- Recognize rational numbers in a list of numbers
- Simplify fractions and fractional expressions
Rational Functions
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.
- Convert the integer [latex]3[/latex] to a rational number.
- Convert the decimal [latex]5.28[/latex] to a rational number.
- 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
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).
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).