Algebraic Equations Quiz

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Questions and Answers

What is the additive identity for real numbers?

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

What is the multiplicative inverse of a real number 'a'?

  • 1/a (correct)
  • -a
  • a
  • 2a

What is the result of a + (-a) for any real number 'a'?

  • a
  • 1
  • 0 (correct)
  • -a

Which property ensures that for any two real numbers a and b, ab is also a real number?

<p>Closure law (D)</p> Signup and view all the answers

What is the distributive law of multiplication over addition?

<p>a(b + c) = ab + ac (B)</p> Signup and view all the answers

What is the additive inverse of 3?

<p>-3 (D)</p> Signup and view all the answers

What is the multiplicative identity for real numbers?

<p>1 (B)</p> Signup and view all the answers

What property ensures that between any two real numbers, there exist infinitely many real numbers?

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

What is true about the rational number if both numerator and denominator are either both positive or both negative?

<p>It is a positive rational number (B)</p> Signup and view all the answers

Which of the following is a false statement?

<p>Every rational number is an integer (A)</p> Signup and view all the answers

What type of number is the quotient of two integers?

<p>Always a rational number except when the denominator is 0 (B)</p> Signup and view all the answers

Where are the rational numbers 1 and -1 located on the number line?

<p>On opposite sides of zero (C)</p> Signup and view all the answers

What is the correct statement about rational numbers?

<p>Every natural number is a rational number (D)</p> Signup and view all the answers

Which of the following is true about fractions and rational numbers?

<p>Every fraction is a rational number but every rational number is not a fraction (A)</p> Signup and view all the answers

What is the additive inverse of 4³/5?

<p>-4³/5 (C)</p> Signup and view all the answers

What is the additive inverse of a rational number?

<p>The negative of the rational number (D)</p> Signup and view all the answers

How can you order rational numbers on the number line?

<p>From smallest to largest (A)</p> Signup and view all the answers

Which of the following rational numbers is smallest?

<p>2/3 (C)</p> Signup and view all the answers

What is the sum of 15/15 and 1/5?

<p>3 (C)</p> Signup and view all the answers

Which property of rational numbers states that the sum of two rational numbers is always a rational number?

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

What is the additive identity of 2009?

<p>0 (C)</p> Signup and view all the answers

If p + q = 3f + 6, then what is the value of p + q?

<p>3f + 6 (B)</p> Signup and view all the answers

What is the equivalent rational number of 3/4?

<p>6/8 (D)</p> Signup and view all the answers

Which property of rational numbers states that the order of the numbers being added does not change the result?

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

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Study Notes

Properties of Real Numbers

  • Additive identity: 0 is a real number such that 0 + a = a for every real number 'a'
  • Additive inverse: For each real number 'a', there exists a real number (-a) such that a + (-a) = 0
  • Additive inverse of a number 'a' is denoted by (-a)
  • Closure property: The sum of two real numbers is always a real number
  • Associative property: (a + b) + c = a + (b + c) for all real numbers a, b, c
  • Commutative property: a + b = b + a for all real numbers a and b

Properties of Multiplication

  • Closure property: The product of two real numbers is always a real number
  • Associative property: (ab) c = a(bc) for all real numbers a, b, c
  • Commutative property: ab = ba for all real numbers a and b
  • Multiplicative identity: 1 is a real number such that 1.a = a for every real number 'a'
  • Multiplicative inverse: For each non-zero real number 'a', there exists a real number 1/a such that a × 1/a = 1

Properties of Rational Numbers

  • The sum of two rational numbers is always a rational number
  • The product of two rational numbers is always a rational number
  • Every fraction is a rational number, but every rational number need not be a fraction
  • Every integer is a rational number, but every rational number need not be an integer

Rational Numbers and Fractions

  • If the numerator and denominator are both positive or both negative, then the number is a positive rational number
  • A rational number can be expressed as a fraction, but a fraction may not be a rational number
  • The quotient of two integers is always a rational number, except when the denominator is 0

Number Line

  • Every real number can be represented by a unique point on the number line
  • Every point on the number line corresponds to a unique real number
  • The rational number 1 and -1 are on opposite sides of 0 on the number line

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