Question

Question 8
If a = -35, b = 10 cm and c = -5, verify that
(1) a + (b + c) = (a + b) + c
(1) a (b + c) = a × b + a × c​

Answer 1

Solution :

1) a + (b + c) = (a + b) + c

→ - 35 + {10 + (- 5)} = (- 35 + 10) + (- 5)

→ - 35 + (10 - 5) = - 25 - 5

→ - 35 + 5 = - 30

→ - 30 = - 30

$\dag\purple{\sf \: Hence,Verified!} \:$

★ This property is known as Associative Property.

2) a (b + c) = a × b + a × c

→ - 35{10 + (- 5)} = (- 35 × 10) + {- 35 × (- 5)}

→ - 35 (10 - 5) = - 350 + 175

→ -35 × 5 = - 350 + 175

→ - 175 = - 175

$\dag\purple{ \sf \: Hence,Verified!} \:$

★ This property is known as Distributive Property.

Answer 2

Answer:

$\textsf{If a = - 35, b = 10 and c = - 5, verify that :}$

⠀

$\sf 1)\: \:a+(b+c)=(a+b)+c\\\\\\\dashrightarrow\sf\:\:-\:35+(10+(-\:5))=(-\:35+10)+(-\:5)\\\\\\\dashrightarrow\sf\:\: - \:35 + (10 - 5) = - \:25 - 5\\\\\\\dashrightarrow\sf\:\: - \:35 + 5 = - \:30\\\\\\\dashrightarrow\sf\:\: - \: \: 30 = - \:30\qquad\bigg\lgroup\bf Hence, \:Verified\bigg\rgroup$

⠀⠀⠀$\rule{160}{0.8}$

$\sf 2)\:\:a(b+c)=(a \times b)+(a \times c)\\\\\\\dashrightarrow\sf\:\:-\:35(10+(-\:5))=(- \:35 \times 10)+(- \:35 \times -5)\\\\\\\dashrightarrow\sf\:\: - \:35(10 - 5) = - \:350 + 175\\\\\\\dashrightarrow\sf\:\: - \:35 \times 5 = - \:175\\\\\\\dashrightarrow\sf\:\: - \: 175 = - \:175\qquad\bigg\lgroup\bf Hence, \:Verified\bigg\rgroup$

$\rule{200}{2}$

⠀⠀Multiplication Properties

$\begin{tabular}{|c|c|}\cline{1-2}\bf\underline{Commutative Property}&\bf\underline{Associative Property}\\&\\\sf Can be Multipled in any Order.&\sf Can group Numbers in any \\&\sf combination \& multiply.\\&\\\sf a \times b = b \times a&\sf a(b \times c) = (a \times b)c\\\cline{1-2}\bf\underline{Identity Property}&\bf\underline{Zero Property}\\&\\\sf Product of 1 and any number&\sf Product of 0 amd any number \\\sf is the number itself.&\sf is 0 only.\\&\\\sf a \times 1 = a&\sf a \times 0 = 0 \\\cline{1-2}\end{tabular}$