Solve for the quotient of the fractions below
4
.
1.
=
2.
10
IN
6 10
2
11
5
10
4.
12
L-
1
5.
-
5
Answers
Step-by-step explanation:
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.
We are used to comparing numbers in terms of their size. The highest common factor (HCF) and lowest common multiple (LCM) allow us to compare numbers in terms of their factors and multiples. For example, when we look at 30 and 12, we see that they are both multiples of 6, and that 6 is the greatest factor common to both numbers. We also see that 60 is a multiple of both numbers, and that 60 is the lowest common multiple of them (apart from 0). The HCF and LCM are essential for fractions and later for algebra.
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CONTENT
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ODD AND EVEN NUMBERS
Here is the usual definition of odd and even whole numbers.
A whole number is called even if it is a multiple of 2.
A whole number is called odd if it is not even.
Thus 10 is even and 11 is odd. We can demonstrate this by writing
10 = 5 + 5 and 11 = 5 + 5 + 1,
and we can illustrate this using arrays with two rows.
E3g1.pdf
10 = 5 + 5
11 = 5 + 5 + 1
The array representing the even number 10 has the dots divided evenly into two equal rows of 5, but the array representing the odd number 11 has an extra odd dot left over.
When we write out the whole numbers in order,
the even and odd numbers alternate, starting with 0, which is an even number because
0 + 0 = 0.
This pattern occurs in all sorts of common situations:
When we walk, we step left, right, left, right,…
When music is written in double time, like the Australian National Anthem, the notes are alternately stressed, unstressed, stressed, unstressed,…
Our time is alternately divided day, night, day, night,…
The squares on each row or column of a chessboard are alternately black, white, black, white,…
Indeed, our concept of the number 2 is so different from our conceptions of all other numbers that we even use different language. We divide a pie between two people, but among three people. We identify two alternatives, but three options. The word ‘doubt’ is related to the Latin ‘duo’, the word ‘two-faced’ means ‘liar’, and the traditional number of the devil is 2.