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I see that you've uploaded an image containing some multiple-choice questions related to rational numbers. Let me help solve each question one by one:

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**1. Which of the following forms a pair of equivalent rational numbers?**

We need to check for equivalent fractions.

- (a) \( \frac{14}{32} \) and \( \frac{21}{35} \)  
  \( \frac{14}{32} = \frac{7}{16} \), \( \frac{21}{35} = \frac{3}{5} \). These are not equivalent.

- (b) \( \frac{-15}{21} \) and \( \frac{20}{-28} \)  
  \( \frac{-15}{21} = \frac{-5}{7} \), \( \frac{20}{-28} = \frac{-5}{7} \). These are equivalent.

- (c) \( \frac{-5}{7} \) and \( \frac{-20}{26} \)  
  \( \frac{-20}{26} = \frac{-10}{13} \). Not equivalent.

- (d) \( \frac{6}{-16} \) and \( \frac{-9}{-36} \)  
  \( \frac{6}{-16} = \frac{-3}{8} \), \( \frac{-9}{-36} = \frac{1}{4} \). Not equivalent.

**Answer: (b)**

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**2. Which of the following rational numbers is in standard form?**

A rational number is in standard form when the numerator and denominator have no common factors other than 1, and the denominator is positive.

- (a) \( \frac{14}{27} \)  
  This is already simplified.

- (b) \( \frac{49}{91} \)  
  Simplifies to \( \frac{7}{13} \).

- (c) \( \frac{13}{52} \)  
  Simplifies to \( \frac{1}{4} \).

- (d) \( \frac{27}{105} \)  
  Simplifies to \( \frac{9}{35} \).

**Answer: (a)**

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**3. Which of the following rational numbers is the greatest?**

We compare all the options by converting them to decimals or by comparing fractions:

- (a) \( \frac{3}{-7} = -\frac{3}{7} \approx -0.4286 \)
- (b) \( \frac{-5}{14} \approx -0.3571 \)
- (c) \( \frac{-16}{56} = -\frac{2}{7} \approx -0.2857 \)
- (d) \( \frac{-13}{28} \approx -0.4643 \)

**Answer: (c)**

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**4. A number which is to be added to \( \frac{7}{3} \) to get \( -2 \) is**

Let the unknown number be \( x \). Then:

\[
\frac{7}{3} + x = -2
\]

Solving for \( x \):

\[
x = -2 - \frac{7}{3} = \frac{-6}{3} - \frac{7}{3} = \frac{-13}{3}
\]

**Answer: (d)**

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**5. The sum of two rational numbers is \( \frac{29}{21} \). If one of the numbers is \( \frac{2}{3} \), then the other number is**

Let the other number be \( x \). Then:

\[
\frac{2}{3} + x = \frac{29}{21}
\]

Solving for \( x \):

\[
x = \frac{29}{21} - \frac{2}{3} = \frac{29}{21} - \frac{14}{21} = \frac{15}{21} = \frac{5}{7}
\]

**Answer: (c)**

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**6. The product of two rational numbers is \( \frac{21}{40} \). If one of the numbers is \( \frac{7}{5} \), then the other number is**

Let the other number be \( x \). Then:

\[
\frac{7}{5} \times x = \frac{21}{40}
\]

Solving for \( x \):

\[
x = \frac{21}{40} \div \frac{7}{5} = \frac{21}{40} \times \frac{5}{7} = \frac{105}{280} = \frac{3}{8}
\]

**Answer: (c)**

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**7. \( \frac{21}{5} \) is the additive inverse of**

The additive inverse of a number \( a \) is the number \( -a \). Thus, the additive inverse of \( \frac{21}{5} \) is:

\[
-\frac{21}{5} = -4.2
\]

**Answer: (a)**

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Do you have any specific question on any of these problems, or would you like more details on the solutions? 

Here are some related questions you might find helpful:
1. How do you find the greatest of a set of rational numbers?
2. What are the properties of standard form for rational numbers?
3. How do you determine the additive inverse of a fraction?
4. What steps do you take when comparing negative fractions?
5. How do you simplify the product of two rational numbers?

**Tip**: When comparing fractions, it can be useful to convert them to a common denominator or to decimal form to make the comparison easier.

Which of the following forms a pair of equivalent rational numbers?; Which of the following rational numbers is in standard form?; Which of the following rational numbers is the greatest?; A number which is to be added to 7/3 to get -2 is; The sum of two rational numbers is 29/21. If one of the numbers is 2/3, then the other number is; The product of two rational numbers is 21/40. If one of the numbers is 7/5, then the other number is; 21/5 is the additive inverse of:

Learn how to solve problems related to rational numbers, including identifying equivalent fractions, finding the greatest rational number, and working with additive inverses. Suitable for students in Grades 6-8.

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