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

The solution to (2-1/2)\div (4+1/3) is 9/26

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

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

\frac{9}{26}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(2 - \frac{1}{2}) : \frac{3}{2}

2 - \frac{1}{2}

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

2 - \frac{1}{2}

Convert element to fraction:

2 = \frac{2 \cdot 2}{2}

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 2 - 1 = 3

2 \cdot 2 - 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 - 1

Subtract the numbers:

4 - 1 = 3

= 3

= \frac{3}{2}

= \frac{3}{2}

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

Calculate within parentheses

(4 + \frac{1}{3}) : \frac{13}{3}

4 + \frac{1}{3}

4 + \frac{1}{3} = \frac{13}{3}

4 + \frac{1}{3}

Convert element to fraction:

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

= \frac{4 \cdot 3}{3} + \frac{1}{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 + 1}{3}

4 \cdot 3 + 1 = 13

4 \cdot 3 + 1

Multiply the numbers:

4 \cdot 3 = 12

= 12 + 1

Add the numbers:

12 + 1 = 13

= 13

= \frac{13}{3}

= \frac{13}{3}

= \frac{3}{2} \div \frac{13}{3}

Multiply and divide (left to right)

\frac{3}{2} \div \frac{13}{3} : \frac{9}{26}

\frac{3}{2} \div \frac{13}{3}

Apply the fraction rule:

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

= \frac{3}{2} \cdot \frac{3}{13}

Multiply fractions:

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

= \frac{3 \cdot 3}{2 \cdot 13}

Multiply the numbers:

3 \cdot 3 = 9

= \frac{9}{2 \cdot 13}

Multiply the numbers:

2 \cdot 13 = 26

= \frac{9}{26}

= \frac{9}{26}

15 \times 37 + 15 \times 63

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

- ((- 8 \div 2) + (4 \times (- 24)) \div (- 3 + (- 1)))

[4 \div 7 (6 + 40) - 5 \div 4 (7 - 9 + 54)] \times 5

(- 2) + (- 3) + (- 20) + (30)