Answer :
Let's address both questions in detail:
### Q1 - Represent √8, 7/8, and √2 on the number line
#### √8 on the Number Line:
1. Approximate the value: √8 is approximately equal to 2.828.
2. Mark points 0, 1, 2, 3 on the number line.
3. Place √8 between 2 and 3, closer to 3 (since 2.828 is closer to 3).
#### 7/8 on the Number Line:
1. Approximate the value: 7/8 is equal to 0.875.
2. Mark points 0 and 1 on the number line.
3. Divide the segment between 0 and 1 into eight equal parts.
4. Identify the 7th division on this segment. This point represents 7/8.
#### √2 on the Number Line:
1. Approximate the value: √2 is approximately equal to 1.414.
2. Mark points 0, 1, and 2 on the number line.
3. Place √2 between 1 and 2, closer to 1 (since 1.414 is between 1 and 2).
### Q2 - Identify the property that justifies each equation or inequality:
- i) -x + 9 = 9 + x:
- This represents the Commutative Property of Addition. This property states that the order in which numbers are added does not affect the sum.
- ii) 2(x + 3) = 2x + 6:
- This represents the Distributive Property. The distributive property states that a(b + c) = ab + ac.
- iii) (5y) * 1 = 5y:
- This represents the Multiplicative Identity Property. This property states that any number multiplied by 1 remains the same.
- iv) If 8 + 2 < 14 < 20, then 8 + 2 < 20:
- This represents the Transitive Property of Inequality. This property states that if a < b and b < c, then a < c.
- v) If (m - n) < (p + q) and r > 0, then (m - n)r < (p + q)r:
- This represents the Multiplication Property of Inequality. If a < b and c > 0, then ac < bc.
- vi) If q + r = 15, then 15 = q + r:
- This represents the Symmetric Property of Equality. This property states that if a = b, then b = a.
### Q1 - Represent √8, 7/8, and √2 on the number line
#### √8 on the Number Line:
1. Approximate the value: √8 is approximately equal to 2.828.
2. Mark points 0, 1, 2, 3 on the number line.
3. Place √8 between 2 and 3, closer to 3 (since 2.828 is closer to 3).
#### 7/8 on the Number Line:
1. Approximate the value: 7/8 is equal to 0.875.
2. Mark points 0 and 1 on the number line.
3. Divide the segment between 0 and 1 into eight equal parts.
4. Identify the 7th division on this segment. This point represents 7/8.
#### √2 on the Number Line:
1. Approximate the value: √2 is approximately equal to 1.414.
2. Mark points 0, 1, and 2 on the number line.
3. Place √2 between 1 and 2, closer to 1 (since 1.414 is between 1 and 2).
### Q2 - Identify the property that justifies each equation or inequality:
- i) -x + 9 = 9 + x:
- This represents the Commutative Property of Addition. This property states that the order in which numbers are added does not affect the sum.
- ii) 2(x + 3) = 2x + 6:
- This represents the Distributive Property. The distributive property states that a(b + c) = ab + ac.
- iii) (5y) * 1 = 5y:
- This represents the Multiplicative Identity Property. This property states that any number multiplied by 1 remains the same.
- iv) If 8 + 2 < 14 < 20, then 8 + 2 < 20:
- This represents the Transitive Property of Inequality. This property states that if a < b and b < c, then a < c.
- v) If (m - n) < (p + q) and r > 0, then (m - n)r < (p + q)r:
- This represents the Multiplication Property of Inequality. If a < b and c > 0, then ac < bc.
- vi) If q + r = 15, then 15 = q + r:
- This represents the Symmetric Property of Equality. This property states that if a = b, then b = a.
