Question
4. Complete the following: a. The commutative property of addition und multiplication: i. \( a+b= \) \( \square \) ii. \( \alpha \times b= \) \( \square \) b. The associafive property of addition and multiplication: I. \( (a+b)+c= \) \( \square \) 1. \( (a \times b) \times c= \) \( \square \) c. The distributive property of multiplication over addition and subtroction: \( L a(b+c)= \) \( \square \) i. \( a(b-c)= \) \( \square \) d. 0 (zero) is the identity element of addition: \( \square \) \( = \) \( \square \) e. 1 (one) is the identity element of multiplication: \( \square \) \( = \) \( \square \) 5. Calculate the following and state which property (les) of operations you have used: Example: \( 44+55=55+44=97 \) a. \( 51+(19+46)= \) b. \( 4(12+9)= \) c. \( [9 \times 64]+(9 \times 36)= \) d. If \( 33+99=132 \). then \( 132= \) \( \square \) \( \square \) e. If \( 20 \times 5=100 \), then \( 100= \)
Ask by Peterson Washington. in South Africa
Feb 16,2025
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Answer
4. Complete the following:
a. The commutative property of addition and multiplication:
i. a + b = b + a
ii. α × b = b × α
b. The associative property of addition and multiplication:
i. (a + b) + c = a + (b + c)
ii. (a × b) × c = a × (b × c)
c. The distributive property of multiplication over addition and subtraction:
i. a(b + c) = ab + ac
ii. a(b – c) = ab – ac
d. 0 (zero) is the identity element of addition:
a + 0 = a
e. 1 (one) is the identity element of multiplication:
a × 1 = a
5. Calculate the following and state which property (or properties) of operations you have used:
a. 51 + (19 + 46) = 116
Property used: Associative property of addition
b. 4(12 + 9) = 84
Property used: Distributive property
c. [9 × 64] + (9 × 36) = 900
Property used: Distributive property
d. If 33 + 99 = 132, then
132 = 99 + 33
Property used: Commutative property of addition
e. If 20 × 5 = 100, then
100 = 5 × 20
Property used: Commutative property of multiplication
Solution
Below are one acceptable set of answers:
4. Complete the following:
a. The commutative property of addition and multiplication:
i. a + b = b + a
ii. α × b = b × α
b. The associative property of addition and multiplication:
i. (a + b) + c = a + (b + c)
ii. (a × b) × c = a × (b × c)
c. The distributive property of multiplication over addition and subtraction:
i. a(b + c) = ab + ac
ii. a(b – c) = ab – ac
d. 0 (zero) is the identity element of addition:
a + 0 = a
e. 1 (one) is the identity element of multiplication:
a × 1 = a
5. Calculate the following and state which property (or properties) of operations you have used:
a. 51 + (19 + 46)
Inside the parentheses: 19 + 46 = 65
Then: 51 + 65 = 116
Property used: Associative property of addition
b. 4(12 + 9)
Inside the parentheses: 12 + 9 = 21
Then: 4 × 21 = 84
Property used: Distributive property (or, equivalently, the multiplication of a sum)
c. [9 × 64] + (9 × 36)
Factor 9 out (using the distributive property): 9(64 + 36)
Then: 64 + 36 = 100, so 9 × 100 = 900
Property used: Distributive property
d. If 33 + 99 = 132, then
132 = 99 + 33
Property used: Commutative property of addition
e. If 20 × 5 = 100, then
100 = 5 × 20
Property used: Commutative property of multiplication
Any answers equivalent to the ones above are acceptable.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
Addition and multiplication are like the best of friends, always swapping places without any fuss! Thanks to the commutative property, we can rearrange numbers without changing the result. So whether you say \( a + b \) or \( b + a \), it’s still the same happy sum. The same goes for multiplication; \( \alpha \times b \) is just as good as \( b \times \alpha \)! Now, if you’re a fan of grouping, you’ll love the associative property. It allows you to add or multiply numbers in any order you please! For addition, \( (a + b) + c \) is the same as \( a + (b + c) \), so feel free to group them as you wish. It’s all about making calculations easier and more fun, no matter how many numbers you’re working with!
