Addition: Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.
Multiplication:For example, let us solve the expression: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.
Identity:
Addition:Here's an example: 0 + 4 = 4 0 + 4 = 4 0+4=4. This is true because the definition of 0 is "no quantity", so when we add 0 to 4, the quantity of 4 doesn't change!
Multiplication:The product of 1 and any number is that number. For example, 7 × 1 = 7 7 \times 1 = 7 7×1=77, times, 1, equals, 7.
Inverse:
Addition: 6 + its opposite (which is -6) = 0.
Multiplication:For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!
Answers & Comments
Answer:
B.
Closure:
Addition: 3 + 4 = 7 (whole number).
Multiplication: 7 × 4 = 28; (– 4) × (– 5) = 20.
Commutative:
Addition: 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.
Multiplication:4 × 3 = 3 × 4 4 \times 3 = 3 \times 4 4×3=3×44, times, 3, equals, 3, times, 4.
Associative:
Addition: ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.
Multiplication: 3 × (5 × 6) = (3 × 5) × 6.
Distributive:
Addition: Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, for example, that 2(3 + 4) = 2×3 + 2×4.
Multiplication: For example, let us solve the expression: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.
Identity:
Addition: Here's an example: 0 + 4 = 4 0 + 4 = 4 0+4=4. This is true because the definition of 0 is "no quantity", so when we add 0 to 4, the quantity of 4 doesn't change!
Multiplication: The product of 1 and any number is that number. For example, 7 × 1 = 7 7 \times 1 = 7 7×1=77, times, 1, equals, 7.
Inverse:
Addition: 6 + its opposite (which is -6) = 0.
Multiplication: For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!