Solve 20/10,30/20,40/30,20/10,40/20,80/40,10/20,5/10 and5/2/5,50/5 and 500/50.Show complete solution

Let's solve each division step by step, showing the complete solution for each:

### 1. \( \frac{20}{10} \)
\[ \frac{20}{10} = 2 \]
*Explanation*: 20 divided by 10 equals 2.

### 2. \( \frac{30}{20} \)
\[ \frac{30}{20} = \frac{3}{2} = 1.5 \]
*Explanation*: Divide the numerator and the denominator by their greatest common divisor, which is 10.

### 3. \( \frac{40}{30} \)
\[ \frac{40}{30} = \frac{4}{3} \approx 1.33 \]
*Explanation*: Divide the numerator and the denominator by their greatest common divisor, which is 10. The fraction simplifies to \( \frac{4}{3} \), which is approximately 1.33 when expressed as a decimal.

### 4. \( \frac{20}{10} \)
\[ \frac{20}{10} = 2 \]
*Explanation*: This is the same as the first problem, so the result is 2.

### 5. \( \frac{40}{20} \)
\[ \frac{40}{20} = 2 \]
*Explanation*: 40 divided by 20 equals 2.

### 6. \( \frac{80}{40} \)
\[ \frac{80}{40} = 2 \]
*Explanation*: 80 divided by 40 equals 2.

### 7. \( \frac{10}{20} \)
\[ \frac{10}{20} = \frac{1}{2} = 0.5 \]
*Explanation*: Simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 10.

### 8. \( \frac{5}{10} \)
\[ \frac{5}{10} = \frac{1}{2} = 0.5 \]
*Explanation*: Similar to the previous problem, simplify by dividing both the numerator and the denominator by their greatest common divisor, which is 5.

### 9. \( \frac{5}{\frac{2}{5}} \)
This is a division of a whole number by a fraction, which is solved by multiplying the whole number by the reciprocal of the fraction:
\[ \frac{5}{\frac{2}{5}} = 5 \times \frac{5}{2} = \frac{25}{2} = 12.5 \]
*Explanation*: Multiply 5 by the reciprocal of \( \frac{2}{5} \) (which is \( \frac{5}{2} \)) to get \( \frac{25}{2} = 12.5 \).

### 10. \( \frac{50}{5} \)
\[ \frac{50}{5} = 10 \]
*Explanation*: 50 divided by 5 equals 10.

### 11. \( \frac{500}{50} \)
\[ \frac{500}{50} = 10 \]
*Explanation*: 500 divided by 50 equals 10.

### Summary of the Solutions:
1. \( \frac{20}{10} = 2 \)
2. \( \frac{30}{20} = 1.5 \)
3. \( \frac{40}{30} \approx 1.33 \)
4. \( \frac{20}{10} = 2 \)
5. \( \frac{40}{20} = 2 \)
6. \( \frac{80}{40} = 2 \)
7. \( \frac{10}{20} = 0.5 \)
8. \( \frac{5}{10} = 0.5 \)
9. \( \frac{5}{\frac{2}{5}} = 12.5 \)
10. \( \frac{50}{5} = 10 \)
11. \( \frac{500}{50} = 10 \)

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How can you simplify fractions before dividing them?
2. Why is multiplying by the reciprocal an effective method for dividing fractions?
3. What is the importance of knowing when to simplify a fraction?
4. How does the process of division change when dealing with decimals?
5. Can all fractions be simplified before performing division?

**Tip:** When dividing fractions, always remember to simplify the fractions first, if possible, before performing the division to make the calculations easier.

Explore detailed solutions for various division problems including 20/10, 30/20, 40/30, 20/10, 40/20, 80/40, 10/20, 5/10, 5/2/5, 50/5, and 500/50. Understand the concepts of division of fractions, multiplication by reciprocals, and decimal division. Suitable for students in Grades 5-8.

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