Comparing and Ordering Fractions - PowerPoint | Maths Year 5 - Free Printable

We are given three fractions to compare and order:

- $ \frac{2}{3} $
- $ \frac{8}{9} $
- $ \frac{5}{6} $

We need to put them in order — probably from smallest to largest (unless otherwise stated, this is the usual convention for “ordering”).

Step 1: Find a common denominator

To compare fractions easily, we can convert them to have the same denominator.

The denominators are: 3, 9, and 6.
Find the least common denominator (LCD):

- Multiples of 3: 3, 6, 9, 12, 15, 18, ...
- Multiples of 6: 6, 12, 18, ...
- Multiples of 9: 9, 18, ...

So the LCD is 18.

Step 2: Convert each fraction to eighteenths

- $ \frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18} $
- $ \frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18} $
- $ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} $

Now we have:
- $ \frac{12}{18} $
- $ \frac{16}{18} $
- $ \frac{15}{18} $

Step 3: Compare numerators

Since all denominators are the same (18), just compare the numerators:

- 12 < 15 < 16

So:
- $ \frac{12}{18} < \frac{15}{18} < \frac{16}{18} $

Which means:
- $ \frac{2}{3} < \frac{5}{6} < \frac{8}{9} $

Let me double-check using decimals (just to be sure):

- $ \frac{2}{3} \approx 0.666... $
- $ \frac{5}{6} \approx 0.833... $
- $ \frac{8}{9} \approx 0.888... $

Yes — 0.666 < 0.833 < 0.888 → same order.

Final Answer:
$ \frac{2}{3} < \frac{5}{6} < \frac{8}{9} $