Basic Math Examples

$3 \frac{1}{3} \div 4 \frac{1}{4} = t \div 5 \frac{1}{5}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $3 \frac{1}{3} \div 4 \frac{1}{4}$ .

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Step 1.1.1

Convert $3 \frac{1}{3}$ 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.

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

Step 1.1.1.2

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

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Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

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

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

Step 1.1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $3$ by $3$ .

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

Step 1.1.1.2.4.2

Add $9$ and $1$ .

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

Step 1.1.2

Convert $4 \frac{1}{4}$ 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.

$\frac{10}{3} \div (4 + \frac{1}{4}) = t \div 5 \frac{1}{5}$

Step 1.1.2.2

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

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Step 1.1.2.2.1

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

$\frac{10}{3} \div (4 \cdot \frac{4}{4} + \frac{1}{4}) = t \div 5 \frac{1}{5}$

Step 1.1.2.2.2

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

$\frac{10}{3} \div (\frac{4 \cdot 4}{4} + \frac{1}{4}) = t \div 5 \frac{1}{5}$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{10}{3} \div \frac{4 \cdot 4 + 1}{4} = t \div 5 \frac{1}{5}$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $4$ by $4$ .

$\frac{10}{3} \div \frac{16 + 1}{4} = t \div 5 \frac{1}{5}$

Step 1.1.2.2.4.2

Add $16$ and $1$ .

$\frac{10}{3} \div \frac{17}{4} = t \div 5 \frac{1}{5}$

Step 1.1.3

To divide by a fraction, multiply by its reciprocal.

$\frac{10}{3} \cdot \frac{4}{17} = t \div 5 \frac{1}{5}$

Step 1.1.4

Multiply $\frac{10}{3} \cdot \frac{4}{17}$ .

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Step 1.1.4.1

Multiply $\frac{10}{3}$ by $\frac{4}{17}$ .

$\frac{10 \cdot 4}{3 \cdot 17} = t \div 5 \frac{1}{5}$

Step 1.1.4.2

Multiply $10$ by $4$ .

$\frac{40}{3 \cdot 17} = t \div 5 \frac{1}{5}$

Step 1.1.4.3

Multiply $3$ by $17$ .

$\frac{40}{51} = t \div 5 \frac{1}{5}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $t \div 5 \frac{1}{5}$ .

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Step 2.1.1

Convert $5 \frac{1}{5}$ 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.

$\frac{40}{51} = t \div (5 + \frac{1}{5})$

Step 2.1.1.2

Add $5$ and $\frac{1}{5}$ .

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Step 2.1.1.2.1

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

$\frac{40}{51} = t \div (5 \cdot \frac{5}{5} + \frac{1}{5})$

Step 2.1.1.2.2

Combine $5$ and $\frac{5}{5}$ .

$\frac{40}{51} = t \div (\frac{5 \cdot 5}{5} + \frac{1}{5})$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{40}{51} = t \div \frac{5 \cdot 5 + 1}{5}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $5$ by $5$ .

$\frac{40}{51} = t \div \frac{25 + 1}{5}$

Step 2.1.1.2.4.2

Add $25$ and $1$ .

$\frac{40}{51} = t \div \frac{26}{5}$

Step 2.1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{40}{51} = t \frac{5}{26}$

Step 2.1.3

Combine $t$ and $\frac{5}{26}$ .

$\frac{40}{51} = \frac{t \cdot 5}{26}$

Step 2.1.4

Move $5$ to the left of $t$ .

$\frac{40}{51} = \frac{5 t}{26}$

Step 3

Rewrite the equation as $\frac{5 t}{26} = \frac{40}{51}$ .

$\frac{5 t}{26} = \frac{40}{51}$

Step 4

Multiply both sides of the equation by $\frac{26}{5}$ .

$\frac{26}{5} \cdot \frac{5 t}{26} = \frac{26}{5} \cdot \frac{40}{51}$

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 $\frac{26}{5} \cdot \frac{5 t}{26}$ .

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Step 5.1.1.1

Cancel the common factor of $26$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{26}{5} \cdot \frac{5 t}{26} = \frac{26}{5} \cdot \frac{40}{51}$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 t) = \frac{26}{5} \cdot \frac{40}{51}$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 t$ .

$\frac{1}{5} (5 (t)) = \frac{26}{5} \cdot \frac{40}{51}$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 t) = \frac{26}{5} \cdot \frac{40}{51}$

Step 5.1.1.2.3

Rewrite the expression.

$t = \frac{26}{5} \cdot \frac{40}{51}$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{26}{5} \cdot \frac{40}{51}$ .

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Step 5.2.1.1

Cancel the common factor of $5$ .

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Step 5.2.1.1.1

Factor $5$ out of $40$ .

$t = \frac{26}{5} \cdot \frac{5 (8)}{51}$

Step 5.2.1.1.2

Cancel the common factor.

$t = \frac{26}{5} \cdot \frac{5 \cdot 8}{51}$

Step 5.2.1.1.3

Rewrite the expression.

$t = 26 (\frac{8}{51})$

Step 5.2.1.2

Combine $26$ and $\frac{8}{51}$ .

$t = \frac{26 \cdot 8}{51}$

Step 5.2.1.3

Multiply $26$ by $8$ .

$t = \frac{208}{51}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$t = \frac{208}{51}$

Decimal Form:

$t = 4.07843137 \dots$

Mixed Number Form:

$t = 4 \frac{4}{51}$