What is 75\div (4 6/9+5/15) ?

The solution to 75\div (4 6/9+5/15) is 15

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75\div (4 6/9+5/15)

75 \div (4 \frac{6}{9} + \frac{5}{15})

15

Solution steps

75 \div (4 \frac{6}{9} + \frac{5}{15})

Convert mixed numbers to improper fractions:

4 \frac{6}{9} = \frac{42}{9}

4 \frac{6}{9}

Convert mixed numbers to improper fraction:

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

4 \frac{6}{9} = \frac{4 \cdot 9 + 6}{9}

= \frac{42}{9}

= 75 \div (\frac{42}{9} + \frac{5}{15})

\frac{42}{9} = \frac{14}{3}

Cancel the common factor:

3

\frac{14}{3}

= 75 \div (\frac{14}{3} + \frac{5}{15})

\frac{5}{15} = \frac{1}{3}

Cancel the common factor:

5

\frac{1}{3}

= 75 \div (\frac{14}{3} + \frac{1}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{14}{3} + \frac{1}{3}) : 5

\frac{14}{3} + \frac{1}{3}

\frac{14}{3} + \frac{1}{3} = 5

\frac{14}{3} + \frac{1}{3}

Apply rule

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

= \frac{14 + 1}{3}

Add the numbers:

14 + 1 = 15

= \frac{15}{3}

Divide the numbers:

\frac{15}{3} = 5

= 5

= 5

= 75 \div 5

Multiply and divide (left to right)

75 \div 5 : 15

75 \div 5

75 \div 5 = 15

= 15

= 15

- 6 - 2 - 2

3 (5)^{4}

12 + (- 5) \times [8 + (- 9)]

9 - 3 + 5

9 - 3 + 1