Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we can add 2 and 2 1/4:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Now, we divide 17/4 by 2:
(17/4)/2 = 17/4 * 1/2 = 17/8
Therefore, a rational number between 2 and 2 1/4 using this method is 17/8.
To write this as a mixed number, we divide 17 by 8:
17 ÷ 8 = 2 remainder 1
So, the mixed number form of 17/8 is 2 1/8.
Show an example of a rational number that is between 10−−√ and 11−−√
16/5
10/3
3.1
3.4
To determine which of the given numbers is a rational number between √10 and √11, we need to evaluate each number and check if it falls within the given range.
Let's calculate each option:
√(10) ≈ 3.16227766017
√(11) ≈ 3.31662479036
a) 16/5 ≈ 3.2
b) 10/3 ≈ 3.33333333333
c) 3.1 (This number falls between √10 and √11)
d) 3.4 (This number falls between √10 and √11)
Therefore, both options c) 3.1 and d) 3.4 are rational numbers that fall between √10 and √11.
How many irrational numbers are there between 11−−√ and 17−−√?
twenty-eight numbers
six numbers
four numbers
an infinite number
To find the number of irrational numbers between the square roots of 11 and 17, we can determine the number of integers between the square roots and subtract them from the total number of numbers between the roots. Since integers are rational numbers, the remaining numbers will be irrational.
Let's calculate the square roots:
√(11) ≈ 3.31662479036
√(17) ≈ 4.12310562562
Now we need to find the number of integers between these two square roots. The integers within this range are 4 and 3, so there are two integers.
The total number of numbers between the square roots is 4 (including the square roots themselves) since we have 3.31662479036 <a< 4 < b< 4.12310562562.
Now we subtract the two integers from the total number of numbers:
4 - 2 = 2
Therefore, there are two irrational numbers between the square roots of 11 and 17.
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, follow these steps:
Step 1: Add the two numbers together:
2 + 2 1/4 = 2 + (9/4) = 8/4 + (9/4) = 17/4
Step 2: Divide the result by 2:
(17/4) ÷ 2 = (17/4) × (1/2) = 17/8
Step 3: Simplify the fraction:
17/8 = 2 1/8
Therefore, a rational number between 2 and 2 1/4 obtained using the method of adding the numbers together and dividing by 2 is 2 1/8.
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, follow these steps:
1. Add the two numbers together:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
2. Divide the sum by 2:
(17/4) / 2 = 17/4 * 1/2 = 17/8
3. Simplify the fraction, if needed:
17/8 cannot be simplified any further.
4. Rewrite the answer as a mixed number:
Divide the numerator (17) by the denominator (8):
17 ÷ 8 = 2 remainder 1
The mixed number representation is:
2 1/8
Therefore, a rational number between 2 and 2 1/4 using this method is 2 1/8.