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VLD [36.1K]
3 years ago
8

Type the correct answer in each box. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
Tom [10]3 years ago
6 0

Given:

The values are a=0.\overline{6},b=0.75.

To find:

The values of ab and \dfrac{a}{b}.

Solution:

We have,

a=0.\overline{6}

a=0.666...                     ...(i)

Multiply both sides by 10.

10a=6.666...                 ...(ii)

Subtracting (i) from (ii), we get

10a-a=6.666...-0.666...

9a=6

a=\dfrac{6}{9}

a=\dfrac{2}{3}

And,

b=0.75

b=\dfrac{75}{100}

b=\dfrac{3}{4}

Now, the product of a and b is:

ab=\dfrac{2}{3}\times \dfrac{3}{4}

ab=\dfrac{1}{2}

The quotient of a and b is:

\dfrac{a}{b}=\dfrac{\dfrac{2}{3}}{\dfrac{3}{4}}

\dfrac{a}{b}=\dfrac{2}{3}\times \dfrac{4}{3}

\dfrac{a}{b}=\dfrac{8}{9}

Therefore, the required values are ab=\dfrac{1}{2} and \dfrac{a}{b}=\dfrac{8}{9}.

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