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- The word "Arithmetic" from Greek "arithmos," meaning "number"Cut The Knot: What Is Arithmetic?
- Elementary arithmetic is taught in primary schoolCut The Knot: What Is Arithmetic?
- "Higher arithmetic" refers to number theoryCut The Knot: What Is Arithmetic?
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Arithmetic is the most basic form of mathematics. It concerns counting and working with numbers and fractions based on the four operations: addition, subtraction, multiplication and division.Cut The Knot: What Is Arithmetic?
The 11 Trick
- When multiplying any two digit number by eleven, separate the two digits and place the sum of the two in between them. For example:
- 35 x 11
- Separate the digits: 3 and 5
- Find the sum: 3 + 5 = 8
- Place the sum in the center: 385
- Thus: 11 x 35= 385
- This can also be done when the central sum is not a single digit. To account for the extra digit take the tens digit and add it to the higher digit of the multiplicand. For example:
- 76 x 11
- Separate the digits: 7 and 6
- Find the sum: 7 + 6 = 13
- Add the 7 and the 1 from the 13: 7 + 1 = 8
- Place the sum in the center: 836
- Thus: 11 x 76= 836
The 5 Trick
- When multiplying by 5, take the other multiplicand and divide it in half. If it is an odd number subtract one and then divide it in half. Then add a zero as the last digit if the multiplicand was even or a five if it was odd. For example:
- 44 x 5
- Divide 44 by 2: 44 / 2 = 22
- Place on a zero at the end: 220
- For an odd number: 33 x 5
- Subtract 1 from 33: 33 - 1 = 32
- Divide 32 in half: 32 / 2 = 16
- Place five at the end: 165
The 9 Trick
- When dividing by 9, for any number less then or equal to ten, count on your fingers and drop the finger that represents the multiplicand. Then, simply count how many fingers are on each side of the dropped finger. The first set of fingers represents the tens digit while the second represents the ones. For example:
- 9 x 7
- Count to the 7th finger and fold it down
- Count the number of fingers before it: 6
- Count the number after: 3
- Thus: 9 x 7 = 63
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Arithmetic Questions
How do you prove -1*x=-x using arithmetic axioms? 1 Answerthe multiplicative identity property states that for any real number a, 1 × a = a. (a × (-1)) + (a × 1) = a × (1 + (-1)) (a × (-1)) + (a × 1) = a × 0 (a ×... read more
Whats the meaning of the arithmetic mean? Not the way its calculated, the signification. 1 AnswerIt is important because it is a way to find the average between a group of numbers. This is probably the most practical of the mean, median, mode you have to le... read more
In Visual Basic an expression can contain arithmetic, comparison and logical operators. What is the precedence in which they are operated? 1 AnswerFrom highest to lowest precidence: arithmetic, comparison, and logical. Operators of equal precendence are evaluted from left to right. read more -
Arithmetic Theories
- University of St. Andrews: Prime Numbers
- Texas University: Non-Linear Arithmetic
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