Mathematics Chapter on Negative Numbers and Exponents

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Questions and Answers

What is the result of adding two negative numbers, such as -3 and -4?

-1

-7 (correct)

When adding a negative number and a positive number, what is the correct process?

Add the numbers normally and keep the positive sign.

Subtract the smaller absolute value from the larger and keep the sign of the larger. (correct)

Ignore the signs and subtract the larger from the smaller.

Add their absolute values.

What is the result of multiplying two negative numbers?

Negative

Zero

Positive (correct)

Undefined

Which of the following is true regarding prime numbers?

Prime numbers have only two factors: one and the number itself. Signup and view all the answers

What does LCM stand for and what does it refer to?

Lowest Common Multiple, the smallest shared multiple. Signup and view all the answers

What is the outcome when applying the rules of HCF to the numbers 12 and 15?

3 Signup and view all the answers

Which of the following statements accurately describes the concept of squares and cubes?

A square is a number multiplied by itself and a cube is a number multiplied by itself twice. Signup and view all the answers

Which of the following is an integer?

-7 Signup and view all the answers

Which of the following statements accurately describes composite numbers?

Composite numbers have more than two factors. Signup and view all the answers

What is the correct result of the expression $3 + 2 \times (4^2 - 2)$ following the order of operations?

31 Signup and view all the answers

Which of the following examples correctly illustrates the rule for adding a positive and a negative number?

$5 + (-8) = -3$ Signup and view all the answers

What is the highest common factor (HCF) of 12 and 18?

6 Signup and view all the answers

Which of the following represents a prime number?

7 Signup and view all the answers

What will be the outcome of multiplying two negative numbers?

Positive Signup and view all the answers

Which expression shows the correct order of operations applied to solve $2 + 3 \times 4 - 5$?

9 Signup and view all the answers

What is the square of 5?

25 Signup and view all the answers

Which of the following expressions represents the cube of 3?

$3 \times 3 \times 3$ Signup and view all the answers

Which of the following is NOT a rule for adding negative numbers?

The sum is always zero. Signup and view all the answers

Study Notes

Negative Numbers

Integers include positive whole numbers, zero, and their negative counterparts.
Negative numbers are less than zero.
Adding two negative numbers results in a more negative number. Example: -3 + (-4) = -7
Adding a positive and a negative number involves subtracting the smaller absolute value from the larger, and using the sign of the larger number. Example: 5 + (-8) = -3.
Multiplying two negative numbers results in a positive number. Example: -2 x -3 = 6
Multiplying a negative and a positive number results in a negative number. Example: -2 x 3 = -6

Squares and Cubes

Squaring a number means multiplying it by itself. Example: 3² = 3 x 3 = 9
Cubing a number means multiplying it by itself three times. Example: 2³ = 2 x 2 x 2 = 8

LCM, HCF, and Primes

Lowest Common Multiple (LCM) is the smallest multiple shared by two numbers. Example: LCM of 4 and 6 is 12.
Highest Common Factor (HCF) is the largest factor shared by two or more numbers. Example: HCF of 12 and 18 is 6.
Prime numbers have only two factors: 1 and the number itself. Examples of prime numbers: 2, 3, 5, 7, 11.
Composite numbers have more than two factors. Examples of composite numbers: 4, 6

Order of Operations (BIDMAS/PEMDAS)

Brackets/parentheses: Solve expressions inside the brackets first.
Indices/Exponents: Calculate the exponents next.
Division/Multiplication: Perform multiplication and division from left to right.
Addition/Subtraction: Perform addition and subtraction from left to right.
Example: 3 + 2 x (4² - 2) = 3 + 2 x (16 - 2) = 3 + 2 x 14 = 3 + 28 = 31

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Description

This quiz covers key concepts related to negative numbers, including addition and multiplication rules. It also explores squares and cubes, explaining how to raise numbers to these powers. Additionally, it includes topics on Lowest Common Multiple (LCM), Highest Common Factor (HCF), and prime numbers.