Comparing and Ordering Fractions | Elementary

Comparing and Ordering Fractions - Cycle 3

Concept sheet | Mathematics

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How to compare and order fractions with common denominators?
How to compare and order fractions with common numerators?
How to compare and order fractions when the numerators and denominators are different?
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How to compare and order fractions with common denominators?

When the denominators are common (identical), the numerators indicate if one fraction is smaller or larger than another. The larger numerator indicates a larger fraction because more parts are used. Similarly, the smaller numerator indicates a smaller fraction because fewer parts are used.

$Exemple de comparaison de fractions dont les dénominateurs sont communs$

For the fractions |\dfrac{3}{8}|, |\dfrac{5}{8}| and |\dfrac{7}{8}|, the smallest numerator is |3| and the biggest is |7|. Therefore, the ascending order of these fractions is |\dfrac{3}{8}| , |\dfrac{5}{8}| and |\dfrac{7}{8}.|

How to compare and order fractions with common numerators?

When the numerators are common (identical), the denominators indicate if one fraction is smaller or larger than another.

The larger denominator indicates the smaller fraction because the whole is divided into smaller parts. Similarly, the smaller denominator indicates the larger fraction because the whole is divided into larger parts.

$Exemple de comparaison de fractions dont les numérateurs sont communs$

For the fractions |\dfrac{2}{12}| , |\dfrac{2}{6}| and |\dfrac{2}{4}| , the smallest denominator is |4| and the largest is |12| . Therefore, the ascending order of these fractions is |\dfrac{2}{12}| , |\dfrac{2}{6}| and |\dfrac{2}{4}| .

How to compare and order fractions when the numerators and denominators are different?

When the numerators and denominators are different, convert the fractions to equivalent fractions with a common denominator.

Rule

I have to follow these steps to compare and order fractions with different numerators and denominators.

I identify the denominator that is the multiple of the others.
For each fraction that needs to be converted, I find out by what number to multiply each denominator to get a common denominator.
I multiply the numerator of each fraction by the same number that I used for their denominators.
I compare the numerators of the fractions with the common denominators.
I write the result using the initial fractions.

Order the fractions |\dfrac{4}{9}|, |\dfrac{2}{3}| and |\dfrac{3}{18}| in ascending order.

I identify the denominator that is the multiple of the others. \|18\| is a multiple of \|3\| and \|9\|.	$Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents - 1$
To convert the other fractions, I find by what number I can multiply each of their denominators to get a common denominator. I multiply \|9\| by \|2\| to get \|18\| as the denominator. I multiply \|3\| by \|6\| to get \|18\| as the denominator.	$Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents - 2$ $Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents-3$
Then, I multiply the numerator of each fraction that must be converted by the same number that I used for their denominators. I multiply \|4\| by \|2\| and I get \|8\|. I multiply \|2\| by \|6\| and I get \|12\|.	$Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents - 4$ $Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents -5$
I compare the numerators of the fractions with common denominators to put them in ascending order. The numerator \|3\| is smaller than \|8\| and \|12\|. Therefore, \|\dfrac{3}{18}\| is the smallest fraction. The numerator \|8\| is smaller than \|12\|. So, the fraction \|\dfrac{8}{18}\| comes before \|\dfrac{12}{18}\| .	$Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents - 6$ $Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents -7$
I write the result using the initial fractions.	$Exemple de comparaison de fractions lorsque les numérateurs et les dénominateurs sont différents -8$

The ascending order of the fractions is |\dfrac{3}{18}|, |\dfrac{4}{9}| and |\dfrac{2}{3}|.

How to compare and order fractions with common denominators?

How to compare and order fractions with common numerators?

How to compare and order fractions when the numerators and denominators are different?

See Also