सिंपलीफाई एंड एक्सप्रेस 10 पावर टू मल्टीप्लाई बाय 15 पावर 3 अपॉन टू पावर टू मल्टीप्लाई बाय 3 मल्टीप्लाई बाई 5 पावर 5 मल्टीप्लाई बाई 6 पावर 4
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The ideas of this module are presented in purely arithmetical form, and no algebra is used except in some remarks that look forward to later work. The only numbers in the module are whole numbers, apart from the final paragraphs, where fractions are used so that the fifth index law can be presented in a more satisfactory form.
Students first meet the distinction between odd numbers and even numbers in early primary school, but it is useful everywhere in mathematics. Even numbers are multiples of 2, and more generally, multiples arise throughout mathematics and everyday life. The mass of a stack of bricks is a multiple of the mass of one brick. The number of pages in a packet of notebooks is a multiple of the number of pages in one notebook.
The factors of a number can be displayed using rectangular arrays. Some numbers, such as 30, can arise in many different ways as a product,
30 = 1 × 30 = 2 × 15 = 3 × 10 = 5 × 6 = 2 × 3 × 5,
whereas a number such as 31 can only be written trivially as the product 31 = 1 × 31. This idea leads to the classification of numbers greater than 1 as either prime or composite, and to a listing of all the factors of a number.
There are several groups of well-known divisibility tests that can check whether a number is a factor without actually performing the division. These tests greatly simplify the listing of factors of numbers.
Repeated addition leads to multiplication. Repeated multiplication in turn leads to powers, and manipulating powers in turn relies on five index laws. Powers are introduced in this module, together with four of the five index laws.