Question

If a = 0.6 repeating and b = 0.75, then a x b = blank and a/b = blank

Answer 1

Answer:

a*b = 1/2

a/ b = 8/9

Step-by-step explanation:

a = 0.66666  and b = 0.75

To multiply it we write the decimal numbers in fraction form

a= 0.666666...

Multiply by 10 on both sides

10 a = 6.66666...

    a = 0.66666...

Subtract the second equation

9a = 6

divide by 9 on both sides

$a=\frac{6}{9}=\frac{2}{3}$

so 0.6666 = 2/3

Now we convert 0.75 into fraction form

$0.75=\frac{0.75}{1}$

Multiply top and bottom by 100 to remove decimal

$\frac{75}{100} = \frac{3}{4}$

so 0.75 is 3/4

a= 2/3  and b = 3/4

$a*b = \frac{2}{3} * \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$

$\frac{a}{b} = \frac{\frac{2}{3}}{\frac{3}{4}} = \frac{2}{3} * \frac{4}{3} =\frac{8}{9}$