ch. 5 math notes name: ____________________ sectioni can

Ch. 5 Math notesName:

____________________

Section I can

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

Divisibility -- Try these out:• Is 168 divisible by 2? – (why)

• Is 168 divisible by 3?– (why)






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

Factors – try these:

• 36

• 12

• 100

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.

Multiples – Try these

• 12

• 20

• 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

Try these:• 68

• 490

• 210

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

GCF try these:

• 45• 120

• 52• 78

• 30• 66

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)

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

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:

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

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