Ordering fractions worksheet with ten sets of unlike fractions to arrange in increasing order.

Let’s solve each set of fractions by ordering them from smallest to largest (increasing order).

To compare unlike fractions, we need to find a common denominator — usually the Least Common Denominator (LCD) — so we can rewrite all fractions with the same bottom number. Then we just compare the top numbers (numerators).

We’ll go one problem at a time.

---

Problem 1:
Fractions:
3/4, 2/6, 1/12, 5/18, 4/9

Step 1: Find LCD of denominators: 4, 6, 12, 18, 9
Prime factors:
- 4 = 2²
- 6 = 2×3
- 12 = 2²×3
- 18 = 2×3²
- 9 = 3²
→ LCD = 2² × 3² = 4 × 9 = 36

Convert each fraction to have denominator 36:

- 3/4 = (3×9)/(4×9) = 27/36
- 2/6 = (2×6)/(6×6) = 12/36? Wait — 6×6=36, but 2×6=12 → yes, 12/36
But actually, 2/6 simplifies to 1/3 first? Let’s not simplify — convert directly.

Actually, better to use equivalent fractions properly:

- 3/4 = ?/36 → 36 ÷ 4 = 9 → 3×9 = 27 → 27/36
- 2/6 = ?/36 → 36 ÷ 6 = 6 → 2×6 = 12 → 12/36
- 1/12 = ?/36 → 36 ÷ 12 = 3 → 1×3 = 3 → 3/36
- 5/18 = ?/36 → 36 ÷ 18 = 2 → 5×2 = 10 → 10/36
- 4/9 = ?/36 → 36 ÷ 9 = 4 → 4×4 = 16 → 16/36

Now list numerators: 27, 12, 3, 10, 16

Order: 3, 10, 12, 16, 27 → corresponding fractions:

1/12, 5/18, 2/6, 4/9, 3/4

✔ Check: 1/12 ≈ 0.083, 5/18≈0.277, 2/6≈0.333, 4/9≈0.444, 3/4=0.75 → correct!

---

Problem 2:
Fractions: 4/8, 7/16, 5/12, 1/8, 3/12

Simplify where possible to make easier:

- 4/8 = 1/2
- 3/12 = 1/4
So now: 1/2, 7/16, 5/12, 1/8, 1/4

Find LCD of 2, 16, 12, 8, 4

Factors:
- 2 = 2
- 16 = 2⁴
- 12 = 2²×3
- 8 = 2³
- 4 = 2²
→ LCD = 2⁴ × 3 = 16×3 = 48

Convert:

- 1/2 = 24/48
- 7/16 = (7×3)/(16×3) = 21/48
- 5/12 = (5×4)/(12×4) = 20/48
- 1/8 = 6/48
- 1/4 = 12/48

Numerators: 24, 21, 20, 6, 12 → ordered: 6, 12, 20, 21, 24

Corresponding fractions: 1/8, 1/4, 5/12, 7/16, 1/2

But original fractions were: 4/8, 7/16, 5/12, 1/8, 3/12 → so write back in original form:

1/8, 3/12, 5/12, 7/16, 4/8

Wait — 3/12 is same as 1/4, and 4/8 is same as 1/2 — but since question says “order each set”, we should keep original forms unless told otherwise. But for correctness, let’s check values:

Originals:
- 4/8 = 0.5
- 7/16 = 0.4375
- 5/12 ≈ 0.4167
- 1/8 = 0.125
- 3/12 = 0.25

Ordered: 0.125, 0.25, 0.4167, 0.4375, 0.5 → so:

1/8, 3/12, 5/12, 7/16, 4/8 ✔

---

Problem 3:
Fractions: 3/8, 1/4, 4/10, 3/6, 5/8

Simplify:
- 4/10 = 2/5
- 3/6 = 1/2

So: 3/8, 1/4, 2/5, 1/2, 5/8

LCD of 8,4,5,2,8 → LCM(8,4,5,2)

8=2³, 4=2², 5=5, 2=2 → LCD = 2³×5 = 8×5 = 40

Convert:

- 3/8 = 15/40
- 1/4 = 10/40
- 2/5 = 16/40
- 1/2 = 20/40
- 5/8 = 25/40

Numerators: 15,10,16,20,25 → ordered: 10,15,16,20,25

Fractions: 1/4, 3/8, 2/5, 1/2, 5/8

Back to originals: 1/4, 3/8, 4/10, 3/6, 5/8 ✔

Check decimals: 0.25, 0.375, 0.4, 0.5, 0.625 → correct.

---

Problem 4:
Fractions: 2/5, 9/15, 8/10, 7/20, 1/5

Simplify:
- 9/15 = 3/5
- 8/10 = 4/5

So: 2/5, 3/5, 4/5, 7/20, 1/5

All fifths except 7/20.

LCD of 5 and 20 → 20

Convert:

- 2/5 = 8/20
- 3/5 = 12/20
- 4/5 = 16/20
- 7/20 = 7/20
- 1/5 = 4/20

Numerators: 8,12,16,7,4 → ordered: 4,7,8,12,16

Fractions: 1/5, 7/20, 2/5, 9/15, 8/10

Originals: 1/5, 7/20, 2/5, 9/15, 8/10 ✔

Decimals: 0.2, 0.35, 0.4, 0.6, 0.8 → correct.

---

Problem 5:
Fractions: 4/9, 9/12, 5/6, 3/18, 1/3

Simplify:
- 9/12 = 3/4
- 3/18 = 1/6

So: 4/9, 3/4, 5/6, 1/6, 1/3

LCD of 9,4,6,6,3 → LCM(9,4,6,3)

9=3², 4=2², 6=2×3, 3=3 → LCD = 2²×3² = 4×9 = 36

Convert:

- 4/9 = 16/36
- 3/4 = 27/36
- 5/6 = 30/36
- 1/6 = 6/36
- 1/3 = 12/36

Numerators: 16,27,30,6,12 → ordered: 6,12,16,27,30

Fractions: 1/6, 1/3, 4/9, 3/4, 5/6

Originals: 3/18, 1/3, 4/9, 9/12, 5/6 ✔

Decimals: ~0.166, 0.333, ~0.444, 0.75, ~0.833 → correct.

---

Problem 6:
Fractions: 5/8, 7/16, 3/4, 1/4, 12/24

Simplify:
- 12/24 = 1/2

So: 5/8, 7/16, 3/4, 1/4, 1/2

LCD of 8,16,4,4,2 → 16

Convert:

- 5/8 = 10/16
- 7/16 = 7/16
- 3/4 = 12/16
- 1/4 = 4/16
- 1/2 = 8/16

Numerators: 10,7,12,4,8 → ordered: 4,7,8,10,12

Fractions: 1/4, 7/16, 1/2, 5/8, 3/4

Originals: 1/4, 7/16, 12/24, 5/8, 3/4 ✔

Decimals: 0.25, 0.4375, 0.5, 0.625, 0.75 → correct.

---

Problem 7:
Fractions: 7/10, 2/5, 9/20, 5/15, 10/20

Simplify:
- 5/15 = 1/3
- 10/20 = 1/2

So: 7/10, 2/5, 9/20, 1/3, 1/2

LCD of 10,5,20,3,2 → LCM(10,5,20,3,2)

10=2×5, 5=5, 20=2²×5, 3=3, 2=2 → LCD = 2²×3×5 = 4×3×5 = 60

Convert:

- 7/10 = 42/60
- 2/5 = 24/60
- 9/20 = 27/60
- 1/3 = 20/60
- 1/2 = 30/60

Numerators: 42,24,27,20,30 → ordered: 20,24,27,30,42

Fractions: 1/3, 2/5, 9/20, 1/2, 7/10

Originals: 5/15, 2/5, 9/20, 10/20, 7/10 ✔

Decimals: ~0.333, 0.4, 0.45, 0.5, 0.7 → correct.

---

Problem 8:
Fractions: 9/15, 5/12, 7/18, 4/9, 1/6

Simplify:
- 9/15 = 3/5

So: 3/5, 5/12, 7/18, 4/9, 1/6

LCD of 5,12,18,9,6

Factor:
- 5 = 5
- 12 = 2²×3
- 18 = 2×3²
- 9 = 3²
- 6 = 2×3
→ LCD = 2² × 3² × 5 = 4×9×5 = 180

Convert:

- 3/5 = (3×36)/180 = 108/180
- 5/12 = (5×15)/180 = 75/180
- 7/18 = (7×10)/180 = 70/180
- 4/9 = (4×20)/180 = 80/180
- 1/6 = 30/180

Numerators: 108,75,70,80,30 → ordered: 30,70,75,80,108

Fractions: 1/6, 7/18, 5/12, 4/9, 3/5

Originals: 1/6, 7/18, 5/12, 4/9, 9/15 ✔

Decimals: ~0.166, ~0.388, ~0.416, ~0.444, 0.6 → correct.

---

Problem 9:
Fractions: 4/9, 2/6, 15/21, 7/12, 9/18

Simplify:
- 2/6 = 1/3
- 15/21 = 5/7
- 9/18 = 1/2

So: 4/9, 1/3, 5/7, 7/12, 1/2

LCD of 9,3,7,12,2

Factors:
- 9=3²
- 3=3
- 7=7
- 12=2²×3
- 2=2
→ LCD = 2² × 3² × 7 = 4×9×7 = 252

Convert:

- 4/9 = (4×28)/252 = 112/252
- 1/3 = 84/252
- 5/7 = (5×36)/252 = 180/252
- 7/12 = (7×21)/252 = 147/252
- 1/2 = 126/252

Numerators: 112,84,180,147,126 → ordered: 84,112,126,147,180

Fractions: 1/3, 4/9, 1/2, 7/12, 5/7

Originals: 2/6, 4/9, 9/18, 7/12, 15/21 ✔

Decimals: ~0.333, ~0.444, 0.5, ~0.583, ~0.714 → correct.

---

Problem 10:
Fractions: 1/25, 7/15, 9/25, 3/10, 2/5

LCD of 25,15,25,10,5

Factors:
- 25=5²
- 15=3×5
- 10=2×5
- 5=5
→ LCD = 2×3×5² = 2×3×25 = 150

Convert:

- 1/25 = 6/150
- 7/15 = 70/150
- 9/25 = 54/150
- 3/10 = 45/150
- 2/5 = 60/150

Numerators: 6,70,54,45,60 → ordered: 6,45,54,60,70

Fractions: 1/25, 3/10, 9/25, 2/5, 7/15

Originals: 1/25, 3/10, 9/25, 2/5, 7/15 ✔

Decimals: 0.04, 0.3, 0.36, 0.4, ~0.466 → correct.

---

Final Answer:

1) 1/12, 5/18, 2/6, 4/9, 3/4
2) 1/8, 3/12, 5/12, 7/16, 4/8
3) 1/4, 3/8, 4/10, 3/6, 5/8
4) 1/5, 7/20, 2/5, 9/15, 8/10
5) 3/18, 1/3, 4/9, 9/12, 5/6
6) 1/4, 7/16, 12/24, 5/8, 3/4
7) 5/15, 2/5, 9/20, 10/20, 7/10
8) 1/6, 7/18, 5/12, 4/9, 9/15
9) 2/6, 4/9, 9/18, 7/12, 15/21
10) 1/25, 3/10, 9/25, 2/5, 7/15