Compare and order rational numbers

Learning Objectives Define and identify rational numbers in various forms (fractions, decimals, integers, percents). Convert rational numbers fluently between fraction and decimal forms. Compare two rational numbers using inequality symbols (<, >, =). Order a set of three or more rational numbers in both ascending and descending order. Accurately locate and plot rational numbers on a number line to visualize their relative values. Apply comparison and ordering skills to solve multi-step word problems. Which is a better deal: a discount of 1/3 off, or a sale of 30% off? 🤔 Knowing how to compare rational numbers helps you make smart choices every day! This tutorial is a review of how to compare and order rational numbers, which include fractions, decimals, and integers...

TermDefinitionExample Rational NumberAny number that can be expressed as a fraction a/b, where 'a' and 'b' are integers and 'b' is not zero. This includes all integers, terminating decimals, and repeating decimals.7, -3/5, 0.6, -2.25, 1/3 (which is 0.333...) IntegerThe set of whole numbers and their opposites.{..., -3, -2, -1, 0, 1, 2, 3, ...} Equivalent FractionsFractions that represent the same value, even though they may have different numerators and denominators.1/2, 2/4, and 50/100 are all equivalent fractions. Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of a given set of fractions. It is also called the Least Common Multiple (LCM) of the denominators.For the fractions 1/4 and 5/6, the LCD is 12. Asc...

Decimal Conversion Method To compare rational numbers, convert them all to their decimal form. This is often the most straightforward method, especially when you have a mix of fractions, decimals, and percents. Once all numbers are in decimal form, compare them by place value from left to right. Common Denominator Method To compare \( \frac{a}{b} \) and \( \frac{c}{d} \), find a common denominator, k. Convert each fraction to an equivalent fraction with denominator k: \( \frac{a'}{k} \) and \( \frac{c'}{k} \). Then, compare the numerators a' and c'. This method is very effective for comparing numbers that are already in fraction form. It avoids potential rounding errors that can occur with decimal conversions of repeating decimals. Cross-Multiplicatio...