https://file.aiquickdraw.com/mathbot/file/1727369018462rierearq.jpg

The image shows a series of mathematical expressions involving division of fractions. Specifically, it focuses on operations with negative fractions and their reciprocals, as suggested by the phrase "daugyba su dalikliui atvirkštiniu," which means "multiplication with the reciprocal of the divisor."

Let me break down each of the three expressions one by one:

1. **First expression**:
   \[
   -\frac{7}{90} : \frac{1}{9}
   \]
   Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, this becomes:
   \[
   -\frac{7}{90} \times \frac{9}{1} = -\frac{7 \times 9}{90} = -\frac{63}{90} = -\frac{7}{10}
   \]

2. **Second expression**:
   \[
   -\frac{7}{900} : \left(-\frac{1}{9}\right)
   \]
   Again, division by a fraction is the same as multiplying by the reciprocal:
   \[
   -\frac{7}{900} \times -\frac{9}{1} = \frac{7 \times 9}{900} = \frac{63}{900} = \frac{7}{100}
   \]
   Since both signs are negative, they cancel out, leaving a positive fraction.

3. **Third expression**:
   \[
   \frac{7}{9000} : \left(-\frac{1}{9}\right)
   \]
   Using the same rule:
   \[
   \frac{7}{9000} \times -\frac{9}{1} = -\frac{7 \times 9}{9000} = -\frac{63}{9000} = -\frac{7}{1000}
   \]

Thus, the final results of the three expressions are:
1. \(-\frac{7}{10}\)
2. \(\frac{7}{100}\)
3. \(-\frac{7}{1000}\)

Would you like more details on any of the steps? Here are 5 related questions to explore:

1. What is the rule for dividing fractions in general?
2. How do we simplify fractions efficiently?
3. What is the significance of multiplying by the reciprocal in division?
4. How do signs (positive or negative) affect multiplication of fractions?
5. How can you express these results as decimals?

**Tip**: Always simplify fractions whenever possible to ensure your answer is in its simplest form!

Solve the following division expressions with fractions: -7/90 ÷ 1/9, -7/900 ÷ (-1/9), 7/9000 ÷ (-1/9).

Learn how to solve fraction division problems involving reciprocals, including -7/90 ÷ 1/9, -7/900 ÷ (-1/9), and 7/9000 ÷ (-1/9). Understand key concepts like dividing fractions by multiplying their reciprocals and simplifying the results. Suitable for middle school students (Grades 6-8).

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