Which number property is being used in each of the following? (1) 8 (3 * 7 + 1) = 8* (7 * 3+1) (ii) 18+ (437) * 9 - 18 +43 (79) (iii) (12+17) * (16+5) = (12 + 17) 16+ (12 + 17) 5 (iv) (13 +22) * (7 + 5) - (13 +22) * ( 5 + 7) (v) (15 x 2 + 9) + 3 - 15 * 2+ (9 + 3) (vi) 59+41 * 8+41 26 -59 +41 ~ (8 +26)
Answers
Step-by-step explanation:
Q7) Which property of addition is satisfied by:
(i) 8 + 7 = 15
(ii) 3+ (5 + 4) = (3 + 5)+ 4
(iii) 8\times\left(8+0\right)=8\times8+8\times0
(iv) \left(7+6\right)\times10=7\times10+6\times10
(v) \left(15-12\right)\times18=15\times18-12\times18
(vi) 16 + 0= 16
(vii) 23 + (-23) = 0
Solution
Transcript
Solution 7:
(i) 8 + 7 = 15
The property used as closure property satisfied by 15
(ii) 3+ (5 + 4) = (3 + 5)+ 4 ,
3+ (5 + 4) = 3 + 9 = 12 and
(3 + 5)+ 4 = 8 + 4 = 12
The property used as Associative law of addition satisfied by 12.
(iii) 8\times\left(8+0\right)=8\times8+8\times0
8\times\left(8+0\right)=8\times8=64
8\times8+8\times0=64+0=64
The property used as Distributive property over addition satisfied by 64
(iv) \left(7+6\right)\times10=7\times10+6\times10
\left(7+6\right)\times10=13\times10=130
7\times10+6\times10=70+60=130
The property used as Distributive over addition satisfied by 130 (v) \left(15-12\right)\times18=15\times18-12\times18
\left(15-12\right)\times18=3\times18=54
15\times18-12\times18=270-216=54
This property used as Distributive over subtraction satisfied by 54
(vi) 16 + 0= 16
The property used as Existence of identity satisfied by 16.
(vii) 23 + (-23) = 0
The property used as Additive inverse satisfied by 0.
Answer:
column A column B
(a) 137 + 63 = 63 + 137 (i) Associativity of multiplication
(b) (16 × 25) is a number (ii) Commutativity of multiplication
(c) 365 × 18 = 18 × 365 (iii) Distributive law of multiplication over addition
(d) (86 × 14) × 25 = 86 × (14 × 25) (iv) Commutativity of addition
(e) 23 × (80 + 5) = (23 × 80) + (23 × 5) (v) Closure property for multiplication
ANSWER:
Column A Column B
(a) 137 + 63 = 63 + 137 (iv) Commutativity of addition
(b) (16 × 25) is a number (v) Closure property for multiplication
(c) 365 × 18 = 18 × 365 (ii) Commutativity of multiplication
(d) (86 × 14) × 25 = 86 × (14 × 25) (i) Associativity of multiplication
(e) 23 × (80 + 5) = (23 × 80) + (23 × 5) (iii) Distributive law of multiplication over addition
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