21 results

odd numbers - Numbers not divisible by 2

1 Die Roll

Free 1 Die Roll Calculator - Calculates the probability for the following events in the roll of one fair dice (1 dice roll calculator or 1 die roll calculator):

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

* Probability of any total from (1-6)

* Probability of the total being less than, less than or equal to, greater than, or greater than or equal to (1-6)

* The total being even

* The total being odd

* The total being a prime number

* The total being a non-prime number

* Rolling a list of numbers i.e. (2,5,6)

* Simulate (n) Monte Carlo die simulations.

1 die calculator

1, 9, 25, 49, .......... What is next

1, 9, 25, 49, .......... What is next
1^2 = 1
3^2 = 9
5^2 = 25
7^2 = 49
So this pattern takes odd numbers and squares them. Our next odd number is 9:
9^2 = [B]81[/B]

2 dice roll

Free 2 dice roll Calculator - Calculates the probability for the following events in a pair of fair dice rolls:

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

* Probability of any sum from (2-12)

* Probability of the sum being less than, less than or equal to, greater than, or greater than or equal to (2-12)

* The sum being even

* The sum being odd

* The sum being a prime number

* The sum being a non-prime number

* Rolling a list of numbers i.e. (2,5,6,12)

* Simulate (n) Monte Carlo two die simulations. 2 dice calculator

A is the set of odd integers between 4 and 12

A is the set of odd integers between 4 and 12
Let A be the set of odd numbers between 4 and 12:
[B]A = {5, 7, 9, 11}[/B]

Find four consecutive odd numbers which add to 64

Find four consecutive odd numbers which add to 64.
Let the first number be x. The next three numbers are:
x + 2
x + 4
x + 6
Add them together to get 64:
x + (x + 2) + (x + 4) + (x + 6) = 64
Group like terms:
4x + 12 = 64
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B12%3D64&pl=Solve']equation calculator[/URL], we get:
[B]x = 13[/B]
The next 3 odd numbers are:
x + 2 = 13 + 2 = 15
x + 4 = 13 + 4 = 17
x + 6 = 13 + 6 = 19
So the 4 consecutive odd numbers which add to 64 are:
[B](13, 15, 17, 19)[/B]

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of

Find the odd number less than 100 that is divisible by 9, and when divided by 10 has a remainder of 7.
From our [URL='http://www.mathcelebrity.com/divisibility.php?num=120&pl=Divisibility']divisibility calculator[/URL], we see a number is divisible by 9 if the sum of its digits is divisible by 9.
Starting from 1 to 99, we find all numbers with a digit sum of 9.
This would be digits with 0 and 9, 1 and 8, 2 and 7, 3 and 6, and 4 and 5.
9
18
27
36
45
54
63
72
81
90
Now remove even numbers since the problem asks for odd numbers
9
27
45
63
81
Now, divide each number by 10, and find the remainder
9/10 = 0
[URL='http://www.mathcelebrity.com/modulus.php?num=27mod10&pl=Calculate+Modulus']27/10[/URL] = 2 R 7
We stop here. [B]27[/B] is an odd number, less than 100, with a remainder of 7 when divided by 10.

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?

Four cousins were born at two-year intervals. The sum of their ages is 36. What are their ages?
So the last cousin is n years old. this means consecutive cousins are n + 2 years older than the next.
whether their ages are even or odd, we have the sum of 4 consecutive (odd|even) integers equal to 36. We [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof4consecutiveevenintegersis36&pl=Calculate']type this into our search engine[/URL] and we get the ages of:
[B]6, 8, 10, 12[/B]

If a is an even integer and b is an odd integer then prove a ? b is an odd integer

If a is an even integer and b is an odd integer then prove a ? b is an odd integer
Let a be our even integer
Let b be our odd integer
We can express a = 2x (Standard form for even numbers) for some integer x
We can express b = 2y + 1 (Standard form for odd numbers) for some integer y
a - b = 2x - (2y + 1)
a - b = 2x - 2y - 1
Factor our a 2 from the first two terms:
a - b = 2(x - y) - 1
Since x - y is an integer, 2(x- y) is always even. Subtracting 1 makes this an odd number.
[MEDIA=youtube]GDVuQ7bGHx8[/MEDIA]

Number Property

Free Number Property Calculator - This calculator determines if an integer you entered has any of the following properties:

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

* Even Numbers or Odd Numbers (Parity Function or even-odd numbers)

* Evil Numbers or Odious Numbers

* Perfect Numbers, Abundant Numbers, or Deficient Numbers

* Triangular Numbers

* Prime Numbers or Composite Numbers

* Automorphic (Curious)

* Undulating Numbers

* Square Numbers

* Cube Numbers

* Palindrome Numbers

* Repunit Numbers

* Apocalyptic Power

* Pentagonal

* Tetrahedral (Pyramidal)

* Narcissistic (Plus Perfect)

* Catalan

* Repunit

Odd Numbers

Free Odd Numbers Calculator - Shows a set amount of odd numbers and cumulative sum

Product of Consecutive Numbers

Free Product of Consecutive Numbers Calculator - Finds the product of (n) consecutive integers, even or odd as well. Examples include:

product of 2 consecutive integers

product of 2 consecutive numbers

product of 2 consecutive even integers

product of 2 consecutive odd integers

product of 2 consecutive even numbers

product of 2 consecutive odd numbers

product of two consecutive integers

product of two consecutive odd integers

product of two consecutive even integers

product of two consecutive numbers

product of two consecutive odd numbers

product of two consecutive even numbers

product of 3 consecutive integers

product of 3 consecutive numbers

product of 3 consecutive even integers

product of 3 consecutive odd integers

product of 3 consecutive even numbers

product of 3 consecutive odd numbers

product of three consecutive integers

product of three consecutive odd integers

product of three consecutive even integers

product of three consecutive numbers

product of three consecutive odd numbers

product of three consecutive even numbers

product of 4 consecutive integers

product of 4 consecutive numbers

product of 4 consecutive even integers

product of 4 consecutive odd integers

product of 4 consecutive even numbers

product of 4 consecutive odd numbers

product of four consecutive integers

product of four consecutive odd integers

product of four consecutive even integers

product of four consecutive numbers

product of four consecutive odd numbers

product of four consecutive even numbers

product of 5 consecutive integers

product of 5 consecutive numbers

product of 5 consecutive even integers

product of 5 consecutive odd integers

product of 5 consecutive even numbers

product of 5 consecutive odd numbers

product of five consecutive integers

product of five consecutive odd integers

product of five consecutive even integers

product of five consecutive numbers

product of five consecutive odd numbers

product of five consecutive even numbers

product of 2 consecutive integers

product of 2 consecutive numbers

product of 2 consecutive even integers

product of 2 consecutive odd integers

product of 2 consecutive even numbers

product of 2 consecutive odd numbers

product of two consecutive integers

product of two consecutive odd integers

product of two consecutive even integers

product of two consecutive numbers

product of two consecutive odd numbers

product of two consecutive even numbers

product of 3 consecutive integers

product of 3 consecutive numbers

product of 3 consecutive even integers

product of 3 consecutive odd integers

product of 3 consecutive even numbers

product of 3 consecutive odd numbers

product of three consecutive integers

product of three consecutive odd integers

product of three consecutive even integers

product of three consecutive numbers

product of three consecutive odd numbers

product of three consecutive even numbers

product of 4 consecutive integers

product of 4 consecutive numbers

product of 4 consecutive even integers

product of 4 consecutive odd integers

product of 4 consecutive even numbers

product of 4 consecutive odd numbers

product of four consecutive integers

product of four consecutive odd integers

product of four consecutive even integers

product of four consecutive numbers

product of four consecutive odd numbers

product of four consecutive even numbers

product of 5 consecutive integers

product of 5 consecutive numbers

product of 5 consecutive even integers

product of 5 consecutive odd integers

product of 5 consecutive even numbers

product of 5 consecutive odd numbers

product of five consecutive integers

product of five consecutive odd integers

product of five consecutive even integers

product of five consecutive numbers

product of five consecutive odd numbers

product of five consecutive even numbers

Prove there is no integer that is both even and odd

Let us take an integer x which is both even [I]and[/I] odd.
[LIST]
[*]As an even integer, we write x in the form 2m for some integer m
[*]As an odd integer, we write x in the form 2n + 1 for some integer n
[/LIST]
Since both the even and odd integers are the same number, we set them equal to each other
2m = 2n + 1
Subtract 2n from each side:
2m - 2n = 1
Factor out a 2 on the left side:
2(m - n) = 1
By definition of divisibility, this means that 2 divides 1.
But we know that the only two numbers which divide 1 are 1 and -1.
Therefore, our original assumption that x was both even and odd must be false.
[MEDIA=youtube]SMM9ubEVcLE[/MEDIA]

sum of 3 consecutive odd integers equals 1 hundred 17

sum of 3 consecutive odd integers equals 1 hundred 17
The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers?
1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4
2) We increment by 2 for each number since we have [I]odd numbers[/I].
3) We set this sum of consecutive [I]odd numbers[/I] equal to 117
n + (n + 2) + (n + 4) = 117
[SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE]
(n + n + n) + 2 + 4 = 117
3n + 6 = 117
[SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE]
3n + 6 - 6 = 117 - 6
[SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE]
3n + [S]6[/S] - [S]6[/S] = 117 - 6
3n = 111
[SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE]
3n/3 = 111/3
[SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE]
[S]3[/S]n/[S]3 [/S]= 111/3
n = 37
Call this n1, so we find our other 2 numbers
n2 = n1 + 2
n2 = 37 + 2
n2 = 39
n3 = n2 + 2
n3 = 39 + 2
n3 = 41
[SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE]
([B]37, 39, 41[/B])
37 ? 1st number, or the Smallest, Minimum, Least Value
39 ? 2nd number
41 ? 3rd or the Largest, Maximum, Highest Value

Sum of Consecutive Numbers

Free Sum of Consecutive Numbers Calculator - Finds the sum of (n) consecutive integers, even or odd as well. Examples include:

sum of 2 consecutive integers

sum of 2 consecutive numbers

sum of 2 consecutive even integers

sum of 2 consecutive odd integers

sum of 2 consecutive even numbers

sum of 2 consecutive odd numbers

sum of two consecutive integers

sum of two consecutive odd integers

sum of two consecutive even integers

sum of two consecutive numbers

sum of two consecutive odd numbers

sum of two consecutive even numbers

sum of 3 consecutive integers

sum of 3 consecutive numbers

sum of 3 consecutive even integers

sum of 3 consecutive odd integers

sum of 3 consecutive even numbers

sum of 3 consecutive odd numbers

sum of three consecutive integers

sum of three consecutive odd integers

sum of three consecutive even integers

sum of three consecutive numbers

sum of three consecutive odd numbers

sum of three consecutive even numbers

sum of 4 consecutive integers

sum of 4 consecutive numbers

sum of 4 consecutive even integers

sum of 4 consecutive odd integers

sum of 4 consecutive even numbers

sum of 4 consecutive odd numbers

sum of four consecutive integers

sum of four consecutive odd integers

sum of four consecutive even integers

sum of four consecutive numbers

sum of four consecutive odd numbers

sum of four consecutive even numbers

sum of 5 consecutive integers

sum of 5 consecutive numbers

sum of 5 consecutive even integers

sum of 5 consecutive odd integers

sum of 5 consecutive even numbers

sum of 5 consecutive odd numbers

sum of five consecutive integers

sum of five consecutive odd integers

sum of five consecutive even integers

sum of five consecutive numbers

sum of five consecutive odd numbers

sum of five consecutive even numbers

sum of 2 consecutive integers

sum of 2 consecutive numbers

sum of 2 consecutive even integers

sum of 2 consecutive odd integers

sum of 2 consecutive even numbers

sum of 2 consecutive odd numbers

sum of two consecutive integers

sum of two consecutive odd integers

sum of two consecutive even integers

sum of two consecutive numbers

sum of two consecutive odd numbers

sum of two consecutive even numbers

sum of 3 consecutive integers

sum of 3 consecutive numbers

sum of 3 consecutive even integers

sum of 3 consecutive odd integers

sum of 3 consecutive even numbers

sum of 3 consecutive odd numbers

sum of three consecutive integers

sum of three consecutive odd integers

sum of three consecutive even integers

sum of three consecutive numbers

sum of three consecutive odd numbers

sum of three consecutive even numbers

sum of 4 consecutive integers

sum of 4 consecutive numbers

sum of 4 consecutive even integers

sum of 4 consecutive odd integers

sum of 4 consecutive even numbers

sum of 4 consecutive odd numbers

sum of four consecutive integers

sum of four consecutive odd integers

sum of four consecutive even integers

sum of four consecutive numbers

sum of four consecutive odd numbers

sum of four consecutive even numbers

sum of 5 consecutive integers

sum of 5 consecutive numbers

sum of 5 consecutive even integers

sum of 5 consecutive odd integers

sum of 5 consecutive even numbers

sum of 5 consecutive odd numbers

sum of five consecutive integers

sum of five consecutive odd integers

sum of five consecutive even integers

sum of five consecutive numbers

sum of five consecutive odd numbers

sum of five consecutive even numbers

Sum of the First (n) Numbers

Free Sum of the First (n) Numbers Calculator - Determines the sum of the first (n)

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

* Whole Numbers

* Natural Numbers

* Even Numbers

* Odd Numbers

* Square Numbers

* Cube Numbers

* Fourth Power Numbers

Sum of two consecutive numbers is always odd

Sum of two consecutive numbers is always odd
Definition:
[LIST]
[*]A number which can be written in the form of 2 m where m is an integer, is called an even integer.
[*]A number which can be written in the form of 2 m + 1 where m is an integer, is called an odd integer.
[/LIST]
Take two consecutive integers, one even, and one odd:
2n and 2n + 1
Now add them
2n + (2n+ 1) = 4n + 1 = 2(2 n) + 1
The sum is of the form 2n + 1 (2n is an integer because the product of two integers is an integer)
Therefore, the sum of two consecutive integers is an odd number.

Take a look at the following sums: 1 = 1 1 + 3 = 4 1 + 3 + 5 = 9 1 + 3 + 5 + 7 = 16 1 + 3 + 5 + 7 +

Take a look at the following sums:
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
a. Come up with a conjecture about the sum when you add the first *n* odd numbers. For example, when you added the first 5 odd numbers (1 + 3 + 5 + 7 + 9), what did you get? What if wanted to add the first 10 odd numbers? Or 100?
b. Can you think of a geometric interpretation of this pattern? If you start with one square and add on three more, what can you make? If you now have 4 squares and add on 5 more, what can you make?
c. Is there a similar pattern for adding the first n even numbers?
2 = 2
2 + 4 = 6
2 + 4 + 6 = 12
2 + 4 + 6 + 8 = 20
a. The formula is [B]n^2[/B].
The sum of the first 10 odd numbers is [B]100[/B] seen on our s[URL='http://www.mathcelebrity.com/sumofthefirst.php?num=10&pl=Odd+Numbers']um of the first calculator[/URL]
The sum of the first 100 odd numbers is [B]10,000[/B] seen on our [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=100&pl=Odd+Numbers']sum of the first calculator[/URL]
b. Geometric is 1, 4, 9 which is our [B]n^2[/B]
c. The sum of the first n even numbers is denoted as [B]n(n + 1)[/B] seen here for the [URL='http://www.mathcelebrity.com/sumofthefirst.php?num=+10&pl=Even+Numbers']first 10 numbers[/URL]

The set of all odd numbers between 10 and 30

The set of all odd numbers between 10 and 30
[B]{11, 13, 15, 17, 19, 21, 23, 25, 27, 29}[/B]

The sum of 5 odd consecutive numbers is 145

The sum of 5 odd consecutive numbers is 145.
Let the first odd number be n. We have the other 4 odd numbers denoted as:
[LIST]
[*]n + 2
[*]n + 4
[*]n + 6
[*]n + 8
[/LIST]
Add them all together
n + (n + 2) + (n + 4) + (n + 6) + (n + 8)
The sum of the 5 odd consecutive numbers equals 145
n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = 145
Combine like terms:
5n + 20 = 145
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5n%2B20%3D145&pl=Solve']equation solver[/URL], we get [B]n = 25[/B]. Using our other 4 consecutive odd numbers above, we get:
[LIST]
[*]27
[*]29
[*]31
[*]33
[/LIST]
Adding the sum up, we get: 25 + 27 + 29 + 31 + 33 = 145.
So our 5 odd consecutive number added to get 145 are [B]{25, 27, 29, 31, 33}[/B].
[MEDIA=youtube]0T2PDuQIIwI[/MEDIA]

Three good friends are in the same algebra class, their scores on a recent test are three consecutiv

Three good friends are in the same algebra class, their scores on a recent test are three consecutive odd integers whose sum is 273. Find the score
In our search engine, we type in [URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=3consecutiveintegerswhosesumis273&pl=Calculate']3 consecutive integers whose sum is 273[/URL] and we get:
[B]90, 91, 92[/B]

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will sto

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stop on an odd number or a number less than 4.
We want P(odd number) or P(n<4).
[LIST]
[*]Odd numbers are {1, 3, 5, 7, 9}
[*]n < 4 is {1, 2, 3}
[/LIST]
We want the union of these 2 sets:
{1, 2, 3, 5, 7, 9}
We have 6 possible pointers in a set of 10.
[B]6/10 = 3/5 = 0.6 or 60%[/B]