Mathematics
Grade 8
15 min
Put rational numbers in order
Put rational numbers in order
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1
Introduction & Learning Objectives
Learning Objectives
Define rational numbers and identify different forms (fractions, decimals, integers).
Convert rational numbers between fraction and decimal forms.
Find a common denominator or common multiple for a set of fractions.
Compare two or more rational numbers using inequality symbols (<, >, =).
Order a set of positive rational numbers from least to greatest or greatest to least.
Order a set of negative rational numbers from least to greatest or greatest to least.
Order a mixed set of positive and negative rational numbers in various forms.
Ever wonder how to tell which slice of pizza is bigger if they're cut differently? 🍕 Or how to compare your test score of 4/5 to your friend's 85%? 🤔
In this lesson, you'll learn how to put rational n...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberA number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q$ is not zero. This includes integers, fractions, and terminating or repeating decimals.$\frac{3}{4}$, $-5$, $0.75$, $2\frac{1}{2}$
NumeratorThe top number in a fraction, representing the number of parts being considered.In the fraction $\frac{3}{5}$, the numerator is $3$.
DenominatorThe bottom number in a fraction, representing the total number of equal parts into which the whole is divided.In the fraction $\frac{3}{5}$, the denominator is $5$.
Common DenominatorA common multiple of the denominators of two or more fractions, used to compare or add/subtract them.For $\frac{1}{2}$ and $\frac{1}{3}$, a common denominator is $6$.
Least Common Multiple (LCM)The...
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Core Formulas
Comparing Fractions with Common Denominators
If two fractions have the same denominator, the fraction with the larger numerator is the greater fraction: If $b > 0$, then $\frac{a}{b} < \frac{c}{b}$ if and only if $a < c$.
This rule allows direct comparison once fractions share a common 'base' or total number of parts.
Comparing Fractions by Finding a Common Denominator
To compare $\frac{a}{b}$ and $\frac{c}{d}$, find the Least Common Denominator (LCD) of $b$ and $d$. Convert both fractions to equivalent fractions with the LCD, then compare their numerators.
This is the primary method for comparing fractions with different denominators. The LCD is usually the LCM of the denominators.
Comparing Rational Numbers by Converting to Decimals
To compare a se...
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, when comparing two fractions like 7/10 and 9/10 that have a common denominator, how do you determine which one is greater?
A.The one with the larger numerator is greater.
B.The one with the smaller numerator is greater.
C.You must convert them to decimals first.
D.You must find a new common denominator.
Easy
What is the essential first step to accurately compare the fractions 2/3 and 3/4?
A.Compare the numerators directly.
B.Find a common denominator for both fractions.
C.Add the numerators and denominators.
D.Assume the fraction with the larger numbers is bigger.
Easy
Which of the following shows the correct order for the numbers 0.5, 0.75, and 0.25 from least to greatest?
A.0.75, 0.5, 0.25
B.0.5, 0.75, 0.25
C.0.25, 0.5, 0.75
D.0.25, 0.75, 0.5
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