Answer/Discussion
to 1a
-5 + (-16)
-5 + (-16) = -21.
Note that we are adding two numbers with the same sign. The sum of the absolute values 5 and 16 is 21 and their common sign is negative. Therefore, our answer is -21.
Answer/Discussion
to 1b
7 + (-3)
7 + (-3) = 4.
Note that we are adding two numbers that have opposite signs. The difference between the absolute values of 7 and 3 is 4 and the sign of the number with the larger absolute value (7) is positive. Therefore, our answer is 4.
Answer/Discussion
to 1c
-10 - (-2)
-10 - (-2) = -10 + 2 = -8.
Subtracting a negative 2 is the same as adding a positive 2. Once we change it to addition, we now are adding two numbers with opposite signs. The difference of the absolute values of 10 and 2 is 8 and the sign of the larger absolute value (-10) is negative. Therefore, our answer is -8.
Answer/Discussion
to 2a
(-4)(9)
(-4)(9) = -36.
We are multiplying two numbers with opposite signs. The product of 4 and 9 is 36 and multiplying with opposite signs gives us a negative. Therefore, our answer is -36.
Answer/Discussion
to 2b
= .5 or ½.
We are dividing two numbers with the same sign. The quotient of 3 and 6 is .5 and dividing with the same signs gives us a positive number. Therefore, our answer is .5.
Answer/Discussion
to 3a
Answer/Discussion
to 3b
Answer/Discussion
to 3c
Answer/Discussion
to 4a
The thought behind this is that we are looking for the square root of 36, which means we are looking for a number that when we square it we get 36. Since 6 squared is 36, 6 is the square root of 36. Note that we are only interested in the principal root and since 36 is positive and there is not a sign in front of the radical, our answer is positive 6. If there had been a negative in front of the radical our answer would have been -6
Answer/Discussion
to 4b
Now we are looking for the fourth root of 1/16, which means we are looking for a number that when we take it to the 4th power, we get 1/16. Since 1/2 to the 4th power is 1/16, our answer is going to be 1/2.
Answer/Discussion
to 5a
Answer/Discussion
to 5b
*Absolute value
*(fancy grouping symbol)
*Square root
*Subtraction in numerator
*Divide
Answer/Discussion
to 6a
Find the value of the expression when a = 3 and b = -2.
Last revised on June 10, 2011 by Kim Seward.
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