Ordering Fractions Worksheets - Math Monks - Free Printable

Explanation:
We need to arrange each set of fractions in ascending order (smallest to largest). To do this, we compare the fractions. The best way is to convert them to decimals (or find a common denominator), but for speed and accuracy, using decimal approximations works well here.

Let’s go one problem at a time.

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Problem 2:
Fractions:
$\frac{4}{7},\ \frac{6}{11},\ \frac{7}{12},\ \frac{3}{17}$

Convert to decimals (approximate):

- $\frac{4}{7} \approx 0.571$
- $\frac{6}{11} \approx 0.545$
- $\frac{7}{12} \approx 0.583$
- $\frac{3}{17} \approx 0.176$

Now order from smallest to largest:

$0.176 < 0.545 < 0.571 < 0.583$
→ $\frac{3}{17},\ \frac{6}{11},\ \frac{4}{7},\ \frac{7}{12}$

✔ Check: Yes — $3/17$ is clearly smallest; $6/11 ≈ 0.545$, $4/7 ≈ 0.571$, $7/12 ≈ 0.583$

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Problem 3:
$\frac{6}{13},\ \frac{1}{3},\ \frac{3}{5},\ \frac{9}{14}$

Decimals:

- $\frac{6}{13} \approx 0.4615$
- $\frac{1}{3} \approx 0.3333$
- $\frac{3}{5} = 0.6$
- $\frac{9}{14} \approx 0.6429$

Order:

$0.3333 < 0.4615 < 0.6 < 0.6429$
→ $\frac{1}{3},\ \frac{6}{13},\ \frac{3}{5},\ \frac{9}{14}$

✔ Check: Correct.

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Problem 4:
$\frac{2}{5},\ \frac{6}{7},\ \frac{11}{12},\ \frac{13}{15}$

Decimals:

- $\frac{2}{5} = 0.4$
- $\frac{6}{7} \approx 0.8571$
- $\frac{11}{12} \approx 0.9167$
- $\frac{13}{15} \approx 0.8667$

Order:

$0.4 < 0.8571 < 0.8667 < 0.9167$
→ $\frac{2}{5},\ \frac{6}{7},\ \frac{13}{15},\ \frac{11}{12}$

Wait — double-check:
$\frac{6}{7} = 0.8571$, $\frac{13}{15} = 0.8667$, so yes, $6/7 < 13/15$.
And $11/12 = 0.9167$ is biggest.

✔ So answer: $\frac{2}{5},\ \frac{6}{7},\ \frac{13}{15},\ \frac{11}{12}$

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Problem 5:
$\frac{5}{9},\ \frac{2}{5},\ \frac{9}{16},\ \frac{15}{17}$

Decimals:

- $\frac{5}{9} \approx 0.5556$
- $\frac{2}{5} = 0.4$
- $\frac{9}{16} = 0.5625$
- $\frac{15}{17} \approx 0.8824$

Order:

$0.4 < 0.5556 < 0.5625 < 0.8824$
→ $\frac{2}{5},\ \frac{5}{9},\ \frac{9}{16},\ \frac{15}{17}$

✔ Correct.

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Problem 6:
$\frac{8}{9},\ \frac{5}{16},\ \frac{13}{18},\ \frac{7}{19}$

Decimals:

- $\frac{8}{9} \approx 0.8889$
- $\frac{5}{16} = 0.3125$
- $\frac{13}{18} \approx 0.7222$
- $\frac{7}{19} \approx 0.3684$

Order:

$0.3125 < 0.3684 < 0.7222 < 0.8889$
→ $\frac{5}{16},\ \frac{7}{19},\ \frac{13}{18},\ \frac{8}{9}$

✔ Check: Yes.

Now write all answers clearly.

Final Answer:
2. $\frac{3}{17},\ \frac{6}{11},\ \frac{4}{7},\ \frac{7}{12}$
3. $\frac{1}{3},\ \frac{6}{13},\ \frac{3}{5},\ \frac{9}{14}$
4. $\frac{2}{5},\ \frac{6}{7},\ \frac{13}{15},\ \frac{11}{12}$
5. $\frac{2}{5},\ \frac{5}{9},\ \frac{9}{16},\ \frac{15}{17}$
6. $\frac{5}{16},\ \frac{7}{19},\ \frac{13}{18},\ \frac{8}{9}$