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Week 11: Number Categories,
Powers and Roots
Created
@May 2, 2024 9:35 AM
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🎀Lesson 31: Integers
When we are trying to figure out more about a number we have to ask if is it a real or
Non-real/imaginary number.
It is a non-real number if it’s the square root of a negative number or if you can divide it
by 0. (FYI: you can not do either of these!)
A rational number is any number that can be written as a fraction.
Week 11: Number Categories, Powers and Roots
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Natural numbers, rational numbers, integers whole numbers, and irrational numbers fall
under real numbers.
NOT ALL FRACTIONS FALL UNDER REAL NUMBERS!
Natural numbers start at 1 and continue without decimals, only whole numbers.
Whole numbers start from 0 and do not include negative numbers.
Integers are sets of positive and negative numbers.
The focus of this lesson is integers
The symbol above is used to denote integers in math.
RULES ABOUT DEALING WITH MULTIPLE SIGNS: ++=+ and - =-[Two of the same signs equal the same signs] And 2 different signs
equal a minus-
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Learning Material Lesson Content
Week 11: Number Categories, Powers and Roots - Mathematics (FIBB)
https://www.cambrilearn.com/learning-material/cambrilearn/found
ation-i/mathematics-fi-bb/week-11-number-categories-powers-and-root
s/lessons/47b26f2c-d19f-42f4-ba96-2debdf2e279c/part/5b5e25f9-4793
🎀Lesson 32: Indices, Primes, Factors and Multiples
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Learning Outcomes:
® Find prime numbers in the first 100 numbers
® Write down the factors and multiples of whole numbers
® Use index notation
Indices or exponents
Index or exponential notation involves a base that is multiplied by itself a certain number
of times. The number 2
4 has a base of 2 and a power of 4 and can be expanded as:
2
4=2 x 2 x 2 x 2=16
Primes
A prime number is a number that has only 2 factors: 1 and itself.
37 is prime because its only factors are 1 and 37.
25 is not prime because it has other factors besides 1 and 25; 5 is the other factor of 25.
Numbers that are not prime are called composite numbers.
1 is not a prime number because it has only one factor, not two!
2 is a prime number. All other even numbers are not prime numbers.
We can work out that the first 5 prime numbers are 2,3,5,7,11.
Primes
A prime number is a number that has only 2 factors: 1 and itself.
-37 is prime because its only factors are 1 and 37.
-25 is not prime because it has other factors besides 1 and 25; 5 is the other factor of 25.
Numbers that are not prime are called composite numbers.
-1 is not ta prime number because it has only one factor, not two!
-2 is a prime number. All other even numbers are not prime numbers.
We can work out that the first 5 prime numbers are 2,3,5,7,11.
Factors
A factor of a number divides into that number without a remainder.
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For example:
-4 is a factor of 16.
-3 and 4 are both factors of 12.
1 is a factor of any number because any number divided by 1 is that number.
1/1=1
5/1=5
25/1=25
Any number is a factor of itself.
5 is a factor of 5 because 5 +5 =1
25 is a factor of 25 because 25 + 25 = 1
Prime Factors
A prime factor is a factor of a number that is itself a prime number.
Any number can be written as a product of prime factors, no matter how big the number is!
For example:
72 can be written as 2 x 2 x 2 x 3 x 3 = 2% x 32 where both 2 and 3 are prime
numbers.
330 can be written as 2 x 3 x 5 x 11 where each of 2, 3, 5, and 11 is a prime number.
Multiples
A multiple is a whole number that can be divided by another whole number without a
remainder.
For example:
16 is a multiple of 4 because 4 divides into 16 exactly 4 times
(16/4 =4 and 4 x 4 = 16). |
-12 is another multiple of 4 because 4 divides into 12 exactly 3 times
(12+4=3 and 3 x 4 =12).
Any number is a multiple of itself.
So, 16 is a multiple of 16. 16 divides into 16 exactly once:
16+16=1 and 16 x 1=16
Finding all the prime numbers up to 100
We know that a prime number has only two factors: 1 and itself.
Here is a grid of numbers up to 100. We can eliminate all the numbers that are not prime as
a way of finding the prime numbers.
Week 11: Number Categories, Powers and Roots
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Learning Material Lesson Content
Week 11: Number Categories, Powers and Roots - Mathematics (FIBB)
https://www.cambrilearn.com/learning-material/cambrilearn/found
ation-i/mathematics-fi-bb/week-11-number-categories-powers-and-root
s/lessons/a9f87f42-2ca8-4699-9088-21d4c8e30f96/part/bf4ac261-b64b
🎀
Lesson 33: Squares, Square Roots, Cubes and Cube
Roots
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Learning Outcomes:
® Solve problems with square and cube numbers
® Solve problems with square and cube roots
® Do calculations with squaring and cubing decimals and
fractions.
Squares
A square is the resulting value when a number is multiplied by itself.
This can be written in exponential form where the base is a and the exponent is 2.
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This can also be expressed in words where: a squared equals a multiplied by a. In other
words, a number that is multiplied by itself is said to be
squared.
Note:
The result of a number squared is also known as a perfect square.
The table below shows ten perfect squares that are produced when multiplying a
number by itself.
Square roots
Obtaining the square root of a number is the inverse operation of squaring a number.
The square root is the number, which when multiplied by itself gives the specified
perfect square.
Thus the square root of a*2 is:
Since:
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Remember:
Squaring and square rooting are inverse operations of each other.
Cube Roots
Obtaining the cube root of a number is the inverse operation of cubing a number.
The cube root is the number, which when multiplied by itself and then by itself again, gives
the specified perfect cube.
The cube root of a*3 is: a
Since:
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