Integer Operations and Evaluating Expressions
21 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the result of dividing 204 by 17?

  • 10
  • 12
  • 16
  • 14 (correct)

    • The statement '0 ÷ 32 = 0' is true.

    True (A)

    What is the result of dividing 0 by (-82)?

    0

    The expression (-37) ÷ 0 is __________.

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

    Match the following expressions with their results:

    <p>204 ÷ 17 = 12 0 ÷ 35 = 0 (-37) ÷ 0 = undefined 0 ÷ 0 = undefined</p> Signup and view all the answers

    What is the result of $427 x 8 + 2 x 427$?

    <p>4270 (B)</p> Signup and view all the answers

    The expression $394 x 12 + 394 x (-2)$ simplifies to $394 x (12 - 2)$.

    <p>True (A)</p> Signup and view all the answers

    If the sum of two integers is -15 and one of them is 9, what is the other integer?

    <p>-24 (D)</p> Signup and view all the answers

    What is the result of $558 x 27 + 3 x 558$?

    <p>16740</p> Signup and view all the answers

    The expression $1925 x 101 - 1925$ can be written as $1925 x (101 - ______)$.

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

    The difference between an integer and -6 is equal to 6 when the integer is 0.

    <p>False (B)</p> Signup and view all the answers

    Match the equations to their distributive property forms:

    <p>37 x {8 + (-3)} = 37 x 8 + 37 x (-3) (-82) x {(-4) + 19} = (-82) x (-4) + (-82) x 19 {7 – (-7)} x 7 = 7 x 7 – (-7) x 7 {(-15) – 8} x -6 = (-15) x (-6) – 8 x (-6)</p> Signup and view all the answers

    What is the value of x if the difference between x and -9 is 6?

    <p>-3 or -15</p> Signup and view all the answers

    Which of the following expressions equals $673 x 9 + 673$?

    <p>673 x 10 (B)</p> Signup and view all the answers

    The sum of two integers is -56. If one integer is -42, the other integer is ____.

    <p>-14</p> Signup and view all the answers

    The equation $(-15) – (8) x -6$ equals to $(-15) x (-6) – 8 x (-6)$ is correct.

    <p>False (B)</p> Signup and view all the answers

    Match the following scenarios with their results:

    <p>(-1) multiplied 60 times = 1 (-1) multiplied 75 times = -1 (5) multiplied 0 times = 0 Any number multiplied by -1 an even number of times = 1</p> Signup and view all the answers

    Evaluate the expression $394 x 10$.

    <p>3940</p> Signup and view all the answers

    What is the result of multiplying -2, -3, -4, -5, and -6?

    <p>120 (B)</p> Signup and view all the answers

    The sum of -45 and another integer is 28. The other integer must be positive.

    <p>True (A)</p> Signup and view all the answers

    Evaluate the result of multiplying (-1) 80 times.

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

    Flashcards

    Distributive Property of Multiplication over Addition

    Multiplying a number by the sum of two or more numbers is the same as multiplying the number by each of the numbers individually and then adding the results.

    Distributive Property of Multiplication over Subtraction

    Multiplying a number by the difference of two or more numbers is the same as multiplying the number by each of the numbers individually and then subtracting the results.

    Commutative Property of Addition

    The sum of two or more integers is equal to the sum of the integers in any order.

    Commutative Property of Multiplication

    The product of two or more integers is equal to the product of the integers in any order.

    Signup and view all the flashcards

    Additive Inverse

    The sum of an integer and its additive inverse is zero.

    Signup and view all the flashcards

    Multiplicative Inverse

    The product of an integer and its multiplicative inverse is one.

    Signup and view all the flashcards

    Zero Property of Multiplication

    A number multiplied by zero equals zero.

    Signup and view all the flashcards

    Identity Property of Addition

    The sum of zero and any integer is equal to the integer itself.

    Signup and view all the flashcards

    Difference

    The result of subtracting a smaller number from a larger number. For example, 5 - 3 = 2, where 2 is the difference.

    Signup and view all the flashcards

    Sum of Integers

    A mathematical operation that combines two or more numbers to get a single value. For example, 2 + 3 = 5, where 5 is the sum.

    Signup and view all the flashcards

    Integer

    A whole number that can be positive, negative, or zero. Examples include -3, 0, 5.

    Signup and view all the flashcards

    Order of Operations

    A process that involves multiple steps, where the value within parentheses is calculated first, followed by brackets, then curly braces.

    Signup and view all the flashcards

    Odd Number of Multiplications of (-1)

    Any number multiplied by an odd number of times will result in a negative number.

    Signup and view all the flashcards

    Even Number of Multiplications of (-1)

    Any number multiplied by an even number of times will result in a positive number.

    Signup and view all the flashcards

    Mathematical Expression

    A combination of numbers, symbols, and operations that represents a complete expression.

    Signup and view all the flashcards

    Evaluation

    A numerical value obtained by performing all the operations within a mathematical expression.

    Signup and view all the flashcards

    Dividing by zero

    When dividing any number by 0, the result is undefined. This means that it's not possible to perform the division.

    Signup and view all the flashcards

    Dividing by 1

    Dividing any number by 1 results in the same number.

    Signup and view all the flashcards

    Dividing a number by itself

    Dividing a number by itself always results in 1.

    Signup and view all the flashcards

    Dividing zero by any number

    When dividing 0 by any non-zero number, the result is always 0.

    Signup and view all the flashcards

    Quotient

    The result of division is called the quotient. It represents how many times the divisor goes into the dividend.

    Signup and view all the flashcards

    Study Notes

    Integer Operations

    • Integer operations involve addition, subtraction, multiplication, and division of integers.
    • Multiplication and division of integers follow specific rules regarding the signs.
    • Multiplication: A positive multiplied by a positive or a negative multiplied by a negative results in a positive product. A positive multiplied by a negative results in a negative product.
    • Division: The rules for division of integers are the same as for multiplication of integers.

    Evaluating Expressions

    • Evaluate expressions using the order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
    • Ensure the correct order of solving operations to obtain the correct answer.
    • Pay attention to the grouping of numerical and algebraic expressions and solve according to the order of their grouping.

    Verification

    • Verification involves showing that both sides of an equation or statement result in the same answer.
    • Both sides of equations need to demonstrate equality.

    Positive and Negative Integers

    • Recognize that multiplying or dividing two integers with the same sign produces a positive result.
    • Multiplying or dividing two integers with different signs produces a negative result.
    • The number of negative factors in a calculation influences the sign of the result. An odd number of negative factors results in a negative product; an even number results in a positive product.

    Identifying Greater Values

    • Employ mathematical order of operations (BODMAS/PEMDAS) to evaluate expressions and calculate values.
    • Determine the values of the expressions using the order of evaluating them to establish which one is greater.

    Integer Concepts

    • The product of a set of integers is positive if there is an even number of negative integers.
    • If there is an odd number of negative integers, the product is negative.
    • The product of any integer with zero is always zero.
    • The product of two integers has the same sign if they have the same signs; opposite signs result in a negative sign.
    • The product of a positive integer and a negative integer results in a negative number.

    Dividing Integers

    • Dividing integers involves determining the quotient (result) of an integer when divided by another.
    • Understand that dividing a positive number by a positive number results in a positive quotient.
    • Dividing a negative number by a positive number results in a negative quotient.
    • Dividing a positive number by a negative number results in a negative quotient.
    • Dividing a negative number by a negative number results in a positive quotient.

    Finding Integer Values

    • Determine the missing integer or integers in a set of integers based on mathematical principles and conditions.
    • Understand and apply procedures for solving equations and calculating unknown values accurately, maintaining correct order of operations.

    Integer Order Of Operations

    • Expressions using a mixture of addition, subtraction, multiplication, and division of integers should evaluate expressions according to the order of operations.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Related Documents

    Selina Concise Maths Solutions Class 7 Chapter 1 Integers PDF

    Description

    This quiz covers the fundamental concepts of integer operations including addition, subtraction, multiplication, and division. It also emphasizes the importance of the order of operations as defined by PEMDAS/BODMAS and guides you through the correct methods of evaluating expressions. Test your knowledge and skills in these key mathematical areas!

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser