Basic Math Examples

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

Step 1

Simplify the right side.

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Step 1.1

Convert $7 \frac{1}{4}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.2

Add $7$ and $\frac{1}{4}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

Combine $7$ and $\frac{4}{4}$ .

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $7$ by $4$ .

$y - \frac{1}{3} = \frac{28 + 1}{4}$

Step 1.1.2.4.2

Add $28$ and $1$ .

$y - \frac{1}{3} = \frac{29}{4}$

Step 2

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

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Step 2.1

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

$y = \frac{29}{4} + \frac{1}{3}$

Step 2.2

To write $\frac{29}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{29}{4} \cdot \frac{3}{3} + \frac{1}{3}$

Step 2.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{29}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{29}{4}$ by $\frac{3}{3}$ .

$y = \frac{29 \cdot 3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4.2

Multiply $4$ by $3$ .

$y = \frac{29 \cdot 3}{12} + \frac{1}{3} \cdot \frac{4}{4}$

Step 2.4.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$y = \frac{29 \cdot 3}{12} + \frac{4}{3 \cdot 4}$

Step 2.4.4

Multiply $3$ by $4$ .

$y = \frac{29 \cdot 3}{12} + \frac{4}{12}$

Step 2.5

Combine the numerators over the common denominator.

$y = \frac{29 \cdot 3 + 4}{12}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $29$ by $3$ .

$y = \frac{87 + 4}{12}$

Step 2.6.2

Add $87$ and $4$ .

$y = \frac{91}{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = \frac{91}{12}$

Decimal Form:

$y = 7.58\overline{3}$

Mixed Number Form:

$y = 7 \frac{7}{12}$