What is 7+5\div 1/2-17\div (3+8/3) ?

The solution to 7+5\div 1/2-17\div (3+8/3) is 14

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7+5\div 1/2-17\div (3+8/3)

7 + 5 \div \frac{1}{2} - 17 \div (3 + \frac{8}{3})

14

Solution steps

7 + 5 \div \frac{1}{2} - 17 \div (3 + \frac{8}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(3 + \frac{8}{3}) : \frac{17}{3}

3 + \frac{8}{3}

3 + \frac{8}{3} = \frac{17}{3}

3 + \frac{8}{3}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 3 + 8 = 17

3 \cdot 3 + 8

Multiply the numbers:

3 \cdot 3 = 9

= 9 + 8

Add the numbers:

9 + 8 = 17

= 17

= \frac{17}{3}

= \frac{17}{3}

= 7 + 5 \div \frac{1}{2} - 17 \div \frac{17}{3}

Multiply and divide (left to right)

5 \div \frac{1}{2} : 10

5 \div \frac{1}{2}

Convert element to fraction:

5 = \frac{5}{1}

= \frac{5}{1} \div \frac{1}{2}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{5}{1} \cdot \frac{2}{1}

Apply rule

\frac{a}{1} = a

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

= 7 + 10 - 17 \div \frac{17}{3}

Multiply and divide (left to right)

17 \div \frac{17}{3} : 3

17 \div \frac{17}{3}

Convert element to fraction:

17 = \frac{17}{1}

= \frac{17}{1} \div \frac{17}{3}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{17}{1} \cdot \frac{3}{17}

Cross-cancel:

17

= \frac{3}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 3

= 7 + 10 - 3

Add and subtract (left to right)

7 + 10 - 3 : 14

7 + 10 - 3

7 + 10 = 17

= 17 - 3

17 - 3 = 14

= 14

= 14

- 2 (1)^{2} + 4

- 2 (1)^{2} - 2

(2 \times 7 - 4^{2}) - 10

9 (30)^{2} - 4 (30) + 12

- 1^{2} - 5 (- 1) - 4

What is 7+5\div 1/2-17\div (3+8/3) ?
The solution to 7+5\div 1/2-17\div (3+8/3) is 14