Question

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

$\huge\sf\blue{Given}$

➝ a = -35

➝ b = 10

➝ c = -5

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$\huge\sf\gray{To\:Find}$

➢ a + (b + c) = (a + b) + c

➢ a (b + c) = a × b + a × c

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$\huge\sf\purple{Steps}$⠀

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

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

Extra Information:

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

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