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The plus and minus signs now have two meanings :
The plus sign can denote the operation of addition or a positive number.
The minus sign can denote the operation of subtraction or a negative number.
To avoid any confusion between "sign" and "operation," it is preferable to read the sign of a number as "positive" or "negative." When "+" is used as an operation sign, it is read as "plus." When " $-$ " is used as an operation sign, it is read as "minus."
Read each expression so as to avoid confusion between "operation" and "sign."
$-8$ should be read as "negative eight" rather than "minus eight."
$\text{4}+(-2)$ should be read as "four plus negative two" rather than "four plus minus two."
$-6+(-3)$ should be read as "negative six plus negative three" rather than "minus six plus minus three."
$-15-(-6)$ should be read as "negative fifteen minus negative six" rather than "minus fifteen minus minus six."
$-5+\text{7}$ should be read as "negative five plus seven" rather than "minus five plus seven."
$0-2$ should be read as "zero minus two."
Write each expression in words.
The opposite of a real number is denoted by placing a negative sign directly in front of the number. Thus, if $a$ is any real number, then $-a$ is its opposite.
If $a$ is any real number, $-a$ is opposite $a$ on the number line.
The number $a$ is opposite $-a$ on the number line. Therefore, $-(-a)$ is opposite $-a$ on the number line. This means that
$-(-a)=a$
From this property of opposites, we can suggest the double-negative property for real numbers.
Find the opposite of each number.
Find the opposite of each number.
Suppose $a$ is a positive number. Is $-a$ positive or negative?
$-a$ is negative
Suppose $a$ is a negative number. Is $-a$ positive or negative?
$-a$ is positive
Suppose we do not know the sign of the number $k$ . Is $-k$ positive, negative, or do we not know?
We must say that we do not know.
A number is denoted as positive if it is directly preceded by
+ (or no sign)
A number is denoted as negative if it is directly preceded by
How should the number in the following 6 problems be read? (Write in words.)
$-\left(-1\right)$
negative negative one, or opposite negative one
$-\left(-5\right)$
For the following 6 problems, write each expression in words.
$1+\left(-9\right)$
$0-\left(-\text{12}\right)$
For the following 6 problems, rewrite each number in simpler form.
$-\left(-\text{16}\right)$
$-\left[-\left(-\text{20}\right)\right]$
$6-\left(-4\right)$
( [link] ) Find the quotient; $8\xf7\text{27}$ .
$0\text{.}\overline{\text{296}}$
( [link] ) Solve the proportion: $\frac{5}{9}=\frac{\text{60}}{x}$
( [link] ) Use the method of rounding to estimate the sum: $\text{5829}+\text{8767}$
$\mathrm{6,}\text{000}+\mathrm{9,}\text{000}=\text{15},\text{000}(\mathrm{5,}\text{829}+\mathrm{8,}\text{767}=\text{14},\text{59}6)\text{or 5,}\text{800}+\mathrm{8,}\text{800}=\text{14},\text{600}$
( [link] ) Use a unit fraction to convert 4 yd to feet.
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