Gr 9 WISKUNDE: Hfst 1 Som HEELGETALLE
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Questions and Answers

What is the set of numbers that we use to count called?

  • Natural Numbers (correct)
  • Whole Numbers
  • Rational Numbers
  • Integers

    • Which of the following operations is not closed under the system of natural numbers?

  • Addition
  • Subtraction (correct)
  • Division (correct)
  • Multiplication

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

  • To represent a negative number
  • To provide a special symbol for counting
  • To write numbers that are multiples of 10
  • To enable the writing of numbers (correct)

    • What is an additive inverse in the system of integers?

    <p>A number that can be added to another number to get 0</p> Signup and view all the answers

    What is a characteristic of rational numbers?

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

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

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

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

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

    Which operation has the identity element 0 in the system of whole numbers?

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

    What is a characteristic of the system of natural numbers?

    <p>It is closed under addition and multiplication</p> Signup and view all the answers

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

    <p>The system of whole numbers includes 0</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 result of multiplying a number by 1, 2, 3, and so on?

    <p>Consecutive multiples of the number</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the formula for calculating average speed?

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

    What is the difference between the HP price and the cash price?

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

    What is the result of calculating the ratio between the numbers of apples collected by different people?

    <p>The ratio of the number of apples collected by each person</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

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

    What is the formula for calculating time?

    <p>Time = Distance / Average speed</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 method of calculating the LCM of two numbers?

    <p>Multiply all the prime factors of both numbers, without repeating any factors unless they appear more than once in one of the numbers</p> Signup and view all the answers

    What is the result of subtracting a natural number from another natural number?

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

    Which of the following is a property of the system of whole numbers?

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

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

    <p>To enable the representation of multiples of 10</p> Signup and view all the answers

    Which of the following is a characteristic of integers?

    <p>The sum of two integers can be zero</p> Signup and view all the answers

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

    <p>The system of integers includes negative numbers</p> Signup and view all the answers

    What is a characteristic of rational numbers?

    <p>They can be expressed as the quotient of two integers</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 a characteristic of irrational numbers?

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

    Which of the following is a property of the system of natural numbers?

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

    What can be said about the system of whole numbers?

    <p>It is closed under addition and multiplication but not under subtraction or division</p> Signup and view all the answers

    What is the main 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 result of subtracting multiples of the divisor from the dividend in long division?

    <p>A quotient with a remainder</p> Signup and view all the answers

    What is the purpose of finding the Lowest Common Multiple (LCM) of two or more numbers?

    <p>To find the common multiples of the numbers</p> Signup and view all the answers

    What is the formula for calculating distance?

    <p>Average speed × 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 simple interest?

    <p>To calculate interest on the principal amount without adding the interest to the principal each year</p> Signup and view all the answers

    What is the purpose of hire purchase?

    <p>To pay a deposit and then make monthly instalments</p> Signup and view all the answers

    What is the result of calculating the ratio of the numbers of apples collected by different people?

    <p>A comparison of their collection rates</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

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

    What is the result of multiplying all the prime factors of two numbers without repeating any factors unless they appear more than once in one of the numbers?

    <p>The Lowest Common Multiple (LCM) of the numbers</p> Signup and view all the answers

    What is true about the system of natural numbers and the system of whole numbers?

    <p>Both systems are closed under addition and multiplication, but not under subtraction and division.</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 difference between the system of integers and the system of whole numbers?

    <p>The system of integers includes negative numbers, but the system of whole numbers does not.</p> Signup and view all the answers

    What can be said about the operation of division in the system of natural numbers?

    <p>It is possible to divide one natural number by another, but the answer may not always be a natural number.</p> Signup and view all the answers

    What is a characteristic of the system of rational numbers?

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

    What is true about the sum of two integers?

    <p>The sum can be zero.</p> Signup and view all the answers

    What is an important property of the identity element for addition in the system of whole numbers?

    <p>When 0 is added to a number, the answer is always the same.</p> Signup and view all the answers

    What can be said about the system of real numbers?

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

    What is true about the operation of subtraction in the system of natural numbers?

    <p>The answer can be a natural number, but not always.</p> Signup and view all the answers

    What is a characteristic of the system of integers?

    <p>It includes both positive and negative numbers, as well as zero.</p> Signup and view all the answers

    When estimating the result of a calculation, which of the following is the most important consideration?

    <p>Using a reasonable approximation</p> Signup and view all the answers

    When multiplying two numbers using column multiplication, what is the purpose of expanding the numbers?

    <p>To ensure accuracy</p> Signup and view all the answers

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

    <p>To determine the common prime factors</p> Signup and view all the answers

    Moeneba collects apples at a rate of 5 apples per minute. If Kate collects apples at a rate of 15 apples per minute, what is the ratio of the numbers of apples collected by Moeneba and Kate?

    <p>1:5</p> Signup and view all the answers

    A biscuit recipe requires 5 parts of flour, 2 parts of oatmeal, and 1 part of cocoa powder. If the recipe requires a total of 18 parts of ingredients, how many parts of flour are needed?

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

    What is the average speed of a person who travels 120 km in 4 hours and then travels 80 km in 2 hours?

    <p>50 km/h</p> Signup and view all the answers

    A shop offers a 10% discount on a product with a marked price of $100. What is the selling price of the product?

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

    If a hire purchase deal involves a deposit of $500 and 12 monthly instalments of $100 each, what is the total HP price?

    <p>$1400</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 and interest</p> Signup and view all the answers

    When finding the LCM of two numbers, what is the purpose of multiplying all the prime factors without repeating any factors unless they appear more than once in one of the numbers?

    <p>To ensure the LCM is the smallest possible value</p> Signup and view all the answers

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

    <p>The system of whole numbers includes 0, whereas the system of natural numbers does not.</p> Signup and view all the answers

    What is a characteristic of the operation of addition in the system of natural numbers?

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

    What is a characteristic of the operation of multiplication in the system of natural numbers?

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

    What is a characteristic of the operation of subtraction in the system of natural numbers?

    <p>The result of subtracting one natural number from another is not always a natural number.</p> Signup and view all the answers

    What is a characteristic of the operation of division in the system of natural numbers?

    <p>The result of dividing one natural number by another is not always a natural number.</p> Signup and view all the answers

    What is a characteristic of the system of integers?

    <p>The system of integers includes both positive and negative numbers, as well as zero.</p> Signup and view all the answers

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

    <p>The identity element for addition is 0.</p> Signup and view all the answers

    What is a characteristic of the system of rational numbers?

    <p>The system of rational numbers includes all numbers that can be expressed as the quotient of two integers.</p> Signup and view all the answers

    What is a characteristic of the system of real numbers?

    <p>The system of real numbers includes both rational and irrational numbers.</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

    <p>Irrational numbers cannot be expressed as the quotient of two integers.</p> Signup and view all the answers

    What is the primary purpose of estimating in calculations?

    <p>To simplify calculations and get an approximate answer</p> Signup and view all the answers

    When finding the LCM of two numbers, what should be done with the prime factors?

    <p>Multiply all the prime factors without repeating any factors</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the formula for calculating average speed?

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

    What is the purpose of compensating for errors in calculations?

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

    What is the formula for calculating distance?

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

    What is the purpose of simple interest?

    <p>To calculate the interest on the principal amount</p> Signup and view all the answers

    What is the purpose of hire purchase?

    <p>To pay a deposit and then make monthly instalments</p> Signup and view all the answers

    What is the result of calculating the ratio between the numbers of apples collected by different people?

    <p>A comparison of their collection rates</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 (HCF)</p> Signup and view all the answers

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