Mathematics
Grade 9
15 min
Put rational numbers in order
Put rational numbers in order
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1
Introduction & Learning Objectives
Learning Objectives
Convert fractions to decimals and percentages to compare their values.
Find a least common denominator (LCD) to order a set of fractions.
Accurately place rational numbers on a number line to determine their order.
Compare and order sets containing a mix of positive and negative rational numbers.
Order sets of rational numbers presented in different formats (fractions, decimals, integers, mixed numbers).
Apply ordering skills to solve word problems involving rational comparisons.
Which is a better score on a test: 21 out of 25, or 17 out of 20? 🤔 Knowing how to order rational numbers helps you find the answer!
This tutorial will teach you three reliable methods for comparing and ordering any set of rational numbers. Mastering this skill is fundamental f...
2
Key Concepts & Vocabulary
TermDefinitionExample
Rational NumberAny number that can be expressed as a fraction \frac{a}{b}, where 'a' and 'b' are integers and 'b' is not zero. This includes integers, fractions, and terminating or repeating decimals.-5, \frac{3}{4}, 0.25, -1.\overline{3}
Number LineA line on which numbers are marked at intervals. Numbers increase from left to right; a number to the right is always greater than a number to its left.On a number line, -1 is to the right of -2, so -1 > -2.
Least Common Denominator (LCD)The smallest positive integer that is a multiple of the denominators of a given set of fractions. It's also called the Least Common Multiple (LCM) of the denominators.For the fractions \frac{1}{4} and \frac{5}{6}, the LCD is 12.
Equivalent FractionsFr...
3
Core Formulas
Common Denominator Method
To compare \frac{a}{b} and \frac{c}{d}, convert them to equivalent fractions with a common denominator, N. The new fractions will be \frac{a'}{N} and \frac{c'}{N}. Compare the numerators a' and c'.
This is the most reliable method for ordering multiple fractions. Find the LCD, create equivalent fractions, and then order them based on their new numerators.
Decimal Conversion Method
To compare \frac{a}{b} and \frac{c}{d}, convert each fraction to a decimal by dividing the numerator by the denominator (a ÷ b and c ÷ d). Then compare the decimals place by place.
This method is very effective when you have a calculator or when the fractions convert to simple, terminating decimals. It's also useful for comparing fractions and deci...
4 more steps in this tutorial
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Challenging
A submarine is at a depth of -350.75 feet. It then moves to four new positions relative to its start: P1: -350 and 4/5 ft, P2: -350 and 1/2 ft, P3: -351.2 ft, P4: -350.6 ft. Which position is the deepest?
A.P1
B.P2
C.P3
D.P4
Challenging
Which of the following inequality statements is true?
A.-5/6 < -6/7 < -7/8
B.-6/7 < -5/6 < -7/8
C.-7/8 < -5/6 < -6/7
D.-7/8 < -6/7 < -5/6
Challenging
Arrange these numbers from least to greatest: -√9, 13/4, 320%, -10/3.
A.-10/3, -√9, 13/4, 320%
B.-√9, -10/3, 13/4, 320%
C.-10/3, -√9, 320%, 13/4
D.-√9, -10/3, 320%, 13/4
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