What is 4\div (5 1/3+2 2/3) ?

The solution to 4\div (5 1/3+2 2/3) is 1/2

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4\div (5 1/3+2 2/3)

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

\frac{1}{2}

Solution steps

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

Convert mixed numbers to improper fractions:

5 \frac{1}{3} = \frac{16}{3}

5 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

5 \frac{1}{3} = \frac{5 \cdot 3 + 1}{3}

= \frac{16}{3}

= 4 \div (\frac{16}{3} + 2 \frac{2}{3})

Convert mixed numbers to improper fractions:

2 \frac{2}{3} = \frac{8}{3}

2 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{8}{3}

= 4 \div (\frac{16}{3} + \frac{8}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{16}{3} + \frac{8}{3}) : 8

\frac{16}{3} + \frac{8}{3}

\frac{16}{3} + \frac{8}{3} = 8

\frac{16}{3} + \frac{8}{3}

Apply rule

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

= \frac{16 + 8}{3}

Add the numbers:

16 + 8 = 24

= \frac{24}{3}

Divide the numbers:

\frac{24}{3} = 8

= 8

= 8

= 4 \div 8

Multiply and divide (left to right)

4 \div 8 : \frac{4}{8}

4 \div 8

4 \div 8 = \frac{4}{8}

= \frac{4}{8}

= \frac{4}{8}

Cancel the common factor:

4

= \frac{1}{2}

(- 3)^{2} + 3 (- 3)

18 + 7 \times 9 + 5

3^{1} + 5^{2}

- 5^{2} + 5

8 \div 4 \div 5 \div 2