https://file.aiquickdraw.com/mathbot/file/1725891254125a9ujtbzv.jpg

Let's solve the problems in the image one by one:

### 3. Arrange the following fractions in ascending order:

We need to compare the fractions given in each part (a, b, c, d) and arrange them in ascending order. To do this, we can either convert each fraction to a decimal or find a common denominator.

#### Part a: 
The fractions are:
\[
\frac{4}{5}, \quad \frac{7}{9}
\]
- \(\frac{4}{5} = 0.8\)
- \(\frac{7}{9} \approx 0.777\)

So, the order is:
\[
\frac{7}{9}, \quad \frac{4}{5}
\]

#### Part b:
The fractions are:
\[
\frac{77}{75}, \quad \frac{41}{36}, \quad \frac{29}{27}
\]
- \(\frac{77}{75} \approx 1.0267\)
- \(\frac{41}{36} \approx 1.1389\)
- \(\frac{29}{27} \approx 1.0741\)

The order is:
\[
\frac{77}{75}, \quad \frac{29}{27}, \quad \frac{41}{36}
\]

#### Part c:
The fractions are:
\[
\frac{13}{27}, \quad \frac{17}{35}, \quad \frac{13}{36}, \quad \frac{12}{25}
\]
- \(\frac{13}{27} \approx 0.4815\)
- \(\frac{17}{35} \approx 0.4857\)
- \(\frac{13}{36} \approx 0.3611\)
- \(\frac{12}{25} = 0.48\)

The order is:
\[
\frac{13}{36}, \quad \frac{12}{25}, \quad \frac{13}{27}, \quad \frac{17}{35}
\]

#### Part d:
The fractions are:
\[
\frac{3}{7}, \quad \frac{4}{9}, \quad \frac{5}{21}, \quad \frac{11}{56}
\]
- \(\frac{3}{7} \approx 0.4286\)
- \(\frac{4}{9} \approx 0.4444\)
- \(\frac{5}{21} \approx 0.2381\)
- \(\frac{11}{56} \approx 0.1964\)

The order is:
\[
\frac{11}{56}, \quad \frac{5}{21}, \quad \frac{3}{7}, \quad \frac{4}{9}
\]

### 4. Arrange the following fractions in descending order:

#### Part a:
The fractions are:
\[
\frac{29}{57}, \quad \frac{31}{35}, \quad \frac{13}{38}
\]
- \(\frac{29}{57} \approx 0.5088\)
- \(\frac{31}{35} \approx 0.8857\)
- \(\frac{13}{38} \approx 0.3421\)

The order is:
\[
\frac{31}{35}, \quad \frac{29}{57}, \quad \frac{13}{38}
\]

#### Part b:
The fractions are:
\[
\frac{19}{23}, \quad \frac{9}{11}, \quad \frac{26}{29}
\]
- \(\frac{19}{23} \approx 0.8261\)
- \(\frac{9}{11} \approx 0.8182\)
- \(\frac{26}{29} \approx 0.8966\)

The order is:
\[
\frac{26}{29}, \quad \frac{19}{23}, \quad \frac{9}{11}
\]

#### Part c:
The fractions are:
\[
\frac{19}{189}, \quad \frac{15}{149}, \quad \frac{95}{949}
\]
- \(\frac{19}{189} \approx 0.1005\)
- \(\frac{15}{149} \approx 0.1007\)
- \(\frac{95}{949} \approx 0.1001\)

The order is:
\[
\frac{15}{149}, \quad \frac{19}{189}, \quad \frac{95}{949}
\]

#### Part d:
The fractions are:
\[
\frac{20}{123}, \quad \frac{4}{129}, \quad \frac{26}{721}
\]
- \(\frac{20}{123} \approx 0.1626\)
- \(\frac{4}{129} \approx 0.0310\)
- \(\frac{26}{721} \approx 0.0361\)

The order is:
\[
\frac{20}{123}, \quad \frac{26}{721}, \quad \frac{4}{129}
\]

---

Would you like further details on any of these steps? Here are some related questions to deepen understanding:

1. How can we compare fractions without converting to decimals?
2. What are the advantages of finding common denominators versus converting to decimals?
3. How do improper fractions affect the comparison process?
4. Can you explain how to quickly estimate fractions without calculating exact values?
5. Why do some fractions have repeating decimal representations?

**Tip**: When comparing fractions with large denominators, converting them into decimals is often faster than finding common denominators.

Arrange the following fractions in ascending and descending order based on the given problems.

Learn how to arrange fractions in ascending and descending order by converting them to decimal form or finding a common denominator. This problem involves comparing fractions like 4/5, 7/9, and others, using basic fraction concepts. Suitable for students in Grades 6-8.

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