https://file.aiquickdraw.com/mathbot/file/1725878520089gcx88hp1.jpg

Let's break down and solve the equations from the image step by step.

### a) \( \frac{4}{12} \div \frac{4}{18} \)

When dividing fractions, we multiply by the reciprocal of the second fraction:

\[
\frac{4}{12} \div \frac{4}{18} = \frac{4}{12} \times \frac{18}{4}
\]

Now, simplify the multiplication:

\[
\frac{4 \times 18}{12 \times 4} = \frac{72}{48}
\]

Simplify the fraction:

\[
\frac{72}{48} = \frac{3}{2}
\]

Thus, the answer is \( \frac{3}{2} \) or 1.5.

---

### d) \( 2 \frac{58}{60} \div 4 \frac{4}{20} \)

First, convert the mixed numbers to improper fractions.

\[
2 \frac{58}{60} = \frac{2 \times 60 + 58}{60} = \frac{178}{60}
\]
\[
4 \frac{4}{20} = \frac{4 \times 20 + 4}{20} = \frac{84}{20}
\]

Now, divide the fractions by multiplying the first by the reciprocal of the second:

\[
\frac{178}{60} \div \frac{84}{20} = \frac{178}{60} \times \frac{20}{84}
\]

Simplify the multiplication:

\[
\frac{178 \times 20}{60 \times 84} = \frac{3560}{5040}
\]

Now simplify the fraction:

\[
\frac{3560}{5040} = \frac{89}{126}
\]

Thus, the answer is \( \frac{89}{126} \).

---

### g) \( 2 \frac{5}{6} \div 4 \frac{2}{9} \)

Convert the mixed numbers to improper fractions.

\[
2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{17}{6}
\]
\[
4 \frac{2}{9} = \frac{4 \times 9 + 2}{9} = \frac{38}{9}
\]

Now divide the fractions by multiplying the first by the reciprocal of the second:

\[
\frac{17}{6} \div \frac{38}{9} = \frac{17}{6} \times \frac{9}{38}
\]

Simplify the multiplication:

\[
\frac{17 \times 9}{6 \times 38} = \frac{153}{228}
\]

Simplify the fraction:

\[
\frac{153}{228} = \frac{51}{76}
\]

Thus, the answer is \( \frac{51}{76} \).

---

Do you have any questions or need further details on any of the steps?

Here are 5 related questions you might find useful:
1. How do you simplify fractions?
2. What is the general method for dividing fractions?
3. How do you convert a mixed number to an improper fraction?
4. How do you multiply fractions?
5. What is the process of finding the reciprocal of a fraction?

**Tip**: Always simplify fractions at the end of your calculations to make the result more readable!

Solve the following: a) 4/12 ÷ 4/18 d) 2 58/60 ÷ 4 4/20 g) 2 5/6 ÷ 4 2/9

Learn how to solve division of fractions and mixed numbers with step-by-step solutions. This example covers dividing fractions and converting mixed numbers to improper fractions.

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