The correct word or phrase to fill in the blank.
Answer to Problem 1PE
a. Opposites
b.
c. Base, n
d. Radical, square
e. Negative, positive
f. Positive, negative
g.
h.
i. 0
Explanation of Solution
a.
The opposite numbers are the numbers which differ in sign and are at an equal distance from 0. Therefore, the given statement can be completed as “Two numbers that are the same distance from 0 but on opposite sides of 0 on the number line, are called opposites.”
b.
The absolute value of a real number is denoted by writing the number within two vertical bars (“|” mark) and it is the distance between 0 and that number. So, the given statement can be completed as “The absolute value of a real number, a, is denoted by
c.
Exponential numbers are written as
Therefore, the given statement can be completed as “Given the expression
d.
The square root of a number x is represented by
Therefore, the given incomplete statement can be completed as “The symbol
e.
The sum of two negative numbers is negative and product of two negative numbers is a positive number. So, the statement can be completed as “If a and b are both negative, then
f.
The addition of two numbers of opposite signs are either positive or negative depending on the sign of the number with higher absolute value. For example, the addition of
If
g.
Subtracting a number from another number is same as adding the opposite of the first number. And, addition of two numbers of opposite signs are either positive or negative depending on the sign of the number with higher absolute value.
The expression
h.
The reciprocal numbers are the numbers whose product is equal to 1. And the reciprocal of a given number can be written by the number in the denominator over 1.
So, the statement can be completed as “If a is a nonzero real number, then the reciprocal of a is
i.
Any number multiplied to 0 gives the result 0. So, in the product
j.
If 0 is divided by any nonzero number the quotient is always 0. But, if a nonzero number is divided by 0, the quotient is undefined because the division by 0 is not defined. So, the statement can be completed as “If
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