\frac{4}{4}$ .

$\frac{y}{3} = \frac{7 \cdot 4}{5 \cdot 4} - \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4.2

Multiply $5$ by $4$ .

$\frac{y}{3} = \frac{7 \cdot 4}{20} - \frac{1}{4} \cdot \frac{5}{5}$

Step 4.4.3

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{y}{3} = \frac{7 \cdot 4}{20} - \frac{5}{4 \cdot 5}$

Step 4.4.4

Multiply $4$ by $5$ .

$\frac{y}{3} = \frac{7 \cdot 4}{20} - \frac{5}{20}$

Step 4.5

Combine the numerators over the common denominator.

$\frac{y}{3} = \frac{7 \cdot 4 - 5}{20}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

Multiply $7$ by $4$ .

$\frac{y}{3} = \frac{28 - 5}{20}$

Step 4.6.2

Subtract $5$ from $28$ .

$\frac{y}{3} = \frac{23}{20}$

Step 5

Multiply both sides of the equation by $3$ .

$3 \frac{y}{3} = 3 (\frac{23}{20})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1

Cancel the common factor.

$3 \frac{y}{3} = 3 (\frac{23}{20})$

Step 6.1.1.2

Rewrite the expression.

$y = 3 (\frac{23}{20})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $3 (\frac{23}{20})$ .

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Step 6.2.1.1

Combine $3$ and $\frac{23}{20}$ .

$y = \frac{3 \cdot 23}{20}$

Step 6.2.1.2

Multiply $3$ by $23$ .

$y = \frac{69}{20}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = \frac{69}{20}$

Decimal Form:

$y = 3.45$

Mixed Number Form:

$y = 3 \frac{9}{20}$