Operations with Negative Numbers - GED Math
Card 1 of 255
Which of these is not equal to 
?
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Which of these is not equal to
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Only one of the choices is positive - 
, which is the quotient of two negative numbers. This must be the correct response.
Only one of the choices is positive -
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Evaluate:
Evaluate:
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How many of these statements are correct?
I) 
II) 
III) 
How many of these statements are correct?
I)
II)
III)
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The absolute value of a nonnegative number is the number itself; the absolute value of a negative number can be obtained by removing the negative symbol. Therefore,
and 
.
This makes the statements 
and 
both equivalent to the statement 
, which is false.
This also makes the statement 
equivalent to 
, which is the only true statement of the three.
The absolute value of a nonnegative number is the number itself; the absolute value of a negative number can be obtained by removing the negative symbol. Therefore,
This makes the statements
This also makes the statement
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Solve: 
Solve:
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Expand the expression by order of operations.
The answer is: 
Expand the expression by order of operations.
The answer is:
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Which of the following operations might yield a positive result?
Which of the following operations might yield a positive result?
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The square of a negative number must be positive. We can analyze each situation using this fact.
Multiplying or dividing the square of a negative number by a negative number results in multiplying or dividing a positive number by a negative number; in both situations, the result is negative.
Subtracting the square of a negative number from a negative number results in subtracting a positive number from a negative number; the result is a negative number.
As seen in this example, however, adding the square of a negative number to a negative number might yield a positive result, so it is the correct choice:
The square of a negative number must be positive. We can analyze each situation using this fact.
Multiplying or dividing the square of a negative number by a negative number results in multiplying or dividing a positive number by a negative number; in both situations, the result is negative.
Subtracting the square of a negative number from a negative number results in subtracting a positive number from a negative number; the result is a negative number.
As seen in this example, however, adding the square of a negative number to a negative number might yield a positive result, so it is the correct choice:
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Solve:
Solve:
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When a negative number is multipied by a positive number, the result is negative.
Therefore,
.
When a negative number is multipied by a positive number, the result is negative.
Therefore,
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Evaluate 
for 
. Do NOT use a calculator.
Evaluate
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Substitute 
for 
in the expression.
Substitute
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Evaluate:
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Evaluate:
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To obtain the product of two numbers of unlike sign, multiply their absolute values and affix a negative symbol.
To obtain the product of two numbers of unlike sign, multiply their absolute values and affix a negative symbol.
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Evaluate:
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Evaluate:
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To subtract with negative numbers, change to an addition and make the second number its opposite:
To add two numbers of unlike sign, if the positive has the greater absolute value, simply subtract the absolute values.
The answer is 45.
To subtract with negative numbers, change to an addition and make the second number its opposite:
To add two numbers of unlike sign, if the positive has the greater absolute value, simply subtract the absolute values.
The answer is 45.
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Evaluate:
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Evaluate:
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To divide two numbers of like sign, just divide their absolute values; their quotient will be positive.
To divide two numbers of like sign, just divide their absolute values; their quotient will be positive.
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Evaluate:
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Evaluate:
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To subtract a larger positive number from a smaller positive number, do the reverse, then affix a negative symbol, as demonstrated here:
So subtract 3.7 from 9.17:
Since the answer must be negative, it is 
.
To subtract a larger positive number from a smaller positive number, do the reverse, then affix a negative symbol, as demonstrated here:
So subtract 3.7 from 9.17:
Since the answer must be negative, it is
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Evaluate:
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Evaluate:
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To obtain the product of two numbers of unlike sign, multiply their absolute values:
The product will remain positive.
To obtain the product of two numbers of unlike sign, multiply their absolute values:
The product will remain positive.
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Which of the following operations might yield a positive result?
Which of the following operations might yield a positive result?
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We analyze all of the situations.
Multiplying three integers, two of which are positive and one of which is negative:
The product of the two positive numbers must be positive; the product of this and a negative number must be negative.
Subtracting the sum of two positive integers from a negative integer:
The sum of two positive integers must be positive. Therefore, we are subtracting a positive number from a negative number, which must be negative.
Dividing a negative integer by the square of a negative integer:
The square of a negative integer is positive. This is therefore the quotient of two numbers of unlike sign, which must be negative.
Adding three integers, two of which are negative and one of which is positive:
As can be seen from this example, the result can be nonnegative:
This is the correct choice.
We analyze all of the situations.
Multiplying three integers, two of which are positive and one of which is negative:
The product of the two positive numbers must be positive; the product of this and a negative number must be negative.
Subtracting the sum of two positive integers from a negative integer:
The sum of two positive integers must be positive. Therefore, we are subtracting a positive number from a negative number, which must be negative.
Dividing a negative integer by the square of a negative integer:
The square of a negative integer is positive. This is therefore the quotient of two numbers of unlike sign, which must be negative.
Adding three integers, two of which are negative and one of which is positive:
As can be seen from this example, the result can be nonnegative:
This is the correct choice.
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An airplane takes off from Death Valley, which is 282 feet below sea level. It ascends 12,879 feet before leveling off, then it descends another 1,276 feet; it finally ascends 4,874 feet. Which of the following expressions is equal to the plane's current elevation in feet?
An airplane takes off from Death Valley, which is 282 feet below sea level. It ascends 12,879 feet before leveling off, then it descends another 1,276 feet; it finally ascends 4,874 feet. Which of the following expressions is equal to the plane's current elevation in feet?
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The initial elevation of the plane is 282 feet below sea level, which is 
feet in elevation. Ascent is an increase in elevation and descent is a decrease, so, to the elevation, in turn, add 12,879 feet, subtract 1,276 feet, and add 4,874 feet.
This expression is
.
The initial elevation of the plane is 282 feet below sea level, which is
This expression is
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An airplane takes off from Death Valley, which is 282 feet below sea level. It ascends 12,879 feet before leveling off, then it ascends 4,276 feet; it finally descends 1,874 feet. Which of the following expressions is equal to the plane's current elevation in feet?
An airplane takes off from Death Valley, which is 282 feet below sea level. It ascends 12,879 feet before leveling off, then it ascends 4,276 feet; it finally descends 1,874 feet. Which of the following expressions is equal to the plane's current elevation in feet?
Tap to reveal answer
The initial elevation of the plane is 282 feet below sea level, which is 
feet in elevation. Ascent is an increase in elevation and descent is a decrease, so, to the elevation, in turn, add 12,879 feet, add 4,276 feet, and subtract 1,874 feet.
This expression is
.
The initial elevation of the plane is 282 feet below sea level, which is
This expression is
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An airplane takes off from Death Valley, which is 282 feet below sea level. It is now flying at an elevation of 
feet. How many feet has the plane ascended since taking off?
An airplane takes off from Death Valley, which is 282 feet below sea level. It is now flying at an elevation of
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We are looking for the difference between the current elevation of the plane and the initial elevation, so we subtract initial elevation 
from current elevation 
. This is
.
is the correct choice.
We are looking for the difference between the current elevation of the plane and the initial elevation, so we subtract initial elevation
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Evaluate without the aid of a calculator:
Evaluate without the aid of a calculator:
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Since absolute value bars are grouping symbols, we first raise 
to the power of 3. An odd power of a negative number is negative, so we do this by raising 5 to the third power, then affixing a negative symbol.
The absolute value of a negative number is the corresponding positive, so
.
Since absolute value bars are grouping symbols, we first raise
The absolute value of a negative number is the corresponding positive, so
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Raise 
to the third power.
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Raise
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An odd power of a negative number is negative, so take 11 to the third power, then affix a negaitve symbol.
The result must be negative, so the correct response is 
.
An odd power of a negative number is negative, so take 11 to the third power, then affix a negaitve symbol.
The result must be negative, so the correct response is
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Order from least to greatest:
Order from least to greatest:
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The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is obtained by removing the negative symbol. Therefore:
In ascening order, the numbers are 
.
The absolute value of a nonnegative number is the number itself; the absolute value of a negative number is obtained by removing the negative symbol. Therefore:
In ascening order, the numbers are
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Evaluate:
Evaluate:
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