What is (3/(3/4))/(1/(1/6)) ?

The solution to (3/(3/4))/(1/(1/6)) is 2/3

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(3/(3/4))/(1/(1/6))

(3/ (3/4)) / (1/ (1/6))

\frac{2}{3}

Solution steps

(3/ (3/4)) / (1/ (1/6))

Follow the PEMDAS order of operations

Calculate within parentheses

(3/ (3/4)) : 4

3/ (3/4)

Calculate within parentheses

(3/4) : \frac{3}{4}

3/4

3/4 = \frac{3}{4}

= \frac{3}{4}

= 3/ \frac{3}{4}

Multiply and divide (left to right)

3/ \frac{3}{4} : 4

3/ \frac{3}{4}

Convert element to fraction:

3 = \frac{3}{1}

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

Apply the fraction rule:

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

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

Cross-cancel:

3

= \frac{4}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 4

= 4

= 4/ (1/ (1/6))

Calculate within parentheses

(1/ (1/6)) : 6

1/ (1/6)

Calculate within parentheses

(1/6) : \frac{1}{6}

1/6

1/6 = \frac{1}{6}

= \frac{1}{6}

= 1/ \frac{1}{6}

Multiply and divide (left to right)

1/ \frac{1}{6} : 6

1/ \frac{1}{6}

Convert element to fraction:

1 = \frac{1}{1}

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

Apply the fraction rule:

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

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

Apply rule

\frac{a}{a} = 1

\frac{1}{1} = 1

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

Apply rule

\frac{a}{1} = a

= 1 \cdot 6

Multiply the numbers:

1 \cdot 6 = 6

= 6

= 6

= 4/6

Multiply and divide (left to right)

4/6 : \frac{4}{6}

4/6

4/6 = \frac{4}{6}

= \frac{4}{6}

= \frac{4}{6}

Cancel the common factor:

2

= \frac{2}{3}

2^{10} - 1

3^{2} - 2^{2}

2 5^{2} - 7^{2}

2^{2} + 4^{2}

6 \div 2 (3 + 1)