Question

The population of Alabama is 6 4/5 times that of Alaska. the population of Alabama is approximately 4700000. what is the population of Alaska?

Answer 1

approximately `690,000`

Explanation:

To find the population of Alaska divide the population of Alabama by the factor given `6 4/5`

Change `6 4/5` to an improper fractions

`(6 xx 5 + 4)/5 = 34/5`

Now divide the population of Alabama by the improper fraction

`(4700000/1)/ (34/5)`

Simplify the complex fraction by multiplying both the top and bottom fractions by the inverse of the bottom fractions.

`( 4700000/1 xx 5/34)/ (34/5 xx 5/34)`

Abracadabra!! math magic and the bottom fraction turns to 1 and disappears, :

`4700000 xx 5/34 = 691176.47`

However since the population of Alabama is only known approximately to two digits the population of Alaska can only be known approximately to two digits. Round off to two significant figures gives.

`690,000.`

Answer 2

The population of Alaska is approximately `691,000` .

Explanation:

Given:
The population of Alabama = `6 4/5` times that of Alaska.

The population of Alabama = `4,700,000`.

Asked:
What is the population of Alaska?

Let population of Alaska be `x`.

As given, population of Alabama = `(6 4/5)\times x`.
i.e.
`4700000 = (6 4/5)\times x`

Convert the mixed number into improper form:

`4700000 =( (6\times 5 +4)/5)\times x`

`4700000 =( 34/5)\times x`

`x = (4700000\times5)/34` -------- by transposition.

`x =691176.47`----------------------- truncating up to two decimal places.

`x approx 691,000` --------------rounding to nearest thousands.

Therefore

The population of Alaska is approximately `691,000` .