Unit Two - Integer Operations

The statement is true because any number raised to the power of 1 is equal to itself. This is a basic mathematical property where the exponent 1 signifies that the number is not being multiplied or divided by any other number. Therefore, the number remains unchanged and is equal to itself.

The given addition problem is -5 + (-2) which equals -7. This is the correct answer because when adding two negative numbers, the result will be negative. Since -5 and -2 are both negative, their sum will also be negative. The sum of -5 and -2 is -7.

Negative times a positive is a negative

The given expression is 5 + (-2). To solve this, we add 5 and -2 together. When we add a positive number and a negative number, we subtract the smaller number from the larger number and keep the sign of the larger number. In this case, 5 is larger than 2, so we subtract 2 from 5 and keep the positive sign. Therefore, 5 + (-2) equals 3.

The given expression is 3 + (-2). When we add a positive number and a negative number, we subtract the absolute value of the smaller number from the absolute value of the larger number and keep the sign of the larger number. In this case, the absolute value of 3 is larger than the absolute value of -2, so we subtract 2 from 3 and keep the positive sign. Therefore, 3 + (-2) equals 1.

The given expression -9/3 can be simplified by dividing -9 by 3, which equals -3. Therefore, the correct answer is -3.

Negative times a positive is a negative

Negative times a positive is a negative

The given expression is (-4) - 9. To simplify this, we subtract 9 from -4. When subtracting a positive number from a negative number, we add the opposite of that positive number. Therefore, -4 - 9 can be rewritten as -4 + (-9). Adding -4 and -9 gives us -13. So, the correct answer is -13.

The given expression is -81 - (-3). When we subtract a negative number, it is equivalent to adding the positive value of that number. Therefore, -81 - (-3) can be rewritten as -81 + 3. Adding -81 and 3 gives us -78. Hence, the correct answer is -78.

The expression -3 - (-4) can be simplified by changing the subtraction of a negative number to addition. So, -3 - (-4) becomes -3 + 4, which equals 1.

Throughout the course of the day, the temperature drops 12º F. Since the initial temperature is 8º F, a drop of 12º F would result in a new temperature of -4º F.

When we simplify -3(-9), we multiply -3 by -9, which gives us 27. Therefore, the correct answer is 27.

Think about these two temperatures on a thermometer. To go from 12 degrees to -2 degrees you have to go 16 spaces. What we're really asking is a subtraction problem. 12 - (-2) and that's the same as 12 + 2

The statement is false because when a negative number is added to a positive number, the sum will always depend on the magnitudes of the numbers involved. If the positive number has a greater magnitude than the negative number, the sum will be positive. However, if the negative number has a greater magnitude, the sum will be negative. Therefore, it is not always true that a negative number plus a positive number gives a negative answer.

The given question asks for the sum of 196 and -8. When adding a positive number to a negative number, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. In this case, the absolute value of 196 is larger than the absolute value of -8. So, we subtract 8 from 196 and keep the positive sign, resulting in 188. Therefore, the correct answer is 188.

When subtracting a negative number from a positive number, we can think of it as adding the positive number to the absolute value of the negative number. In this case, 19 - (-5) becomes 19 + 5, which equals 24.

All the given expressions involve addition of a positive number and a negative number, except for 5 + (-4). In this expression, both numbers are negative.

The given expression is asking for the sum of -7 and -9. When we add these two negative numbers, we get a more negative number. In this case, -7 + (-9) equals -16.

When two negative numbers are multiplied, the result is always a positive number. This can be understood by considering the concept of multiplication as repeated addition. If we have a negative number, adding it to itself multiple times will result in a negative number. However, when we multiply two negative numbers, the negative signs cancel out, and we are left with a positive product. Therefore, a negative number times a negative number will always result in a positive answer.

When we add two negative integers, the result will always be a negative integer. This is because adding two negative numbers is essentially combining two quantities that are less than zero, resulting in a value that is even smaller and negative. Therefore, the sum of two negative integers is always negative.

The difference in temperature between Alaska and Florida is 100 degrees. This is calculated by subtracting the temperature in Alaska (-10 degrees) from the temperature in Florida (90 degrees). The result is 100 degrees.

Negative times negative is positive

Negative times negative is positive

The given question is a simple addition problem. When we add 243 and 18, we get a sum of 261. However, the answer given is -225. This suggests that there is a mistake in the calculation or the answer choices provided. Without further information, it is not possible to determine the correct explanation or provide a valid answer.

When two negative integers are added, the result will always be negative. This is because adding a negative number is equivalent to subtracting a positive number. So, when two negative numbers are added, the negatives cancel out and the result remains negative.

Mrs. Shumate fell down a 22-foot deep hole. She climbed up 10 feet, which is represented by the positive addition of 10. However, she then fell back 5 feet, which is represented by the negative addition of -5. Therefore, the correct addition problem is -22 + 10 + (-5), which equals -17.

The absolute value of a number represents its distance from zero on the number line, so it is always positive. Since negative integers are less than zero, their absolute values will be positive. Therefore, the statement is true.

The expression 5 - (-9) can be simplified by applying the rule of subtracting a negative number, which is equivalent to adding the positive value. Therefore, -(-9) becomes +9, resulting in 5 + 9. Adding 5 and 9 gives the final answer of 14.

When multiplying a negative number by a positive number, the negative sign of the first number indicates a reversal or opposite direction. This means that the two numbers are in opposite directions, resulting in a negative product. Therefore, it is true that a negative number times a positive number always gives a negative answer.

Negative times negative is positive

The question asks for the difference between the high temperature on December 22 and the temperature that evening. Since the temperature dropped, we can assume that the high temperature was higher than the temperature in the evening. Therefore, the difference between the two temperatures would be the high temperature minus the evening temperature. Since the answer is 24 degrees, it means that the high temperature was 24 degrees higher than the evening temperature.

To find the solution to the equation -48 - 12, we need to subtract 12 from -48. Subtracting a negative number is the same as adding its positive counterpart. So, subtracting 12 from -48 is equivalent to adding 12 to -48. When we add 12 to -48, we get -36. Therefore, the correct answer is -36.

The given numbers "True" and "False" are placed in ascending order correctly. In ascending order, "True" comes before "False" alphabetically. Therefore, the correct answer is "True".

The absolute value of any integer is always positive because it represents the distance of the integer from zero on the number line. Since distance cannot be negative, the absolute value is always positive.

The difference between the temperature at 3:00 PM (15 degrees) and the temperature at midnight (-2 degrees) is calculated by subtracting the lower temperature from the higher temperature. In this case, 15 - (-2) = 17 degrees. Therefore, the correct answer is 17 degrees.

The product of a positive integer and its opposite will always result in a negative number. This is because when we multiply a positive number by a negative number, the result is always negative. Therefore, the answer is negative.

When multiplying a negative integer with its opposite, the result is always negative. This is because when we multiply two numbers with opposite signs, the product will have the sign of the negative number. In this case, since one of the numbers is negative, the product will also be negative.

The difference in elevation between Apple Valley and Death Valley is 3,182 feet. This is calculated by subtracting the elevation of Death Valley (-282 feet) from the elevation of Apple Valley (2,900 feet). The negative sign indicates that Death Valley is below sea level, while Apple Valley is above sea level.

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The statement "subtracting a negative number from a negative number will always result in a negative answer" is false. When subtracting a negative number from a negative number, it is equivalent to adding a positive number. This results in a positive answer, not a negative one.

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The statement "Any number to the 0 power is always 0" is incorrect. In fact, any number to the power of 0 is always equal to 1. This is a fundamental mathematical rule that applies to all numbers.

The bird is flying 20 feet above sea level, while the fish is 10 feet below sea level. To find the difference between their locations, we can subtract the fish's location from the bird's location. So, 20 feet - (-10 feet) = 20 feet + 10 feet = 30 feet. However, the question asks for the difference, not the sum. Therefore, the correct answer is -10 feet, indicating that the fish is 10 feet below the bird's location.

The given equation 3 - (-8) = 11 is true because when we subtract a negative number from a positive number, the two negatives cancel out and become positive. In this case, -8 becomes +8, and then we have 3 + 8 = 11.

The fraction 4/5 can be converted to a decimal by dividing the numerator (4) by the denominator (5). When we do this calculation, we get 0.8. Therefore, the correct answer is 0.8.