Compare rational numbers

Learning Objectives Define rational numbers and identify examples. Represent rational numbers on a number line. Compare any two positive rational numbers using various strategies. Compare any two negative rational numbers using various strategies. Compare rational numbers with different signs. Use inequality symbols (<, >, =) correctly to express comparisons. Order a set of three or more rational numbers from least to greatest or greatest to least. Ever wondered who has a better batting average in baseball, or which stock performed better? ⚾️📈 Comparing numbers helps us make sense of the world! In this lesson, you'll learn how to compare rational numbers, whether they're fractions, decimals, or integers. Understanding how to compare these numbers is a fu...

TermDefinitionExample Rational NumberA number that can be expressed as a fraction \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\). This includes integers, fractions, and terminating or repeating decimals.\(\frac{1}{2}\), \(-3\), \(0.75\), \(0.\overline{3}\) NumeratorThe top number in a fraction, which indicates how many parts of the whole are being considered.In the fraction \(\frac{3}{4}\), the numerator is \(3\). DenominatorThe bottom number in a fraction, which indicates the total number of equal parts the whole is divided into.In the fraction \(\frac{3}{4}\), the denominator is \(4\). Number LineA visual representation of numbers as points on a straight line, ordered from least to greatest. Numbers to the right are greater, and numbers to the left are smaller.Plott...

Comparing Positive Rational Numbers If \(a\) and \(b\) are positive rational numbers, then \(a > b\) if \(a\) is to the right of \(b\) on the number line. To compare fractions, convert them to a common denominator or decimal form. When comparing two positive rational numbers, the one with the larger value is greater. For fractions, make sure they have the same denominator or convert them to decimals to compare their magnitudes directly. Comparing Negative Rational Numbers If \(a\) and \(b\) are negative rational numbers, then \(a > b\) if \(|a| < |b|\). In other words, the negative number closer to zero is greater. For negative numbers, the number that is 'less negative' (closer to zero on the number line) is actually greater. For example, \(-2 > -5\) b...