What is 1-8/27 \div 16/9 ?

The solution to 1-8/27 \div 16/9 is 5/6

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1-8/27 \div 16/9

1 - \frac{8}{27} \div \frac{16}{9}

\frac{5}{6}

Solution steps

1 - \frac{8}{27} \div \frac{16}{9}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{8}{27} \div \frac{16}{9} : \frac{1}{6}

\frac{8}{27} \div \frac{16}{9}

Apply the fraction rule:

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

= \frac{8}{27} \cdot \frac{9}{16}

Multiply fractions:

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

= \frac{8 \cdot 9}{27 \cdot 16}

Multiply the numbers:

8 \cdot 9 = 72

= \frac{72}{27 \cdot 16}

Multiply the numbers:

27 \cdot 16 = 432

= \frac{72}{432}

Cancel the common factor:

72

= \frac{1}{6}

= 1 - \frac{1}{6}

Add and subtract (left to right)

1 - \frac{1}{6} : \frac{5}{6}

1 - \frac{1}{6}

1 - \frac{1}{6} = \frac{5}{6}

1 - \frac{1}{6}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 6 - 1 = 5

1 \cdot 6 - 1

Multiply the numbers:

1 \cdot 6 = 6

= 6 - 1

Subtract the numbers:

6 - 1 = 5

= 5

= \frac{5}{6}

= \frac{5}{6}

= \frac{5}{6}

3^{4} - 3

\frac{1}{4} \cdot 6 + 3 \cdot 7

5 (1) - 3

4 \cdot 25 + 17

\frac{3 ^{3} \cdot 3 \div 3 ^{2}}{3 ^{2}}