Question

The proportion of American adults who spend between 6 and 9.99 hours a day, inclusive, on digital devises is approximately 1/3. The proportion of Americans adults who spend more than 9.99 hours on a digital dev is approximately 2/7. Find the proportion of American adults who spend at least 6 hours on digital devices. Write your result as a fraction.

Answer 1

Answer: 13/21 of the American adults spend at least 6 hours on digital services.

Explanation:

The proportion that spends between 6 hours and 9.99 hours is 1/3

The proportion that spends more than 9.99 hours is 2/7

We want to find the proportion who spends at least 6 hours.

This is easy, we just need to combine the two groups from above, and that will give use the proportion that spends 6 hours or more.

We only need to add:

1/3 + 2/7

Now, the first problem we see here is that the denominators are different, then we need to rewrite both fractions to have the same denominator.

We know that 3*7 = 21, then we can use 21 as the common denominator, by multipliying by 7/7 (this is equal to 1) the first fraction, and by 3/3 the second one:

1/3 = (1/3)*1 = (1/3)*(7/7) = 7/21

2/7 = (2/7)*1 = (2/7)*(3/3) = (3*2)/21 = 6/21

Then the previous sum becomes:

1/3 + 2/7 = 7/21 + 6/21 = 13/21

This means that 13/21 of the american adults spend at least 6 hours on digital services.