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Yogita Ingle 5 years, 7 months ago
When the numerator is less than the denominator, it is called a Proper function.
- If you want to describe a part of a whole, it is called a Fraction.
- Denominator – The number on the bottom of the fraction and it shows the number of equal parts the whole is divided into.
- Numerator – The numerator is the number on the top of the fraction and it shows the number of the parts we are considering.
- Example, in the fraction 5/6 it shows “5 of 6 equal parts.” 5 is the numerator, and 6 is the denominator.
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Yogita Ingle 5 years, 7 months ago
The sum of the measures of supplementary angles is 180º.
49°
Supplement = 180° − 49° = 131°
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Sanjay Kumar 5 years, 7 months ago
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Yogita Ingle 5 years, 7 months ago
The word integer originated from the Latin word “Integer” which means whole. It is a special set of whole numbers comprised of zero, positive numbers and negative numbers and denoted by the letter Z.
Examples of Integers – 1, 6, 15.
Fractions, decimals, and percents are out of this basket. Examples – -2.4, 3/4, 90.6.
Posted by Sai Sharanya 5 years, 7 months ago
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Yogita Ingle 5 years, 7 months ago
Integers have 5 main properties of operation which are:
- Closure Property:
Among the various properties of integers, closure property under addition and subtraction states that the sum or difference of any two integers will always be an integer i.e. if x and y are any two integers, x + y and x − y will also be an integer.
Example : 3 – 4 = 3 + (−4) = −1;
(–5) + 8 = 3,
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Associative Property:
The associative property of addition and multiplication states that the way of grouping of numbers doesn’t matter; the result will be same. One can group numbers in any way but the answer will remain same. Parenthesis can be done irrespective of the order of terms. Let x, y and z be any three integers, then
⇒ x + (y + z) = (x + y) +z
⇒ x × (y × z) = (x × y) × z
Example : 1 + (2 + (-3)) = 0 = (1 + 2) + (−3);
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Commutative Property: The commutative property of addition and multiplication states that the order of terms doesn’t matter, the result will be the same. Whether it is addition or multiplication, swapping of terms will not change the sum or product. Suppose, x and y are any two integers, then
⇒ x + y = y + x
⇒ x × y = y × x
Example : 4 + (−6) = −2 = (−6) + 4; -
Distributive Property:The distributive property explains the distributing ability of operation over another mathematical operation within a bracket. It can be either distributive property of multiplication over addition or distributive property of multiplication over subtraction. Here integers are added or subtracted first and then multiplied or multiply first with each number within the bracket and then added or subtracted. This can be represented for any integers x, y and z as:
⇒ x × (y + z) = x × y + x × z
⇒ x × (y − z) = x × y − x × z
Example: −5 (2 + 1) = −15 = (−5 × 2) + (−5 × 1)
- Identity Property:
Among the various properties of integers, additive identity property states that when any integer is added to zero it will give the same number. Zero is called additive identity. For any integer x,
x + 0 = x = 0 + x
The multiplicative identity property for integers says that whenever a number is multiplied by the number 1 it will give the integer itself as the product. Therefore, the integer 1 is called the multiplicative identity for a number. For any integer x,
x × 1 = x = 1 × x
If any integer multiplied by 0, the product will be zero:
x × 0 = 0 =0 × x
If any integer multiplied by -1, the product will be opposite of the number:
x × (−1) = −x = (−1) × x
Posted by Lakshay Gupta 5 years, 7 months ago
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Meghna Thapar 5 years, 7 months ago
A natural number is an integer greater than 0. ... For example, if you are timing something in seconds, you would use natural numbers (usually starting with 1). When written, natural numbers do not have a decimal point (since they are integers), but large natural numbers may include commas, e.g. 1,000 and 234,567,890.
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Yogita Ingle 5 years, 7 months ago
A prime number is a positive integer having exactly two factors. If p is a prime, then it’s only factors are necessarily 1 and p itself. Any number which does not follow this is termed as composite numbers which means that they can be factored into other positive integers.
First Ten Prime Numbers
The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
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Daniel James 5 years, 7 months ago
1Thank You