Basic Math Examples

$1 \frac{3}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div 1 \frac{1}{5} \cdot \frac{1}{2}$

Step 1

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 1.1

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

$(1 + \frac{3}{4}) \cdot (\frac{4}{9} + \frac{2}{3}) \div 1 \frac{1}{5} \cdot \frac{1}{2}$

Step 1.2

Add $1$ and $\frac{3}{4}$ .

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Step 1.2.1

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

$(\frac{4}{4} + \frac{3}{4}) \cdot (\frac{4}{9} + \frac{2}{3}) \div 1 \frac{1}{5} \cdot \frac{1}{2}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{4 + 3}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div 1 \frac{1}{5} \cdot \frac{1}{2}$

Step 1.2.3

Add $4$ and $3$ .

$\frac{7}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div 1 \frac{1}{5} \cdot \frac{1}{2}$

Step 2

Convert $1 \frac{1}{5}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div (1 + \frac{1}{5}) \cdot \frac{1}{2}$

Step 2.2

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

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Step 2.2.1

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

$\frac{7}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div (\frac{5}{5} + \frac{1}{5}) \cdot \frac{1}{2}$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{7}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div \frac{5 + 1}{5} \cdot \frac{1}{2}$

Step 2.2.3

Add $5$ and $1$ .

$\frac{7}{4} \cdot (\frac{4}{9} + \frac{2}{3}) \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3

Simplify the numerator.

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Step 3.1

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{4} (\frac{4}{9} + \frac{2}{3} \cdot \frac{3}{3}) \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3.2

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1

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

$\frac{7}{4} (\frac{4}{9} + \frac{2 \cdot 3}{3 \cdot 3}) \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{7}{4} (\frac{4}{9} + \frac{2 \cdot 3}{9}) \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{7}{4} \cdot \frac{4 + 2 \cdot 3}{9} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3.4

Simplify the numerator.

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Step 3.4.1

Multiply $2$ by $3$ .

$\frac{7}{4} \cdot \frac{4 + 6}{9} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 3.4.2

Add $4$ and $6$ .

$\frac{7}{4} \cdot \frac{10}{9} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4

Simplify terms.

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Step 4.1

Multiply $\frac{7}{4}$ by $\frac{10}{9}$ .

$\frac{7 \cdot 10}{4 \cdot 9} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.2

Multiply.

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Step 4.2.1

Multiply $7$ by $10$ .

$\frac{70}{4 \cdot 9} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.2.2

Multiply $4$ by $9$ .

$\frac{70}{36} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.3

Cancel the common factor of $70$ and $36$ .

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Step 4.3.1

Factor $2$ out of $70$ .

$\frac{2 (35)}{36} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $36$ .

$\frac{2 \cdot 35}{2 \cdot 18} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 35}{2 \cdot 18} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 4.3.2.3

Rewrite the expression.

$\frac{35}{18} \div \frac{6}{5} \cdot \frac{1}{2}$

Step 5

To divide by a fraction, multiply by its reciprocal.

$\frac{35}{18} \cdot \frac{5}{6} \cdot \frac{1}{2}$

Step 6

Multiply $\frac{35}{18} \cdot \frac{5}{6}$ .

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Step 6.1

Multiply $\frac{35}{18}$ by $\frac{5}{6}$ .

$\frac{35 \cdot 5}{18 \cdot 6} \cdot \frac{1}{2}$

Step 6.2

Multiply $35$ by $5$ .

$\frac{175}{18 \cdot 6} \cdot \frac{1}{2}$

Step 6.3

Multiply $18$ by $6$ .

$\frac{175}{108} \cdot \frac{1}{2}$

Step 7

Multiply $\frac{175}{108} \cdot \frac{1}{2}$ .

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Step 7.1

Multiply $\frac{175}{108}$ by $\frac{1}{2}$ .

$\frac{175}{108 \cdot 2}$

Step 7.2

Multiply $108$ by $2$ .

$\frac{175}{216}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{175}{216}$

Decimal Form:

$0.810\overline{185}$