- Order and the Inequality Symbols
- Comparing Fractions
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to compare fractions. By the end of the module students should be able to understand ordering of numbers and be familiar with grouping symbols and compare two or more fractions.
Our number system is called an ordered number system because the numbers in the system can be placed in order from smaller to larger. This is easily seen on the number line.
On the number line, a number that appears to the right of another number is larger than that other number. For example, 5 is greater than 2 because 5 is located to the right of 2 on the number line. We may also say that 2 is less than 5.
To make the inequality phrases "greater than" and "less than" more brief, mathematicians represent them with the symbols > and <, respectively.
> represents the phrase "greater than."
< represents the phrase "less than."
5 > 2 represents "5 is greater than 2."
2 < 5 represents "2 is less than 5."
Recall that the fraction
We have just observed that when two fractions have the same denominator, we can determine which is larger by comparing the numerators.
If two fractions have the same denominators, the fraction with the larger numerator is the larger fraction.
Thus, to compare the sizes of two or more fractions, we need only convert each of them to equivalent fractions that have a common denominator. We then compare the numerators. It is convenient if the common denominator is the LCD. The fraction with the larger numerator is the larger fraction.
Compare
Convert each fraction to an equivalent fraction with the LCD as the denominator. Find the LCD.
Since
Thus
Write
Convert each fraction to an equivalent fraction with the LCD as the denominator.
Find the LCD.
Since
Writing these numbers in order from smallest to largest, we get
Compare
To compare mixed numbers that have different whole number parts, we need only compare whole number parts. Since 6 < 8,
Compare
To compare mixed numbers that have the same whole number parts, we need only compare fractional parts.
Since 14 < 15,
Hence,
Compare
Compare
Write
Compare
Compare
Arrange each collection of numbers in order from smallest to largest.
((Reference)) Round 267,006,428 to the nearest ten million.
270,000,000
((Reference)) Is the number 82,644 divisible by 2? by 3? by 4?
((Reference)) Convert
((Reference)) Find the value of
((Reference)) Find the value of
"Used as supplemental materials for developmental math courses."