Fractions and Algebra
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Questions and Answers

What is the reciprocal of the fraction 2/5?

  • 1/5
  • 2/5
  • 1/2
  • 5/2 (correct)

    • The reciprocal of a fraction is always less than 1.

    False

    What is the result of multiplying a fraction by its reciprocal?

    1

    To simplify a fraction, we need to find the greatest common divisor (GCD) of the _______ and denominator.

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

    Match the following operations with their equivalent fraction operations:

    <p>Addition = Combining like terms with the same denominator Subtraction = Combining like terms with the same denominator Multiplication = Multiplying numerator and denominator by the same number Division = Multiplying by the reciprocal of the divisor</p> Signup and view all the answers

    What do you do to find the reciprocal of a fraction?

    <p>Swap the numerator and denominator</p> Signup and view all the answers

    The result of multiplying a fraction by its reciprocal is always zero.

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

    What is an example of an algebraic expression that can be written as a fraction?

    <p>2/x can be written as the fraction 2/1 × 1/x</p> Signup and view all the answers

    To simplify a fraction, you need to divide both the numerator and denominator by their _______________________.

    <p>greatest common divisor (GCD)</p> Signup and view all the answers

    Match the following with their equivalent operations:

    <p>Multiplying a fraction by its reciprocal = Resulting in 1 Simplifying a fraction = Dividing by the greatest common divisor (GCD) Finding the reciprocal of a fraction = Swapping the numerator and denominator</p> Signup and view all the answers

    You can simplify a fraction by multiplying both the numerator and denominator by the same number.

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

    Study Notes

    Finding Reciprocals

    • To find the reciprocal of a fraction, swap the numerator and denominator.
    • Example: The reciprocal of 3/4 is 4/3.

    Multiplying By Reciprocals

    • Multiplying a fraction by its reciprocal equals 1.
    • Example: (3/4) × (4/3) = 1
    • This property can be used to simplify fractions and solve equations.

    Fractions In Algebra

    • Fractions can be used to represent algebraic expressions.
    • Example: 2/x can be written as 2 × (1/x) or 2/x
    • Fractions can be added, subtracted, multiplied, and divided just like numbers.

    Simplifying Fractions

    • To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
    • Example: Simplify 6/8
      • Find the GCD of 6 and 8, which is 2.
      • Divide both numerator and denominator by 2: 6 ÷ 2 = 3, 8 ÷ 2 = 4
      • Simplified fraction: 3/4

    Finding Reciprocals

    • Swap the numerator and denominator to find the reciprocal of a fraction.
    • For example, the reciprocal of 3/4 is 4/3.

    Multiplying By Reciprocals

    • Multiplying a fraction by its reciprocal results in 1.
    • This property is useful for simplifying fractions and solving equations.
    • Example: (3/4) × (4/3) = 1.

    Fractions In Algebra

    • Fractions can represent algebraic expressions.
    • Example: 2/x can be written as 2 × (1/x) or 2/x.
    • Fractions can be added, subtracted, multiplied, and divided just like numbers.

    Simplifying Fractions

    • To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
    • Steps to simplify a fraction:
      • Find the GCD of the numerator and denominator.
      • Divide both numerator and denominator by the GCD.
    • Example: Simplify 6/8.
      • GCD of 6 and 8 is 2.
      • Divide both numerator and denominator by 2: 6 ÷ 2 = 3, 8 ÷ 2 = 4.
      • Simplified fraction: 3/4.

    Finding Reciprocals

    • To find the reciprocal of a fraction, swap the numerator and denominator.
    • The reciprocal of a whole number is 1 divided by that number.
    • Example: reciprocal of 3/4 is 4/3, and reciprocal of 5 is 1/5.

    Multiplying By Reciprocals

    • Multiplying a fraction by its reciprocal always results in 1.
    • Example: 3/4 × 4/3 = 1.
    • The numerator and denominator cancel each other out when multiplying by reciprocals.

    Fractions In Algebra

    • Fractions can represent algebraic expressions.
    • Example: 2/x can be written as 2/1 × 1/x.
    • Fractions can simplify algebraic expressions and make them easier to work with.

    Simplifying Fractions

    • To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD).
    • Example: 6/8 can be simplified by dividing both numbers by their GCD, which is 2, resulting in 3/4.
    • Simplifying fractions makes them easier to work with and compare.

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    Description

    Learn how to find reciprocals, multiply by reciprocals, and use fractions in algebraic expressions.

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