a, b and c are three rational numbers where a = (2/3) , b = (4/5) and c = (-5/6) Verify: (i) a + (b + c) = (a + b) + c (ii) a x (b + c) = (a x b) + (a x c) Also mention the name of the property in each case. *
Answers
Answer:
I don't know thank you
Step-by-step explanation:
Solution :
When
• a = \sf\dfrac{2}{3}
32
• b = \sf\dfrac{4}{5}
54
• c = \sf\dfrac{-5}{6}
6−5
1. Associative Property of Addition
\longrightarrow \sf \: a + (b + c) = (a + b) + c⟶a+(b+c)=(a+b)+c
\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{4}{5} + \dfrac{ - 5}{6} ) = ( \dfrac{2}{3} + \dfrac{4}{5} ) + \dfrac{ - 5}{6}⟶
32 +( 54+ 6−5 )=( 32+ 54)+ 6−5
\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{4}{5} - \dfrac{ 5}{6} ) = ( \dfrac{2}{3} + \dfrac{4}{5} ) - \dfrac{ 5}{6}⟶ 32 +( 54 − 65 ). b=( 32+ 54 )− 65
\longrightarrow \sf \: \dfrac{2}{3} + ( \dfrac{24 - 25}{30} )= (\dfrac{10 + 12}{15} )- \dfrac{ 5}{6}⟶. 32+( 30
24−25)=( 1510+12 )− 65
\longrightarrow \sf \: \dfrac{2}{3} - \dfrac{1}{30} = \dfrac{22}{15} - \dfrac{ 5}{6}⟶
32 − 301
= 1522 − 65
\longrightarrow \sf \: \dfrac{20 -1}{30} = \dfrac{ 44 - 25}{30}⟶ 3020−1
= 3044−25
\longrightarrow \sf \red{ \dfrac{19}{30} = \dfrac{ 19}{30} }⟶ 3019
= 3019
Hence,Verified!
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2. Associative Property of Multiplication :
\longrightarrow \sf \: a \times( b \times c )=( a \times b) \times c⟶a×(b×c)=(a×b)×c
\longrightarrow \sf \: \dfrac{2}{3} \times( \dfrac{5}{6} \times \dfrac{4}{3}) =( \dfrac{2}{3} \times \dfrac{5}{6} ) \times \dfrac{4}{3}⟶
32 ×( 65 × 34 ). =( 32 × 65 )× 34
\longrightarrow \sf \: \dfrac{2}{3} \times \dfrac{20}{18} = \dfrac{10}{18} \times \dfrac{4}{3}⟶ 32× 1820
= 1810 × 34
\longrightarrow \sf \: \cancel\dfrac{40}{54} = \cancel\dfrac{40}{54}⟶
5440= 5440
\longrightarrow \sf \red{ \dfrac{20}{27} = \dfrac{ 20}{27} }⟶ 2720= 2720
Hence,Verified!