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REY [17]
3 years ago
10

How to find rational numbers between any two numbers for example like finding six rational numbers between three and four please

elaborate
Mathematics
1 answer:
Drupady [299]3 years ago
5 0

Answer:

<em>The whole series is: </em>

<em>3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4</em>

Step-by-step explanation:

<u>Inserting Numbers Between Two Given Endpoints</u>

Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].

To place n numbers, we need to open n+1 slots, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1) each.

For example, let's add 6 rational numbers between 3 and 4. The width of the given interval is 4-3=1, and we need to place 6 numbers separated by 1/(6+1) = 1/7.

Start by the left endpoint:

3

The first number to add is 3+1/7=22/7

22/7

The second number to add is 22/7+1/7=23/7

23/7

The third number is 23/7+1/7=24/7

24/7

The next numbers follow the same pattern:

25/7

26/7

27/7

The last number is 28/7=4

4

The whole series is:

3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4

We have inserted 6 rational numbers between 3 and 4.

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3 years ago
Latoya drives 8 miles to work in 13 minutes. What is her average rate, in miles per hour, when rounded to the nearest wholes num
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Answer:

37 miles per hour

Step-by-step explanation:

To find the average rate (average speed) of Latoya in miles per hour, you would divide the distance traveled (in miles) by the time taken to travel (in hours).

So we know that Latoya traveled 8 miles in 13 minutes. We cannot divide 8 by 13, because 13 is in minutes, not hours. We must convert 13 minutes to hours before dividing.

There are 60 minutes in one hour, so to covert minutes into hours, we would divide the minutes (13) by 60. Doing this would give you 13/60. You cannot simplify the fraction 13/60, because 13 is a prime number. It would be best to just leave it as it is for now. So Latoya traveled for 13/60 hours.

Now, to find her average rate in miles per hour, you divide the distance traveled in miles (8 miles) by the time it took to travel in hours (13/60):

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Remember, a ÷ b/c = a × c/b. Using this:

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Latoya had an average rate of about 37 miles per hour.

I hope this helps. :)

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