Basic Math Examples

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

Step 1

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

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Step 1.1

Add $\frac{1}{3}$ to both sides of the equation.

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

Step 1.2

To write $\frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 1.4

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{4}{7}$ by $\frac{3}{3}$ .

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

Step 1.4.2

Multiply $7$ by $3$ .

$4 y = \frac{4 \cdot 3}{21} + \frac{1}{3} \cdot \frac{7}{7}$

Step 1.4.3

Multiply $\frac{1}{3}$ by $\frac{7}{7}$ .

$4 y = \frac{4 \cdot 3}{21} + \frac{7}{3 \cdot 7}$

Step 1.4.4

Multiply $3$ by $7$ .

$4 y = \frac{4 \cdot 3}{21} + \frac{7}{21}$

Step 1.5

Combine the numerators over the common denominator.

$4 y = \frac{4 \cdot 3 + 7}{21}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $4$ by $3$ .

$4 y = \frac{12 + 7}{21}$

Step 1.6.2

Add $12$ and $7$ .

$4 y = \frac{19}{21}$

Step 2

Divide each term in $4 y = \frac{19}{21}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y = \frac{19}{21}$ by $4$ .

$\frac{4 y}{4} = \frac{\frac{19}{21}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{\frac{19}{21}}{4}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{19}{21}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{19}{21} \cdot \frac{1}{4}$

Step 2.3.2

Multiply $\frac{19}{21} \cdot \frac{1}{4}$ .

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Step 2.3.2.1

Multiply $\frac{19}{21}$ by $\frac{1}{4}$ .

$y = \frac{19}{21 \cdot 4}$

Step 2.3.2.2

Multiply $21$ by $4$ .

$y = \frac{19}{84}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{19}{84}$

Decimal Form:

$y = 0.22619047 \dots$