What is (1 1/9)\div (4-2 1/3) ?

The solution to (1 1/9)\div (4-2 1/3) is 2/3

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(1 1/9)\div (4-2 1/3)

(1 \frac{1}{9}) \div (4 - 2 \frac{1}{3})

\frac{2}{3}

Solution steps

(1 \frac{1}{9}) \div (4 - 2 \frac{1}{3})

Convert mixed numbers to improper fractions:

1 \frac{1}{9} = \frac{10}{9}

1 \frac{1}{9}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{1}{9} = \frac{1 \cdot 9 + 1}{9}

= \frac{10}{9}

= (\frac{10}{9}) \div (4 - 2 \frac{1}{3})

Convert mixed numbers to improper fractions:

2 \frac{1}{3} = \frac{7}{3}

2 \frac{1}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

2 \frac{1}{3} = \frac{2 \cdot 3 + 1}{3}

= \frac{7}{3}

= (\frac{10}{9}) \div (4 - \frac{7}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(4 - \frac{7}{3}) : \frac{5}{3}

4 - \frac{7}{3}

4 - \frac{7}{3} = \frac{5}{3}

4 - \frac{7}{3}

Convert element to fraction:

4 = \frac{4 \cdot 3}{3}

= \frac{4 \cdot 3}{3} - \frac{7}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{4 \cdot 3 - 7}{3}

4 \cdot 3 - 7 = 5

4 \cdot 3 - 7

Multiply the numbers:

4 \cdot 3 = 12

= 12 - 7

Subtract the numbers:

12 - 7 = 5

= 5

= \frac{5}{3}

= \frac{5}{3}

= (\frac{10}{9}) \div \frac{5}{3}

Multiply and divide (left to right)

(\frac{10}{9}) \div \frac{5}{3} : \frac{( \frac{10}{9} )}{\frac{5}{3}}

(\frac{10}{9}) \div \frac{5}{3}

(\frac{10}{9}) \div \frac{5}{3} = \frac{( \frac{10}{9} )}{\frac{5}{3}}

= \frac{( \frac{10}{9} )}{\frac{5}{3}}

= \frac{( \frac{10}{9} )}{\frac{5}{3}}

Simplify

\frac{( \frac{10}{9} )}{\frac{5}{3}} : \frac{2}{3}

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= \frac{10 \cdot 3}{9 \cdot 5}

Multiply the numbers:

9 \cdot 5 = 45

= \frac{10 \cdot 3}{45}

Multiply the numbers:

10 \cdot 3 = 30

= \frac{30}{45}

Cancel the common factor:

15

= \frac{2}{3}

5^{2} + 4

- 8 - (- 11) + 17

(2)^{2} - 3

16 - 3 (8 - 3)^{2} \div 5

(- 2)^{2} - 2 (- 2)