Negative Numbers - SAT Math

Card 0 of 19

Question

a, b, c are integers.

abc < 0

ab > 0

bc > 0

Which of the following must be true?

Answer

Let's reductively consider what this data tells us.

Consider each group (a,b,c) as a group of signs.

From abc < 0, we know that the following are possible:

(–, +, +), (+, –, +), (+, +, –), (–, –, –)

From ab > 0, we know that we must eliminate (–, +, +) and (+, –, +)

From bc > 0, we know that we must eliminate (+, +, –)

Therefore, any of our answers must hold for (–, –, –)

This eliminates immediately a > 0, b > 0

Likewise, it eliminates a – b > 0 because we do not know the relative sizes of a and b. This could therefore be positive or negative.

Finally, ac is a product of negatives and is therefore positive. Hence ac < 0 does not hold.

We are left with a + b < 0, which is true, for two negatives added must be negative.

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Question

Add:

Answer

Anytime a negative number is added, it is similar to subtraction. Recovert the expression to the correct form. Simplify.

The correct answer is .

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Question

Add the negative numbers:

Answer

In order to add the negative numbers, we need to eliminate the double signs and the parentheses. A positive and a negative sign will result in a negative sign.

Evaluate the terms on the right.

The answer is:

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Question

What is $\frac{-36}{-9}$ ?

Answer

A negative number divided by a negative number always results in a positive number. divided by equals . Since the answer is positive, the answer cannot be or any other negative number.

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Question

Solve for :

Answer

Begin by isolating your variable.

Subtract from both sides:

, or

Next, subtract from both sides:

, or

Then, divide both sides by :

$x=\frac{-10}{-5}$

Recall that division of a negative by a negative gives you a positive, therefore:

$x=\frac{10}{5}$ or

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Question

Divide: $\frac{36}{-8}$

Answer

Anytime a positive number is divided by a negative number, or vice versa, the end result is a negative number. Find the common factors.

$\frac{36}{-8}= \frac{4\times 9}{-4\times 2}= \frac{9}{-2}= -\frac{9}{2}$

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Question

Divide: $\frac{-8+4}{3-6}$

Answer

In order to divide, it is necessary to simplify the numerator and denominator first.

$\frac{-8+4}{3-6} = \frac{-4}{-3}$

Divide both negative numbers. Two negatives divided will result in a positive number.

The answer is $\frac{4}{3}$ .

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Question

If is a positive number, and is also a positive number, what is a possible value for ?

Answer

Because $\dpi{100} \small -3b$ is positive, $\dpi{100} \small b$ must be negative since the product of two negative numbers is positive.

Because $\dpi{100} \small ab$ is also positive, $\dpi{100} \small a$ must also be negative in order to produce a prositive product.

To check you answer, you can try plugging in any negative number for $\dpi{100} \small a$ .

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Question

Multiply the following negative numbers: $(-4)\cdot(-6)$ .

Answer

When two negative numbers are multiplied by each other, the result is a positive number.

When a negative and a nonnegative number are multiplied with each other, the result is a negative number.

Therefore, since and are negative numbers, the product must be positive.

Therefore, the answer is positive .

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Question

Multiply: $(-3)(-6\times3)(-3+2)$

Answer

Simplify the expression term by term.

$(-3)(-6\times3)(-3+2) = (-3)(-18)(-1)$

A negative number multiplied by a negative number gives a positive number.

A negative number multiplied by a positive number gives a negative number.

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Question

Multiply: $-9 \cdot -3 \cdot -2$

Answer

Multiply the first two terms. A negative number times another negative will result in a positive number.

$-9 \cdot -3 = 27$

Multiply 27 with negative 2. A positive number times a negative number will result in a negative number.

$27\cdot -2 = -54$

The answer is:

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Question

Solve the following equation:

$\frac{-10-8}{2-11}$

Answer

$\frac{-10-8}{2-11}=\frac{-18}{-9}$

If there are two negative signs, then the answer will be positive. If there were only one negative sign, the answer will be negative.

$\frac{-18}{-9}=2$

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Question

Simplify the following expression:

Answer

Simplify the following expression:

Let's begin by expanding the inside of the parentheses.

Now, it is important to use all three negative signs. The first two will cancel out, but the third one will remain, ensuring our final answer will be negative.

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Question

If x is a negative integer, what else must be a negative integer?

Answer

By choosing a random negative number, for example: –4, we can input the number into each choice and see if we come out with another negative number. When we put –4 in for x, we would have –4 – (–(–4)) or –4 – 4, which is –8. Plugging in the other options gives a positive answer. You can try other negative numbers, if needed, to confirm this still works.

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Question

–7 – 7= x

–7 – (–7) = y

what are x and y, respectively

Answer

x: –7 – 7= –7 + –7 = –14

y: –7 – (–7) = –7 + 7 = 0

when subtracting a negative number, turn it into an addition problem

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Question

Evaluate:

Answer

Reconvert into single signs. Remember that double negatives will turn into a positive.

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Question

Subtract:

Answer

Subtracting a negative number moves the number farther left of the zero digit on the number line.

The answer is:

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Question

Subtract:

Answer

Simplify the expression by eliminating the double negative signs. Two negatives multiplied by one another will result in a positive number.

Convert the signs.

Add the right side of the equation.

The answer is .

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Question

Simplify the following expression:

Answer

Simplify the following expression:

To subtract negative numbers, we must recall that subtracting negative numbers is the same as adding a positive. The two negatives cancel each other out to become positive.

So our answer is negative 220

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