Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $4$ and $1$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Write $1$ as a fraction with a common denominator.

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

Step 2.2.2

Combine the numerators over the common denominator.

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

Step 2.2.3

Add $4$ and $1$ .

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

Step 3

Simplify each term.

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Step 3.1

Rewrite the division as a fraction.

$\frac{\frac{3}{4}}{\frac{1}{3} \div 4 + \frac{5}{4}} + \frac{5}{4}$

Step 3.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

Combine the numerators over the common denominator.

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

Step 3.3.2

Rewrite $(\frac{1}{3} + 5) \div 4$ in a factored form.

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Step 3.3.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3.3.2.2

Combine $5$ and $\frac{3}{3}$ .

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

Step 3.3.2.3

Combine the numerators over the common denominator.

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

Step 3.3.2.4

Simplify the numerator.

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Step 3.3.2.4.1

Multiply $5$ by $3$ .

$\frac{3}{4} \cdot \frac{1}{\frac{1 + 15}{3} \div 4} + \frac{5}{4}$

Step 3.3.2.4.2

Add $1$ and $15$ .

$\frac{3}{4} \cdot \frac{1}{\frac{16}{3} \div 4} + \frac{5}{4}$

Step 3.3.3

Rewrite the division as a fraction.

$\frac{3}{4} \cdot \frac{1}{\frac{\frac{16}{3}}{4}} + \frac{5}{4}$

Step 3.3.4

Multiply the numerator by the reciprocal of the denominator.

$\frac{3}{4} \cdot \frac{1}{\frac{16}{3} \cdot \frac{1}{4}} + \frac{5}{4}$

Step 3.3.5

Cancel the common factor of $4$ .

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Step 3.3.5.1

Factor $4$ out of $16$ .

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

Step 3.3.5.2

Cancel the common factor.

$\frac{3}{4} \cdot \frac{1}{\frac{4 \cdot 4}{3} \cdot \frac{1}{4}} + \frac{5}{4}$

Step 3.3.5.3

Rewrite the expression.

$\frac{3}{4} \cdot \frac{1}{\frac{4}{3}} + \frac{5}{4}$

Step 3.4

Multiply the numerator by the reciprocal of the denominator.

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

Step 3.5

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

$\frac{3}{4} \cdot \frac{3}{4} + \frac{5}{4}$

Step 3.6

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

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Step 3.6.1

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

$\frac{3 \cdot 3}{4 \cdot 4} + \frac{5}{4}$

Step 3.6.2

Multiply $3$ by $3$ .

$\frac{9}{4 \cdot 4} + \frac{5}{4}$

Step 3.6.3

Multiply $4$ by $4$ .

$\frac{9}{16} + \frac{5}{4}$

Step 4

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

$\frac{9}{16} + \frac{5}{4} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

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

$\frac{9}{16} + \frac{5 \cdot 4}{4 \cdot 4}$

Step 5.2

Multiply $4$ by $4$ .

$\frac{9}{16} + \frac{5 \cdot 4}{16}$

Step 6

Combine the numerators over the common denominator.

$\frac{9 + 5 \cdot 4}{16}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $5$ by $4$ .

$\frac{9 + 20}{16}$

Step 7.2

Add $9$ and $20$ .

$\frac{29}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{16}$

Decimal Form:

$1.8125$

Mixed Number Form:

$1 \frac{13}{16}$