Gr 9 MATH: Ch 1 Sum WHOLE NUMBERS
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Questions and Answers

What is the result of adding two or more natural numbers?

  • A whole number or an integer
  • A natural number only (correct)
  • An integer or a rational number
  • A natural number or zero

    • What is the purpose of 0 in the system of whole numbers?

  • To write numbers that are multiples of 10
  • To write negative numbers
  • To write numbers that are not possible without it (correct)
  • To represent a special symbol for 10

    • What is the identity element for addition in the system of whole numbers?

  • Any number
  • 0 (correct)
  • -1
  • 1

    • What is the result of subtracting a natural number from another natural number that is smaller than itself?

    <p>Not always a natural number</p> Signup and view all the answers

    What is the characteristic of the system of integers that allows for the existence of negative numbers?

    <p>The system extends whole numbers to include negative numbers</p> Signup and view all the answers

    What is the result of the sum of two integers?

    <p>Can be zero</p> Signup and view all the answers

    What is the characteristic of each integer?

    <p>It has an additive inverse</p> Signup and view all the answers

    What are rational numbers?

    <p>Numbers that can be expressed as the quotient of two integers</p> Signup and view all the answers

    What are examples of irrational numbers?

    <p>√2, √5, π</p> Signup and view all the answers

    What is the set of real numbers composed of?

    <p>Rational and irrational numbers</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

    <p>To get close to an answer without performing precise calculations</p> Signup and view all the answers

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest Common Factor</p> Signup and view all the answers

    What is the formula to calculate the average speed of a journey?

    <p>Average speed = Distance / Time</p> Signup and view all the answers

    What is the term for the process of expressing a number as a product of its prime factors?

    <p>Prime Factorization</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

    <p>To correct for errors introduced by rounding</p> Signup and view all the answers

    What is the term for the total amount paid in a hire purchase, including the deposit and the total of instalments, and the interest?

    <p>Total HP Price</p> Signup and view all the answers

    What is the term for a common multiple of two or more numbers that is the smallest of all common multiples?

    <p>Lowest Common Multiple</p> Signup and view all the answers

    What is the formula to calculate the time taken for a journey?

    <p>Time = Distance / Average speed</p> Signup and view all the answers

    What is the term for the process of collecting apples at a certain rate per minute?

    <p>Collecting Apples</p> Signup and view all the answers

    What is the term for the interest calculated on the principal amount without adding the interest to the principal each year?

    <p>Simple Interest</p> Signup and view all the answers

    What is the main difference between natural numbers and whole numbers?

    <p>The inclusion of zero</p> Signup and view all the answers

    Which property of natural numbers states that subtraction is not always possible?

    <p>Not closed under subtraction or division</p> Signup and view all the answers

    What is the characteristic of irrational numbers?

    <p>They cannot be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the relationship between the system of integers and the system of whole numbers?

    <p>The system of integers is a superset of the system of whole numbers</p> Signup and view all the answers

    What is the term for the set of numbers that includes both rational and irrational numbers?

    <p>Real numbers</p> Signup and view all the answers

    What is the purpose of the number 0 in the system of whole numbers?

    <p>To write numbers and represent place value</p> Signup and view all the answers

    Which property of natural numbers states that addition is always possible?

    <p>Closure under addition</p> Signup and view all the answers

    What is the characteristic of rational numbers?

    <p>They can be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the main difference between the system of integers and the system of natural numbers?

    <p>The existence of negative numbers</p> Signup and view all the answers

    What is the relationship between the system of real numbers and the system of rational numbers?

    <p>The system of real numbers is a superset of the system of rational numbers</p> Signup and view all the answers

    What is the purpose of prime factorization in calculating the LCM and HCF of two numbers?

    <p>To identify the common prime factors and multiply them</p> Signup and view all the answers

    What is the result of multiplying the numbers 24 and 36 by their prime factors?

    <p>The product of their prime factors</p> Signup and view all the answers

    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?

    <p>4:5</p> Signup and view all the answers

    What is the formula to calculate the average speed of a journey with different sections?

    <p>Average speed = Total distance / Total time</p> Signup and view all the answers

    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?

    <p>5:2</p> Signup and view all the answers

    What is the result of compensating for errors in calculations?

    <p>The calculation becomes more accurate</p> Signup and view all the answers

    If the marked price of an item is $100, and a 20% discount is applied, what is the selling price?

    <p>$80</p> Signup and view all the answers

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount plus interest</p> Signup and view all the answers

    What is the purpose of dividing the number step-by-step in long division?

    <p>To subtract multiples of the divisor from the dividend</p> Signup and view all the answers

    What is the result of subtracting a multiple of the divisor from the dividend in long division?

    <p>The dividend is reduced</p> Signup and view all the answers

    Which of the following statements about the natural numbers is NOT true?

    <p>The difference of two natural numbers is always a natural number.</p> Signup and view all the answers

    What is a characteristic that distinguishes the system of whole numbers from the system of natural numbers?

    <p>The inclusion of zero</p> Signup and view all the answers

    Which of the following is an example of an irrational number?

    <p>The square root of 2</p> Signup and view all the answers

    What is a property of the system of integers that is not true for the system of natural numbers?

    <p>The existence of additive inverses</p> Signup and view all the answers

    Which of the following statements about the system of real numbers is true?

    <p>It includes both rational and irrational numbers</p> Signup and view all the answers

    What is a difference between the system of whole numbers and the system of natural numbers?

    <p>The system of whole numbers includes zero</p> Signup and view all the answers

    Which of the following is a characteristic of rational numbers?

    <p>They can be expressed as a fraction of two integers</p> Signup and view all the answers

    What is a common property of the system of natural numbers, whole numbers, and integers?

    <p>Closure under addition and multiplication</p> Signup and view all the answers

    Which of the following is NOT a type of number?

    <p>Fractional number</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

    <p>They cannot be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the main advantage of using compensation when estimating?

    <p>It reduces the error introduced by rounding</p> Signup and view all the answers

    What is the least common multiple of 12 and 15?

    <p>60</p> Signup and view all the answers

    A recipe requires a ratio of 3:5 of flour to sugar. If 15 kg of flour is used, how much sugar is required?

    <p>25 kg</p> Signup and view all the answers

    What is the highest common factor of 24 and 36?

    <p>6</p> Signup and view all the answers

    A person travels 120 km at an average speed of 40 km/h. How much time did they take to travel?

    <p>4 hours</p> Signup and view all the answers

    A shopkeeper sells an item at a 20% discount. If the marked price is $100, what is the selling price?

    <p>$90</p> Signup and view all the answers

    What is the main difference between simple and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and interest</p> Signup and view all the answers

    What is the purpose of long division?

    <p>To divide a number step-by-step</p> Signup and view all the answers

    What is the ratio of the numbers of apples collected by Moeneba and Garth?

    <p>5:12</p> Signup and view all the answers

    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?

    <p>$1,500</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

    <p>To get a close approximation of the answer</p> Signup and view all the answers

    What is the result of multiplying a number by its prime factors?

    <p>The prime factorization of the number</p> Signup and view all the answers

    What is the formula to calculate the distance traveled?

    <p>Distance = Average speed × Time</p> Signup and view all the answers

    What is the purpose of long division?

    <p>To divide a number step-by-step</p> Signup and view all the answers

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and the interest</p> Signup and view all the answers

    What is the purpose of finding the lowest common multiple of two numbers?

    <p>To find the common multiple of the two numbers that is the smallest of all common multiples</p> Signup and view all the answers

    What is the result of compensating for errors in calculations?

    <p>The correction of errors introduced by rounding</p> Signup and view all the answers

    What is the purpose of finding the highest common factor of two numbers?

    <p>To find the largest number that divides each of the two numbers without leaving a remainder</p> Signup and view all the answers

    What is the result of multiplying the numbers 24 and 36 by their prime factors?

    <p>The product of the prime factors of the two numbers</p> Signup and view all the answers

    What is the purpose of calculating the ratio of apples collected by Garth and Kate?

    <p>To compare the rates of collecting apples</p> Signup and view all the answers

    Which property of natural numbers is not true for subtraction and division?

    <p>Not always possible</p> Signup and view all the answers

    What is the main difference between the system of whole numbers and the system of natural numbers?

    <p>The presence of 0</p> Signup and view all the answers

    What is the result of multiplying two or more natural numbers?

    <p>Always a natural number</p> Signup and view all the answers

    What is the characteristic of the system of whole numbers that is not true for the system of natural numbers?

    <p>Presence of 0</p> Signup and view all the answers

    What is the set of numbers that includes both rational and irrational numbers?

    <p>The set of real numbers</p> Signup and view all the answers

    What is the characteristic of the system of integers that is not true for the system of natural numbers?

    <p>Presence of negative numbers</p> Signup and view all the answers

    What is the result of adding 0 to a whole number?

    <p>The same number</p> Signup and view all the answers

    What is the characteristic of irrational numbers that distinguishes them from rational numbers?

    <p>They cannot be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the relationship between the system of integers and the system of whole numbers?

    <p>The system of whole numbers is a subset of the system of integers</p> Signup and view all the answers

    What is the characteristic of the system of real numbers that is not true for the system of rational numbers?

    <p>They include irrational numbers</p> Signup and view all the answers

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