1. Arithmetic All about the art & science of numbers
2. Number systems What is the difference between number sense
and counting?(Brahmagupta, 596 AD) 3. A history of number systems
46,206 = One important part of every number system is its base. 4.
Types of numbers What types of numbers can you recall? 5. Types of
numbers TermDefinitionExamplesNatural numbersCounting numbers.1, 2,
3, 4, 5, 6Whole numbersCounting numbers and zero.0, 1, 2,
3IntegersWhole numbers, their opposites and zero.2, 1, 0, 1, 2,
3Rational NumbersRepeating or terminal decimals.1/3, 1/2Irrational
numbersNon-repeating and non terminating decimals22/7 ,Real
numbersEvery number on the number lineAnything! 6. The set of
numbers 7. Consecutive numbers and the number line 8. Odd and Even
Numbers AdditionSubtractioneven + even = even even even =
evenMultiplicationeven . even = evenodd + odd = evenodd odd =
evenodd . odd = oddeven + odd = oddeven odd = oddeven . odd =
evenodd +even = oddodd even = oddodd . even = even 9. Positives and
Negatives MultiplicationDivisionpositive . positive =
positivepositive / positive = positivenegative . negative =
positive negative / negative = positive positive . negative =
negative positive / negative = negative negative . positive =
negative negative / positive = negative 10. Divisibility and
Remainders What rules do you remember for divisibility? For example
all even numbers are divisible by 2. 11. Divisibility and
Remainders All whole numbers are divisible by 1. A number that ends
in an even digit is divisible by 2. A number is divisible by 3 if
its digits add up to a number divisible by 3. For example, 384 is
divisible by 3 because 3 + 8 + 4 = 15, and 15 is divisible by 3. A
number is divisible by 4 if its last two digits are divisible by 4.
The number 5,764 is divisible by 4 because 64 is divisible by 4. A
number is divisible by 5 if it ends in 0 or 5. A number is
divisible by 6 if it is even and divisible by 3. This rule is a
combo of rules 2 and 3. Sadly, there is no rule for 7. A number is
divisible by 8 if its last three digits are divisible by 8. For
example, 1,249,216 is divisible by 8 because 216 is divisible by 8.
A number is divisible by 9 if its digits add up to a number
divisible by 9. The number 2,952 is divisible by 9 because 2 + 9 +
5 + 2 = 18. A number is divisible by 10 if it ends in 0. 12.
Divisibility and Remainders: Squares 13. Divisibility and
Remainders: Squares0 -> then the ending digit is a 0 1 ->
then the ending digit is 1 or 9. 4 -> then the ending digit is 2
or 8. 5 -> then the ending digit is a 5. 6 -> then the ending
digit is 4 or 6. 9 -> then the ending digit is 3 or 7. C. After
finding the last digit (or possibility between two digits) mentally
chop off the last two digits and focus on the remaining digits. 14.
Example 1: Q) The number n is a 2 digit integer. When n is divided
by 5it leaves a remainder of 4 and when n is divided by 9, it
leaves a remainder of 7. What is the value of n? 15. Strategies 1a)
Picking Numbers Step 1. Pick Simple Numbers and substitute for
variables. Step 2. Try Them Out Try out all the answer choices
using the numbers you picked, eliminating those that gave you a
different result. Step 3. Try Different Values If more than one
answer choice works, use different values and start again 1b)
Recognition by prolonged and multiple use of Picking Numbers 16.
1a) Picking Numbers 17. 1b) RecognitionUse different and easy
Number Picks to eliminate any possible integer answers. 18. 2)
Back-solving Step 1: Estimate the answer. Step 2: Plug in an
answer. Step 3: Keep plugging in till you find one that works. Step
4: Try out all answers. Q. If x is an integer and 2 is the
remainder when 3x + 4 is divided by 5, then x could equal (A) 3 (B)
4 (C) 5 (D) 6 (E) 7 19. 3) Elimination
