Let's solve the problem step by step based on the worksheet you've provided.
---
Objective:
Order fractions with the
same denominator in either
ascending or
descending order.
---
## 🔷 Part 1: Order in
Ascending Order (smallest to largest)
We are given several groups of fractions with the same denominator. Since the denominators are the same, we only need to compare the
numerators — the larger the numerator, the larger the fraction.
---
Group 1: Denominator = 5
Fractions:
- $ \frac{1}{5} $, $ \frac{3}{5} $, $ \frac{5}{5} $, $ \frac{2}{5} $
Compare numerators: 1, 3, 5, 2
Ordered numerators: 1 < 2 < 3 < 5
✔ Ascending order:
$$
\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{5}{5}
$$
---
Group 2: Denominator = 8
Fractions:
- $ \frac{5}{8} $, $ \frac{3}{8} $, $ \frac{7}{8} $, $ \frac{4}{8} $
Numerators: 5, 3, 7, 4
Ordered: 3 < 4 < 5 < 7
✔ Ascending order:
$$
\frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{7}{8}
$$
---
Group 3: Denominator = 12
Fractions:
- $ \frac{12}{12} $, $ \frac{11}{12} $, $ \frac{5}{12} $, $ \frac{9}{12} $
Numerators: 12, 11, 5, 9
Ordered: 5 < 9 < 11 < 12
✔ Ascending order:
$$
\frac{5}{12}, \frac{9}{12}, \frac{11}{12}, \frac{12}{12}
$$
---
## 🔷 Part 2: Order in
Descending Order (largest to smallest)
Now we sort from largest to smallest.
---
Group 4: Denominator = 6
Fractions:
- $ \frac{2}{6} $, $ \frac{1}{6} $, $ \frac{5}{6} $, $ \frac{3}{6} $
Numerators: 2, 1, 5, 3
Ordered descending: 5 > 3 > 2 > 1
✔ Descending order:
$$
\frac{5}{6}, \frac{3}{6}, \frac{2}{6}, \frac{1}{6}
$$
---
Group 5: Denominator = 7
Fractions:
- $ \frac{4}{7} $, $ \frac{2}{7} $, $ \frac{7}{7} $, $ \frac{6}{7} $
Numerators: 4, 2, 7, 6
Ordered descending: 7 > 6 > 4 > 2
✔ Descending order:
$$
\frac{7}{7}, \frac{6}{7}, \frac{4}{7}, \frac{2}{7}
$$
---
Group 6: Denominator = 4
Fractions:
- $ \frac{3}{4} $, $ \frac{2}{4} $, $ \frac{1}{4} $, $ \frac{4}{4} $
Numerators: 3, 2, 1, 4
Ordered descending: 4 > 3 > 2 > 1
✔ Descending order:
$$
\frac{4}{4}, \frac{3}{4}, \frac{2}{4}, \frac{1}{4}
$$
---
##
✔ Final Answers:
Ascending Order:
1. $ \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{5}{5} $
2. $ \frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{7}{8} $
3. $ \frac{5}{12}, \frac{9}{12}, \frac{11}{12}, \frac{12}{12} $
Descending Order:
4. $ \frac{5}{6}, \frac{3}{6}, \frac{2}{6}, \frac{1}{6} $
5. $ \frac{7}{7}, \frac{6}{7}, \frac{4}{7}, \frac{2}{7} $
6. $ \frac{4}{4}, \frac{3}{4}, \frac{2}{4}, \frac{1}{4} $
---
📝 Explanation:
When fractions have the
same denominator, their size depends
only on the numerator. So:
- To order
ascending: list fractions from smallest numerator to largest.
- To order
descending: list from largest numerator to smallest.
This is a key concept in understanding fractions and helps build fluency and precision in comparing them.
Let me know if you'd like this printed out or turned into a cut-and-paste activity!
Parent Tip: Review the logic above to help your child master the concept of order fractions worksheet.
