What is (6-3/5)\div 5 1/2 ?

The solution to (6-3/5)\div 5 1/2 is 54/55

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(6-3/5)\div 5 1/2

(6 - \frac{3}{5}) \div 5 \frac{1}{2}

\frac{54}{55}

Solution steps

(6 - \frac{3}{5}) \div 5 \frac{1}{2}

Convert mixed numbers to improper fractions:

5 \frac{1}{2} = \frac{11}{2}

5 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

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

= \frac{11}{2}

= (6 - \frac{3}{5}) \div \frac{11}{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(6 - \frac{3}{5}) : \frac{27}{5}

6 - \frac{3}{5}

6 - \frac{3}{5} = \frac{27}{5}

6 - \frac{3}{5}

Convert element to fraction:

6 = \frac{6 \cdot 5}{5}

= \frac{6 \cdot 5}{5} - \frac{3}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 5 - 3}{5}

6 \cdot 5 - 3 = 27

6 \cdot 5 - 3

Multiply the numbers:

6 \cdot 5 = 30

= 30 - 3

Subtract the numbers:

30 - 3 = 27

= 27

= \frac{27}{5}

= \frac{27}{5}

= \frac{27}{5} \div \frac{11}{2}

Multiply and divide (left to right)

\frac{27}{5} \div \frac{11}{2} : \frac{54}{55}

\frac{27}{5} \div \frac{11}{2}

Apply the fraction rule:

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

= \frac{27}{5} \cdot \frac{2}{11}

Multiply fractions:

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

= \frac{27 \cdot 2}{5 \cdot 11}

Multiply the numbers:

27 \cdot 2 = 54

= \frac{54}{5 \cdot 11}

Multiply the numbers:

5 \cdot 11 = 55

= \frac{54}{55}

= \frac{54}{55}

7 - (- 12) \div (- 3) + 2^{2}

(12 - 42 - 52) \times \frac{1}{6}

[- 7 + (- 3) \cdot (- 4)] \cdot [5 - 6 \div (+ 2)] - 11

\frac{10}{5} - \frac{10}{2} (4 - 6)

- 3 - (- 2) + 10