Published on March 9, 2014
Arithmetic All about the art & science of numbers
Number systems What is the difference between number sense and counting? (Brahmagupta, 596 AD)
A history of number systems 46,206 = One important part of every number system is its base.
Types of numbers What types of numbers can you recall?
Types of numbers Term Definition Examples Natural numbers Counting numbers. 1, 2, 3, 4, 5, 6 Whole numbers Counting numbers and zero. 0, 1, 2, 3 Integers Whole numbers, their opposites and zero. –2, –1, 0, 1, 2, 3 Rational Numbers Repeating or terminal decimals. 1/3, 1/2 Irrational numbers Non-repeating and non terminating decimals 22/7 , Real numbers Every number on the number line Anything!
The set of numbers
Consecutive numbers and the number line
Odd and Even Numbers Addition Subtraction even + even = even even – even = even Multiplication even . even = even odd + odd = even odd – odd = even odd . odd = odd even + odd = odd even – odd = odd even . odd = even odd +even = odd odd – even = odd odd . even = even
Positives and Negatives Multiplication Division positive . positive = positive positive / positive = positive negative . negative = positive negative / negative = positive positive . negative = negative positive / negative = negative negative . positive = negative negative / positive = negative
Divisibility and Remainders What rules do you remember for divisibility? For example all even numbers are divisible by 2.
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.
Divisibility and Remainders: Squares
Divisibility and Remainders: Squares 0 -> 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.
Example 1: Q) The number n is a 2 digit integer. When n is divided by 5 it leaves a remainder of 4 and when n is divided by 9, it leaves a remainder of 7. What is the value of n?
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
1a) Picking Numbers
1b) Recognition Use different and easy Number Picks to eliminate any possible integer answers.
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
Arithmetic or arithmetics (from the Greek ἀριθμός arithmos, "number") is the oldest  and most elementary branch of mathematics. It consists of ...
noun 1. the method or process of computation with figures: the most elementary branch of mathematics. 2. Also called higher arithmetic, theoretical ...
a·rith·me·tic (ə-rĭth′mĭ-tĭk) n. The mathematics of integers, rational numbers, real numbers, or complex numbers under addition, subtraction ...
Englisch-Deutsch-Übersetzung für arithmetic im Online-Wörterbuch dict.cc (Deutschwörterbuch).
Übersetzung für arithmetic im Englisch-Deutsch-Wörterbuch dict.cc.
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arithmetic, branch of mathematics mathematics, deductive study of numbers, geometry, and various abstract constructs, or structures; the latter often ...
Die Arithmetik (griechisch ἀριθμητική [τέχνη] arithmetiké [téchne], wörtlich „die Zahlenmäßige [Kunst]“) ist ein Teilgebiet der ...
Middle English arsmetrik, from Anglo-French arismatike, from Latin arithmetica, from Greek arithmētikē, from feminine of arithmētikos arithmetical, from ...
Definition. The arithmetic mean (or mean or average) is the most commonly used and readily understood measure of central tendency. In statistics, the term ...