What is 1 1/3 \div 6-1/9 ?

The solution to 1 1/3 \div 6-1/9 is 1/9

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1 1/3 \div 6-1/9

1 \frac{1}{3} \div 6 - \frac{1}{9}

\frac{1}{9}

Solution steps

1 \frac{1}{3} \div 6 - \frac{1}{9}

Convert mixed numbers to improper fractions:

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

1 \frac{1}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{4}{3}

= \frac{4}{3} \div 6 - \frac{1}{9}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{4}{3} \div 6 : \frac{2}{9}

\frac{4}{3} \div 6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{4}{3} \div \frac{6}{1}

Apply the fraction rule:

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

= \frac{4}{3} \cdot \frac{1}{6}

Cross-cancel common factor:

2

4, 6

Greatest Common Divisor (GCD)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

The prime factors common to

4, 6

are

= 2

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

Multiply fractions:

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

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

Multiply the numbers:

2 \cdot 1 = 2

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{2}{9}

= \frac{2}{9} - \frac{1}{9}

Add and subtract (left to right)

\frac{2}{9} - \frac{1}{9} : \frac{1}{9}

\frac{2}{9} - \frac{1}{9}

\frac{2}{9} - \frac{1}{9} = \frac{1}{9}

\frac{2}{9} - \frac{1}{9}

Apply rule

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

= \frac{2 - 1}{9}

Subtract the numbers:

2 - 1 = 1

= \frac{1}{9}

= \frac{1}{9}

= \frac{1}{9}

4 - 2 - 3

4 - 2 + 4

(2^{2} + 1) (2^{4} + 1)

(5 + 7) (5 + 5)

(4 - \frac{3}{4}) \times 1