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 (B)

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

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

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

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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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