Comparing and Ordering fractions. Steps|Examples

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In comparing and ordering fractions of the same quantity, we often use the symbols > and < to indicate how the numbers are compared in size.

< simply means “less than” or is “smaller than” and the symbol > means “greater than” or “larger than”

Let’s go straight to looking at how to compare and order fractions.

Steps in comparing and ordering fractions

To compare and order fractions, follow the steps below

Step1: make the given fractions have the same denominator. Fractions with the same denominator are easy to compare

Step2: Then compare the given fractions using the symbols (< less than) and (> greater than) after the fractions are in the same denominator.

Let’s go straight to look at some examples

\text{Example: Compare the following fractions using < or >}. \space\frac{3}{7},\frac{1}{7},\frac{2}{7},\frac{4}{7}

Answer: Since the given fractions have the same denominator or common denominator, simply compare the fractions. Arranging or ordering the fractions in ascending order starting with the smallest and ending with the biggest or largest. Let’s use the example given to arrange them in ascending order of magnitude.

\text{ comparing the fraction using the sign <}\space i.e\space \frac{1}{7}<\frac{2}{7}<\frac{3}{7}<\frac{4}{7}

Now comparing the same fraction in descending order means arranging the fraction in decreasing order of magnitude or largest to smallest. Let’s look at the example below.

\text{comparing it using the sign >}\space i.e \frac{4}{7}>\frac{3}{7}>\frac{2}{7}>\frac{1}{7}

How to compare fractions with different denominators

The fraction that has different denominators are considered to be different fractions and to compare such fractions, write them with the same denominator before you go ahead to compare or order them.

Ways of writing fractions to have the same denominator

There are two ways to find the common denominator of a given fraction

• Multiply all the denominators to get a common denominator. 

\text{Example: Arrange }\space\frac{1}{3},\frac{2}{5},\frac{1}{6}

we can use 3×5×6 =90as the common denominator

\begin{aligned}&\frac{1}{3}=\frac{1×30}{3×30}=\frac{30}{90}\\
&\frac{2}{5}=\frac{2×18}{5×18}=\frac{36}{90}\\
&\frac{1}{6}=\frac{1×15}{6×15}=\frac{15}{90}\end{aligned}

we can now arrange the given fractions in order of size, because all of them now has the same denominator.

\text{Arranging the fractions in ascending order of magnitude }\space i.e\space \frac{1}{6}<\frac{1}{3}<\frac{2}{5}

• Using the LCM (Lowest common multiple) to find the common denominator of the given fractions. Let’s look at the example below.

\text{Example: Arrange the fractions in descending order} \space\frac{1}{3},\frac{2}{5},\frac{1}{6}

The LCM of 3,5, and 6 is 30. So let’s express the given fractions as a fraction with the same denominator. 

i.e \space \frac{1}{3},\frac{2}{5},\frac{1}{6}=\frac{10}{30},\frac{12}{30},\frac{5}{30}\\
\text{Now arranging the fractions in descending order of magnitude, we have}\space=\frac{2}{5}>\frac{1}{3}>\frac{1}{6}

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