Importance of Youth in Building Nation
Grade 8 Rational Number
Natural numbers are a collection of all positive numbers starting from 1. Whole numbers are a collection of all natural numbers including 0. Rational numbers are the numbers that can be written in p form, where p and q are q
integers and q 0 Closure property 1. Whole numbers are closed under addition and multiplication. However, they are not closed under subtraction and division. 2. Integers are also closed under addition and multiplication. However, they are not closed under subtraction and division. 3. Rational numbers: i. Rational numbers are closed under addition.
2 5 3 2 3 4
3 5
19 is a rational number. 10 11 is rational number. 20
2 is a rational number. 5
ii. iii.
Rational numbers are closed under subtraction.
1 5
2 3
Rational numbers are closed under multiplication.
iv.
Rational numbers are not closed under division. For example, 2 0 is not defined.
Commutativity 1. Whole numbers are commutative under addition and multiplication. However, they are not commutative under subtraction and division. 2. Integers are commutative under addition and multiplication. However, they are not commutative under subtraction and division. 3. Rational numbers: i. Rational numbers are commutative under addition.
2 3 3 2 3 2 2 3 5 6
ii.
Rational numbers are not commutative under multiplication.
3 4 3 4 5 2 5 2
2 6
7 5 and 4 2 5 2
2 6
3 4
7 4
3 4
3 4 1 4
iii.
Rational numbers are commutative under multiplication.
3 4
iv.
Rational numbers are not commutative under division.
2 5 5 2
Associativity 1. Whole numbers are associative under addition and multiplication. However, they are associative not under subtraction and division. 2. Integers are associative under addition and multiplication. However, they are not associative under subtraction and division. 3. Rational numbers: i. Rational numbers are associative under addition.
2 3 1 3 1 2 3 1 1 3 2
ii.
Rational
Natural numbers are a collection of all positive numbers starting from 1. Whole numbers are a collection of all natural numbers including 0. Rational numbers are the numbers that can be written in p form, where p and q are q
integers and q 0 Closure property 1. Whole numbers are closed under addition and multiplication. However, they are not closed under subtraction and division. 2. Integers are also closed under addition and multiplication. However, they are not closed under subtraction and division. 3. Rational numbers: i. Rational numbers are closed under addition.
2 5 3 2 3 4
3 5
19 is a rational number. 10 11 is rational number. 20
2 is a rational number. 5
ii. iii.
Rational numbers are closed under subtraction.
1 5
2 3
Rational numbers are closed under multiplication.
iv.
Rational numbers are not closed under division. For example, 2 0 is not defined.
Commutativity 1. Whole numbers are commutative under addition and multiplication. However, they are not commutative under subtraction and division. 2. Integers are commutative under addition and multiplication. However, they are not commutative under subtraction and division. 3. Rational numbers: i. Rational numbers are commutative under addition.
2 3 3 2 3 2 2 3 5 6
ii.
Rational numbers are not commutative under multiplication.
3 4 3 4 5 2 5 2
2 6
7 5 and 4 2 5 2
2 6
3 4
7 4
3 4
3 4 1 4
iii.
Rational numbers are commutative under multiplication.
3 4
iv.
Rational numbers are not commutative under division.
2 5 5 2
Associativity 1. Whole numbers are associative under addition and multiplication. However, they are associative not under subtraction and division. 2. Integers are associative under addition and multiplication. However, they are not associative under subtraction and division. 3. Rational numbers: i. Rational numbers are associative under addition.
2 3 1 3 1 2 3 1 1 3 2
ii.
Rational