Basic Math Examples

$2 \frac{1}{2} \div 3 \frac{1}{3} = y \div 4 \frac{1}{4}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{1}{2} \div 3 \frac{1}{3}$ .

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Step 1.1.1

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

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

$(2 + \frac{1}{2}) \div 3 \frac{1}{3} = y \div 4 \frac{1}{4}$

Step 1.1.1.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

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

$(2 \cdot \frac{2}{2} + \frac{1}{2}) \div 3 \frac{1}{3} = y \div 4 \frac{1}{4}$

Step 1.1.1.2.2

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

$(\frac{2 \cdot 2}{2} + \frac{1}{2}) \div 3 \frac{1}{3} = y \div 4 \frac{1}{4}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 + 1}{2} \div 3 \frac{1}{3} = y \div 4 \frac{1}{4}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $2$ .

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

Step 1.1.1.2.4.2

Add $4$ and $1$ .

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

Step 1.1.2

Convert $3 \frac{1}{3}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{5}{2} \div (3 + \frac{1}{3}) = y \div 4 \frac{1}{4}$

Step 1.1.2.2

Add $3$ and $\frac{1}{3}$ .

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Step 1.1.2.2.1

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

$\frac{5}{2} \div (3 \cdot \frac{3}{3} + \frac{1}{3}) = y \div 4 \frac{1}{4}$

Step 1.1.2.2.2

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

$\frac{5}{2} \div (\frac{3 \cdot 3}{3} + \frac{1}{3}) = y \div 4 \frac{1}{4}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $3$ by $3$ .

$\frac{5}{2} \div \frac{9 + 1}{3} = y \div 4 \frac{1}{4}$

Step 1.1.2.2.4.2

Add $9$ and $1$ .

$\frac{5}{2} \div \frac{10}{3} = y \div 4 \frac{1}{4}$

Step 1.1.3

To divide by a fraction, multiply by its reciprocal.

$\frac{5}{2} \cdot \frac{3}{10} = y \div 4 \frac{1}{4}$

Step 1.1.4

Cancel the common factor of $5$ .

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Step 1.1.4.1

Factor $5$ out of $10$ .

$\frac{5}{2} \cdot \frac{3}{5 (2)} = y \div 4 \frac{1}{4}$

Step 1.1.4.2

Cancel the common factor.

$\frac{5}{2} \cdot \frac{3}{5 \cdot 2} = y \div 4 \frac{1}{4}$

Step 1.1.4.3

Rewrite the expression.

$\frac{1}{2} \cdot \frac{3}{2} = y \div 4 \frac{1}{4}$

Step 1.1.5

Multiply $\frac{1}{2}$ by $\frac{3}{2}$ .

$\frac{3}{2 \cdot 2} = y \div 4 \frac{1}{4}$

Step 1.1.6

Multiply $2$ by $2$ .

$\frac{3}{4} = y \div 4 \frac{1}{4}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $y \div 4 \frac{1}{4}$ .

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Step 2.1.1

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

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Step 2.1.1.1

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

$\frac{3}{4} = y \div (4 + \frac{1}{4})$

Step 2.1.1.2

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

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Step 2.1.1.2.1

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

$\frac{3}{4} = y \div (4 \cdot \frac{4}{4} + \frac{1}{4})$

Step 2.1.1.2.2

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

$\frac{3}{4} = y \div (\frac{4 \cdot 4}{4} + \frac{1}{4})$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

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

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $4$ by $4$ .

$\frac{3}{4} = y \div \frac{16 + 1}{4}$

Step 2.1.1.2.4.2

Add $16$ and $1$ .

$\frac{3}{4} = y \div \frac{17}{4}$

Step 2.1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{4} = y \frac{4}{17}$

Step 2.1.3

Combine $y$ and $\frac{4}{17}$ .

$\frac{3}{4} = \frac{y \cdot 4}{17}$

Step 2.1.4

Move $4$ to the left of $y$ .

$\frac{3}{4} = \frac{4 y}{17}$

Step 3

Rewrite the equation as $\frac{4 y}{17} = \frac{3}{4}$ .

$\frac{4 y}{17} = \frac{3}{4}$

Step 4

Multiply both sides of the equation by $\frac{17}{4}$ .

$\frac{17}{4} \cdot \frac{4 y}{17} = \frac{17}{4} \cdot \frac{3}{4}$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $\frac{17}{4} \cdot \frac{4 y}{17}$ .

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Step 5.1.1.1

Cancel the common factor of $17$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{17}{4} \cdot \frac{4 y}{17} = \frac{17}{4} \cdot \frac{3}{4}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{17}{4} \cdot \frac{3}{4}$

Step 5.1.1.2

Cancel the common factor of $4$ .

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Step 5.1.1.2.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{17}{4} \cdot \frac{3}{4}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{17}{4} \cdot \frac{3}{4}$

Step 5.1.1.2.3

Rewrite the expression.

$y = \frac{17}{4} \cdot \frac{3}{4}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $\frac{17}{4} \cdot \frac{3}{4}$ .

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Step 5.2.1.1

Multiply $\frac{17}{4}$ by $\frac{3}{4}$ .

$y = \frac{17 \cdot 3}{4 \cdot 4}$

Step 5.2.1.2

Multiply $17$ by $3$ .

$y = \frac{51}{4 \cdot 4}$

Step 5.2.1.3

Multiply $4$ by $4$ .

$y = \frac{51}{16}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{51}{16}$

Decimal Form:

$y = 3.1875$

Mixed Number Form:

$y = 3 \frac{3}{16}$