Classify and Convert Rational Numbers: Fresh Take

  • Recognize rational numbers in a list of numbers
  • Simplify fractions and fractional expressions

Rational Functions

The Main Idea 

Rational numbers are more than just fractions or decimals; they are numbers that can be expressed as a ratio of two integers. This includes all integers, fractions, and even some decimals.

A rational number is a number that can be written in the form [latex]{\Large\frac{p}{q}}[/latex], where [latex]p[/latex] and [latex]q[/latex] are integers and [latex]q\ne o[/latex].

Quick Tips:

  • Converting an Integer to a Fraction: Any integer can be expressed as a fraction by placing it over [latex]1[/latex].
  • Converting an Integer to a Decimal: To convert an integer to a decimal, simply add a decimal point followed by a zero to the integer.
  • Converting Fractions to Decimals: Divide the numerator by the denominator.
  1. Convert the integer [latex]3[/latex] to a rational number.
  2. Convert the decimal [latex]5.28[/latex] to a rational number.
  3. Convert the mixed number [latex]−2\frac{4}{9}[/latex] to a rational number.

You can view the transcript for “What are Rational Numbers? | Number System Concept | Infinity Learn” here (opens in new window).

You can view the transcript for “Rational Numbers” here (opens in new window).

Simplify Fractions

The Main Idea 

Simplifying fractions is more than just reducing numbers; it’s about understanding the essence of a ratio. This skill is crucial for making calculations easier and more understandable. A fraction is considered simplified if there are no common factors in the numerator and denominator. Quick Tips:

  • Simplifying Fractions: Use the Equivalent Fractions Property to remove common factors in the numerator and denominator.
  • Prime Factorization: Use the factor tree method to break down the numerator and denominator into prime factors for easier simplification.

You can view the transcript for “Math Antics – Simplifying Fractions” here (opens in new window).

You can view the transcript for “How to Simplify Fractions | Math with Mr. J” here (opens in new window).

Simplify: [latex]\Large-\frac{18}{24}[/latex]

Simplify: [latex]\Large-\frac{56}{32}[/latex]

Watch the following video to see another example of how to simplify a fraction.

You can view the transcript for “Ex 1: Simplify Fractions” here (opens in new window).

Here’s a video with another example of how to simplify a fraction that contains variables.

You can view the transcript for “Ex 3: Simplify Fractions Containing Variables” here (opens in new window).