Worksheet: Properties of Rational Numbers

Level: Apply and Analyse

Instructions: Answer the following questions based on your understanding of the properties of closure, commutative, associative, and distributive, as well as the concepts of additive inverse, additive identity, multiplicative inverse, and multiplicative identity of rational numbers in relation to addition, subtraction, multiplication, and division.

1. Apply the property of closure to determine if the sum of two rational numbers is also a rational number.
2. Analyze the commutative property of addition and explain how it applies to rational numbers.
3. Apply the associative property of multiplication to simplify the expression: (2/3) * [(4/5) * (6/7)].
4. Analyze the distributive property of multiplication over addition and simplify the expression: 3 * (2/5 + 1/3).
5. Apply the property of closure to determine if the difference of two rational numbers is also a rational number.
6. Analyze the commutative property of subtraction and explain how it applies to rational numbers.
7. Apply the associative property of addition to simplify the expression: (3/4) + [(1/2) + (5/6)].
8. Analyze the distributive property of multiplication over subtraction and simplify the expression: 4 * (3/5 - 1/4).
9. Apply the property of closure to determine if the product of two rational numbers is also a rational number.
10. Analyze the commutative property of multiplication and explain how it applies to rational numbers.
11. Apply the associative property of addition to simplify the expression: (2/3) * [(4/5) * (6/7)].
12. Analyze the distributive property of addition over multiplication and simplify the expression: (2/5 + 1/3) * 3.
13. Apply the property of closure to determine if the quotient of two rational numbers is also a rational number.
14. Analyze the commutative property of division and explain how it applies to rational numbers.
15. Apply the associative property of multiplication to simplify the expression: (3/4) / [(1/2) / (5/6)].
16. Analyze the distributive property of subtraction over multiplication and simplify the expression: (3/5 - 1/4) * 4.
17. Apply the property of additive inverse to find the additive inverse of -5/6.
18. Analyze the property of additive identity and explain how it applies to rational numbers.
19. Apply the property of multiplicative inverse to find the multiplicative inverse of 2/3.
20. Analyze the property of multiplicative identity and explain how it applies to rational numbers.

Note: The questions provided above are just examples. You can modify or add more questions based on your specific learning intention and curriculum requirements.