1. Ch. 5 Math notes Name: ____________________ SectionI can

2. 5.1 Factors, Multiples, Divisibility Rules: a number is divisible by: 2 – if the last digit is even 3 – if the sum of the digits in divisible by 3 4 – if the number formed by the last two digits is divisible by 4 5 – if the last digit is 0 or 5 6 if the number is divisible by 2 AND 3 9 – if the sum of the digits is divisible by 9 10 – if the last digit is 0

3. Divisibility -- Try these out: Is 168 divisible by 2? – (why) Is 168 divisible by 3? – (why) Is 316 divisible by 4? – (why) Is 195 divisible by 5? – (why) Is 168 divisible by 6? – (why) Is 549 divisible by 9? – (why) Is 450 divisible by 10? – (why)

4. Factors: Are numbers that go into the number A factor is smaller than the number you are finding the factor for, for instance if you are finding the factors for 45, they CANNOT be bigger than 45 It is the rainbow For instance the factors of 28: 1, 2, 4, 7, 14, 28 – Always start with 1 and the number and then work your way in – If a number is multiplied by itself you write it once

5. Factors – try these: 36 12 100

6. Multiples Multiples are answers when you take a number and multiply by it by something else For instance if you find the multiplies of 4, it is just like writing the fact tables of 4 – 4, 8, 12, 16, 20 Multiples are unlike factors in the fact that they are always BIGGER than the number.

7. Multiples – Try these 12 20 8

8. 5.2 Prime Factorization A prime number can only be divided EVENLY by 1 and itself – for instance 13, 17, 23 A composite number can be divided by different numbers (it is every number that is NOT prime) Prime factorization – is when you break the number down to only the prime numbers If it is prime – it cannot be broken down any further than the number itself

9. Try these: 68 490 210

10. 5.3 Greatest Common Factor (GCF) Is the greatest number that is a factor of two or more numbers The biggest number that can evenly go INTO a set of numbers 12 and 18 – 12: 1, 2, 3, 4, 6, 12 – 18: 1, 2, 3, 6, 9, 18 – The numbers that they have in common are 1, 2, 3, and 6 – The greatest number is 6

11. GCF try these: 45 120 52 78 30 66

12. 5.4 Understanding Fractions Fractions are numbers that describe the division of a whole into equal parts. Numerator – the parts being considered (the top number) Denominator – the total number of equal parts or objects (the bottom number)

13. 5.5 Equivalent Fractions Fractions that have different numerators and denominators but name the same amount are called equivalent or equal For instance 1/3 and 1/3 is the same as 2/3, 4/6, 6/9, 8/12 You can either multiply or divide MOST IMPORTANT – whatever you do to the numerator – you MUST do the exact same to the denominator in order for it to be equal

14. 5.6 Simplest Form To find the simplest form – Divide by the GCF of the numerator and denominator Continue to divide until there is no other common number that can go into numerator and denominator besides 1 Try these:

15. Reminders: Factors – start with 1 and number and CANNOT be bigger than the number Multiples – Start with number and are the fact tables Divisibility – use chart – must be able to DIVIDE out evenly Prime number – only 1 and itself can evenly divide it Composite number – any number that is not prime Greatest Common Factor – the largest common factor of a set of numbers You must BE FAIR whatever you do to numerator, you MUST do to denominator! Equivalent – fractions that use different numbers but name same amount Simplest form – a fraction divided down until nothing can divide it besides on