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Grade 8 Mathematics > The number system, ratio, rate and financial mathematics > Flashcards

The number system, ratio, rate and financial mathematics Flashcards

To master the theory and formulas covered in this section

1
Q

Define the term ‘Natural Numbers’.

A

Natural numbers start at 1 and increase in ones up to infinity

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2
Q

Define the term ‘Whole Numbers’.

A

Whole numbers start at 0 and increase in ones up to infinity

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3
Q

What type of numbers are used in the following number series: {1; 2; 3; 4; 5; 6; 7; …}?

A

Natural numbers

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4
Q

What type of numbers are used in the following number series: {0; 1; 2; 3; 4; 5; 6; 7; …}?

A

Whole numbers

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5
Q

What does BODMAS stand for?

A

Brackets of Divide, Multiply, Add, Subtract

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6
Q

List the order of operations.

A

Brackets of Divide, Multiply, Add, Subtract

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7
Q

Correct the order of operations in the following statement:

Brackets, Divide, Subtract, Multiply, Add

A

Brackets, Divide, Multiply, Add, Subtract

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8
Q

List a series of natural numbers.

A

{1; 2; 3; 4; 5; 6; 7; …} or any other series that does not include the number 0

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9
Q

List a series of whole numbers.

A

{0; 1; 2; 3; 4; 5; 6; 7; …} or any other series that includes the number 0

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10
Q

Solve the following equation:

10 - 10 ÷ 5 x 2

A 
10 - 10 ÷ 5 x 2 = 10 - (10 ÷ 5) x 2
                        = 10 - 2 x 2
                        = 10 - (2 x 2)
                        = 10 - 4
                        = 6
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11
Q

Write the following numbers in ascending order:

152; 148; 200; 353; 1 254; 987; 382

A

148; 152; 200; 353; 382; 987; 1 254

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12
Q

Write the following numbers in ascending order:

222; 135; 128; 98; 5524; 857; 85

A

85; 98; 128; 135; 222; 857; 5 524

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13
Q

Write the following numbers in descending order:

58; 21; 36; 18; 235; 25; 27

A

235; 58; 26; 27; 25; 21; 18

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14
Q

Write the following numbers in descending order:

58; 285; 167; 75; 44; 1; 3

A

285; 167; 75; 58; 44; 3; 1

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15
Q

What are you expected to do when a question asks you to evaluate an equation?

A

Evaluate means determine the value of the equation, in other words, solve the equation.

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16
Q

List the properties of whole numbers.

A 
The commutative property
The associative property
The distributive property
The identity property
 - the additive identity
 - the multiplicative identity
Division by zero
Inverse operations
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17
Q

Define the term ‘commutative property’.

A

In addition and multiplication, numbers may be add or multiplied together in any order.
The commutative property does not apply to division and subtraction.

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18
Q

Define the term ‘associative property’.

A

In addition and multiplication, no matter how the numbers are grouped, the answer will always be the same.
The associative property does not apply to division and subtraction.

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19
Q

Which property is represented by the following equation:

a + b) + c = a + (b + c

A

The associative property

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20
Q

Which property is represented by the following equation:

a x b) x c = a x (b x c

A

The associative property

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21
Q

Which property is represented by the following equation:

a + b = b + a

A

The commutative property

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22
Q

Which property is represented by the following equation:

a x b = b x a

A

The commutative property

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23
Q

Define the term ‘distributive property’.

A

The distributive property applies to multiplication over addition and subtraction.
Using this property, a number outside of a bracket can be multiplied by every number inside of a bracket, provided the numbers inside of the bracket are added or subtracted.

24
Q 
Which property is represented by the following equation:
a x (b + c) = (a x b) + (a x c)
A

The distributive property

25
Q

Define the term ‘identity property’.

A

When the identity property is applied to a number the number does not change.

26
Q

How many identity properties do whole numbers have?

A

Two

27
Q

Name the Identity properties that apply to whole numbers.

A

The additive identity (0)

The multiplicative identity (1)

28
Q

Define the term ‘additive identity’.

A

Zero is the additive identity.

Adding or subtracting 0 to or from a number does not change the number.

29
Q

Define the term ‘multiplicative identity’.

A

One (1) is the multiplicative identity.

Multiplying or dividing a number by 1 does not change the number.

30
Q

Discuss two rules for division by zero.

A

Zero divided by any number (except 0) is always equal to 0.

Any number divided by zero is undefined.

31
Q

Define the term ‘inverse operations’.

A

An inverse operation reverses the effect of another operation.

32
Q

Name two types of inverse operations that apply to whole numbers.

A

Addition and subtraction

Multiplication and division

33
Q

Define the term ‘factors’.

A

Factors of a number are all of the numbers which can divide exactly into the number without a remainder.

34
Q

Define the term ‘multiples’.

A

Multiples of a number are all of the numbers which the number can divide into, without leaving a remainder.

35
Q

Define the term ‘prime number’.

A

Prime numbers are natural numbers greater than 1, which only have two factors - 1 and itself.

36
Q

Define the term ‘composite numbers’.

A

Composite numbers are numbers which have more than two factors.
In other words, they are all the numbers which are not prime.

37
Q

What is the purpose of the ladder method?

A

The ladder method is used to write any natural number as a product of its prime factors.

38
Q

What are prime factors?

A

Prime factors are factors of a number which are prime.

39
Q

What are the steps for using the ladder method?

A
  1. Divide the number by its smallest prime factor
  2. Divide the answer by its smallest prime factor
  3. Repeat the process of dividing the answer by its smallest prime factor until an answer of 1 is obtained
40
Q

What does HCF stand for?

A

Highest common factor.

41
Q

What does RHS stand for?

A

Right hand stand

42
Q

What does LHS stand for?

A

Left hand side

43
Q

Define the term ‘highest common factor’?

A

The highest common factor is the largest factor which is common to two or more numbers

44
Q

Which method follows the steps below?

  1. Divide the number by its smallest prime factor
  2. Divide the answer by its smallest prime factor
  3. Repeat the process of dividing the answer by its smallest prime factor until an answer of 1 is obtained
A

The ladder method

45
Q

What does LCM stand for?

A

Lowest common multiple

46
Q

Define the term ‘lowest common multiple’.

A

The lowest common multiple is the lowest multiple which is common to two or more numbers.

47
Q

Which method do we use to determine the LCM?

A

The ladder method to determine the prime factors of each number.
The LCM is the product of each base with the highest exponent.

48
Q

Which method do we use to determine the HCF?

A

The ladder method to determine the prime factors of each number.
The HCF will always be the product of the bases which are common to both numbers with the lowest exponent.

49
Q

What is the rule for bases when calculating HCF?

A

The bases MUST be common.

50
Q

What is the rule for bases when calculating LCM?

A

All the bases must be used regardless of whether they are common or not.

51
Q

Define the term ‘rounding off’.

A

Rounding off means that you change a number to a more convenient value.

52
Q

What is the rule for rounding off numbers.

A

If the digit of the number is below a 5 you round down by dropping all the digits to the right of the digit while keeping the number the same.
If the digit is equal to or higher than a 5 you round up by adding 1 to the number you are rounding off and dropping all the numbers to the right of it.

53
Q

Define the term ‘ratio’.

A

A ratio is the comparative value of two or more amounts.

54
Q

How is a ratio written?

A

It can be written as 10:20 or as a fraction.

55
Q

How do you write a ratio in its simplest form?

A
  1. Determine the HCF for all the numbers.

2. Divide each number by the HCF

Grade 8 Mathematics (1 decks)

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