ch. 5 math notes name: ____________________ sectioni can
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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)
• 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)
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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