Question

Verify the property:-12/13×(-7/18×-7/5)=(-12/13×-7/18)×-7/5 solve urgent it should be done by associative property ​

Answer 1

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Answer 2

What to do?

• Verify the associative property by taking a = 12/13, b = -7/18 and c = -7/5.

Solution :-

• To verify the associative property, we have to show that :-

$\sf \dfrac{ - 12}{ \: \: \: 13} \times \left(\dfrac{ - 7}{18} \times \dfrac{ - 7}{ \: \: \: 5} \right) = \left(\dfrac{ - 12}{ \: \: \: 13} \times \dfrac{ - 7}{ \: 18} \right) \times \dfrac{ - 7}{ \: \: \: 5}$

LHS

$\dashrightarrow\tt \dfrac{ - 12}{ \: \: \: 13} \times \left(\dfrac{ - 7}{ \: 18} \times \dfrac{ - 7}{ \: \: 5} \right)$

$\dashrightarrow\tt \dfrac{ - 12}{ \: \: \: 13} \times \dfrac{49}{90}$

Cancelling the numbers,

$\dashrightarrow\tt \dfrac{ - 2}{13} \times \dfrac{49}{15}$

$\dashrightarrow\tt\dfrac{ - 98}{ \: 195}$

RHS

$\dashrightarrow\tt \left(\dfrac{ - 12}{ \: \: \: 13} \times \dfrac{ - 7}{ \: 18} \right) \times \dfrac{ - 7}{ \: \: \: 5}$

$\dashrightarrow\tt \dfrac{84}{234} \times \dfrac{ - 7}{ \: \: \: 5}$

Cancelling the numbers,

$\dashrightarrow\tt \dfrac{14}{39} \times \dfrac{ - 7}{ \: \: \: 5}$

$\dashrightarrow \tt\dfrac{ - 98}{ \: 135}$

LHS = RHS.

Hence verified!!

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Know more :-

What is associative property?

• Associative Property : If a/b, c/d and e/f are three rational numbers, then (a/b + c/d) + e/f = a/b + (c/d + e/f).

It is one of the properties of addition of rational numbers.