80 Questions
What is the result of adding two or more natural numbers?
A natural number only
What is the purpose of 0 in the system of whole numbers?
To write numbers that are not possible without it
What is the identity element for addition in the system of whole numbers?
0
What is the result of subtracting a natural number from another natural number that is smaller than itself?
Not always a natural number
What is the characteristic of the system of integers that allows for the existence of negative numbers?
The system extends whole numbers to include negative numbers
What is the result of the sum of two integers?
Can be zero
What is the characteristic of each integer?
It has an additive inverse
What are rational numbers?
Numbers that can be expressed as the quotient of two integers
What are examples of irrational numbers?
√2, √5, π
What is the set of real numbers composed of?
Rational and irrational numbers
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the term for the largest number that divides each of two or more numbers without leaving a remainder?
Highest Common Factor
What is the formula to calculate the average speed of a journey?
Average speed = Distance / Time
What is the term for the process of expressing a number as a product of its prime factors?
Prime Factorization
What is the purpose of compensating for errors in calculations?
To correct for errors introduced by rounding
What is the term for the total amount paid in a hire purchase, including the deposit and the total of instalments, and the interest?
Total HP Price
What is the term for a common multiple of two or more numbers that is the smallest of all common multiples?
Lowest Common Multiple
What is the formula to calculate the time taken for a journey?
Time = Distance / Average speed
What is the term for the process of collecting apples at a certain rate per minute?
Collecting Apples
What is the term for the interest calculated on the principal amount without adding the interest to the principal each year?
Simple Interest
What is the main difference between natural numbers and whole numbers?
The inclusion of zero
Which property of natural numbers states that subtraction is not always possible?
Not closed under subtraction or division
What is the characteristic of irrational numbers?
They cannot be expressed as a fraction of two integers
What is the relationship between the system of integers and the system of whole numbers?
The system of integers is a superset of the system of whole numbers
What is the term for the set of numbers that includes both rational and irrational numbers?
Real numbers
What is the purpose of the number 0 in the system of whole numbers?
To write numbers and represent place value
Which property of natural numbers states that addition is always possible?
Closure under addition
What is the characteristic of rational numbers?
They can be expressed as a fraction of two integers
What is the main difference between the system of integers and the system of natural numbers?
The existence of negative numbers
What is the relationship between the system of real numbers and the system of rational numbers?
The system of real numbers is a superset of the system of rational numbers
What is the purpose of prime factorization in calculating the LCM and HCF of two numbers?
To identify the common prime factors and multiply them
What is the result of multiplying the numbers 24 and 36 by their prime factors?
The product of their prime factors
If Garth collects apples at a rate of 12 apples per minute, and Kate collects apples at a rate of 15 apples per minute, what is the ratio of apples collected by Garth to Kate?
4:5
What is the formula to calculate the average speed of a journey with different sections?
Average speed = Total distance / Total time
If a biscuit recipe requires 5 parts of flour, 2 parts of oatmeal, and 1 part of cocoa powder, what is the ratio of flour to oatmeal?
5:2
What is the result of compensating for errors in calculations?
The calculation becomes more accurate
If the marked price of an item is $100, and a 20% discount is applied, what is the selling price?
$80
What is the difference between simple interest and compound interest?
Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount plus interest
What is the purpose of dividing the number step-by-step in long division?
To subtract multiples of the divisor from the dividend
What is the result of subtracting a multiple of the divisor from the dividend in long division?
The dividend is reduced
Which of the following statements about the natural numbers is NOT true?
The difference of two natural numbers is always a natural number.
What is a characteristic that distinguishes the system of whole numbers from the system of natural numbers?
The inclusion of zero
Which of the following is an example of an irrational number?
The square root of 2
What is a property of the system of integers that is not true for the system of natural numbers?
The existence of additive inverses
Which of the following statements about the system of real numbers is true?
It includes both rational and irrational numbers
What is a difference between the system of whole numbers and the system of natural numbers?
The system of whole numbers includes zero
Which of the following is a characteristic of rational numbers?
They can be expressed as a fraction of two integers
What is a common property of the system of natural numbers, whole numbers, and integers?
Closure under addition and multiplication
Which of the following is NOT a type of number?
Fractional number
What is a characteristic of irrational numbers?
They cannot be expressed as a fraction of two integers
What is the main advantage of using compensation when estimating?
It reduces the error introduced by rounding
What is the least common multiple of 12 and 15?
60
A recipe requires a ratio of 3:5 of flour to sugar. If 15 kg of flour is used, how much sugar is required?
25 kg
What is the highest common factor of 24 and 36?
6
A person travels 120 km at an average speed of 40 km/h. How much time did they take to travel?
4 hours
A shopkeeper sells an item at a 20% discount. If the marked price is $100, what is the selling price?
$90
What is the main difference between simple and compound interest?
Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and interest
What is the purpose of long division?
To divide a number step-by-step
What is the ratio of the numbers of apples collected by Moeneba and Garth?
5:12
A person buys an item on hire purchase for 10 monthly instalments of $100 each, with a deposit of $500. What is the total HP price?
$1,500
What is the purpose of estimating in calculations?
To get a close approximation of the answer
What is the result of multiplying a number by its prime factors?
The prime factorization of the number
What is the formula to calculate the distance traveled?
Distance = Average speed × Time
What is the purpose of long division?
To divide a number step-by-step
What is the difference between simple interest and compound interest?
Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and the interest
What is the purpose of finding the lowest common multiple of two numbers?
To find the common multiple of the two numbers that is the smallest of all common multiples
What is the result of compensating for errors in calculations?
The correction of errors introduced by rounding
What is the purpose of finding the highest common factor of two numbers?
To find the largest number that divides each of the two numbers without leaving a remainder
What is the result of multiplying the numbers 24 and 36 by their prime factors?
The product of the prime factors of the two numbers
What is the purpose of calculating the ratio of apples collected by Garth and Kate?
To compare the rates of collecting apples
Which property of natural numbers is not true for subtraction and division?
Not always possible
What is the main difference between the system of whole numbers and the system of natural numbers?
The presence of 0
What is the result of multiplying two or more natural numbers?
Always a natural number
What is the characteristic of the system of whole numbers that is not true for the system of natural numbers?
Presence of 0
What is the set of numbers that includes both rational and irrational numbers?
The set of real numbers
What is the characteristic of the system of integers that is not true for the system of natural numbers?
Presence of negative numbers
What is the result of adding 0 to a whole number?
The same number
What is the characteristic of irrational numbers that distinguishes them from rational numbers?
They cannot be expressed as a fraction of two integers
What is the relationship between the system of integers and the system of whole numbers?
The system of whole numbers is a subset of the system of integers
What is the characteristic of the system of real numbers that is not true for the system of rational numbers?
They include irrational numbers
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