Order fractions III
No benchmarks?
You may have seen how we can use benchmarks such as $0$0, $\frac{1}{2}$12 and $1$1to put our fractions in order, by getting a sense of how big our fractions are. We can also compare fractions without using these benchmarks. There are a few types of fractions we can look at.
Comparing fractions
When we compare fractions, the first thing to do is check the denominator of each fraction. If they are the same, we can look at the numerators. But what if they're not? In this video, we'll look at both cases, and find out how to compare fractions either way.
Worked Example
Question 1
Use $<$< or $>$> to complete the following number sentence.
$\frac{1}{9}\editable{}\frac{1}{8}$1918
Mixed numbers and improper fractions
What if we have want to compare mixed fractions to improper fractions? Fear not! We have a plan, so watch how we tackle this type of comparison in this video.
Worked Examples
Question 2
We want to arrange the following fractions in ascending order: $\frac{9}{16}$916, $\frac{11}{112}$11112, $\frac{5}{7}$57
What is the lowest common denominator of the $3$3 fractions?
Rewrite all three fractions with the lowest common denominator between them.
$\frac{5}{7}=\frac{\editable{}}{112}$57=112
$\frac{9}{16}=\frac{\editable{}}{112}$916=112
$\frac{11}{112}=\frac{\editable{}}{112}$11112=112
Hence, which of the following lists the fractions in ascending order?
$\frac{11}{112},\frac{9}{16},\frac{5}{7}$11112,916,57
A$\frac{5}{7},\frac{9}{16},\frac{11}{112}$57,916,11112
B$\frac{9}{16},\frac{11}{112},\frac{5}{7}$916,11112,57
C
Question 3
We want to arrange the following in ascending order:
$2\frac{1}{7}$217, $\frac{33}{14}$3314, $\frac{16}{7}$167
First, rewrite all $3$3 fractions as improper fractions with the common denominator of $14$14.
$2\frac{1}{7}=\frac{\editable{}}{14}$217=14
$\frac{33}{14}=\frac{\editable{}}{14}$3314=14
$\frac{16}{7}=\frac{\editable{}}{14}$167=14
Therefore which of the following lists the fractions in ascending order:
$\frac{16}{7}$167, $2\frac{1}{7}$217, $\frac{33}{14}$3314
A$\frac{33}{14}$3314, $\frac{16}{7}$167, $2\frac{1}{7}$217
B$2\frac{1}{7}$217, $\frac{16}{7}$167, $\frac{33}{14}$3314
C$2\frac{1}{7}$217, $\frac{33}{14}$3314, $\frac{16}{7}$167
D
In order to compare fractions, having the same denominator helps enormously, so you may need to find equivalent fractions if they are not the same. Converting mixed numbers to improper fractions might be needed as well, so remember to think of which steps can help you achieve the same denominators. Then, you're ready to compare, and order, your fractions.