To verify the associative property of multiplication and addition for the given pair of rational numbers, we'll check if the following equation holds true:
(a + b) + c = a + (b + c)
Let's substitute the given values:
(a + b) + c = (-5/3 + -2/5) + -9/10
= (-25/15 + -6/15) + -9/10
= (-31/15) + -9/10
Now, let's calculate the right-hand side of the equation:
a + (b + c) = -5/3 + (-2/5 + -9/10)
= -5/3 + (-20/10 + -9/10)
= -5/3 + -29/10
To determine if the equation holds true, we'll simplify both sides of the equation:
(-31/15) + -9/10 = -31/15 - 27/30
= (-31/15) - (27/30)
= (-62/30) - (27/30)
= (-62 - 27)/30
= -89/30
and
-5/3 + -29/10 = (-50/30) + (-87/30)
= (-50 - 87)/30
= -137/30
Since (-89/30) is equal to -137/30, the equation holds true. Therefore, we have verified the associative property of multiplication and addition for the given pair of rational numbers (-5/3, -2/5, -9/10).
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Answer:
To verify the associative property of multiplication and addition for the given pair of rational numbers, we'll check if the following equation holds true:
(a + b) + c = a + (b + c)
Let's substitute the given values:
(a + b) + c = (-5/3 + -2/5) + -9/10
= (-25/15 + -6/15) + -9/10
= (-31/15) + -9/10
Now, let's calculate the right-hand side of the equation:
a + (b + c) = -5/3 + (-2/5 + -9/10)
= -5/3 + (-20/10 + -9/10)
= -5/3 + -29/10
To determine if the equation holds true, we'll simplify both sides of the equation:
(-31/15) + -9/10 = -31/15 - 27/30
= (-31/15) - (27/30)
= (-62/30) - (27/30)
= (-62 - 27)/30
= -89/30
and
-5/3 + -29/10 = (-50/30) + (-87/30)
= (-50 - 87)/30
= -137/30
Since (-89/30) is equal to -137/30, the equation holds true. Therefore, we have verified the associative property of multiplication and addition for the given pair of rational numbers (-5/3, -2/5, -9/10).