Question

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

Answer 1

a*b = 1/2

a/ b = 8/9

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=(6)/(9)=(2)/(3)`

so 0.6666 = 2/3

Now we convert 0.75 into fraction form

`0.75=(0.75)/(1)`

Multiply top and bottom by 100 to remove decimal

`(75)/(100) = (3)/(4)`

so 0.75 is 3/4

a= 2/3 and b = 3/4

`a*b = (2)/(3) * (3)/(4) = (6)/(12) = (1)/(2)`

`(a)/(b) = ((2)/(3))/((3)/(4)) = (2)/(3) * (4)/(3) =(8)/(9)`