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SAT Math : Arithmetic

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Example Questions

Example Question #1 : How To Multiply Negative Numbers

If is a positive number, and -3b is also a positive number, what is a possible value for ?

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

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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Example Question #1 : How To Multiply Negative Numbers

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

Possible Answers:

Correct answer:

Explanation:

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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Example Question #1 : Negative Numbers

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

Possible Answers:

972

270

Correct answer:

Explanation:

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.

(-3)(-18)(-1)= 54(-1)=-54

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Example Question #1561 : Sat Mathematics

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

Possible Answers:

Correct answer:

Explanation:

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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Example Question #1 : How To Multiply Negative Numbers

Solve the following equation:

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

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

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

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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Example Question #11 : Negative Numbers

Simplify the following expression:

(-7)^3

Possible Answers:

343

Correct answer:

Explanation:

Simplify the following expression:

(-7)^3

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

-7*-7*-7=49*-7=-343

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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Example Question #11 : Negative Numbers

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

Possible Answers:

-(+4)

Correct answer:

Explanation:

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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Example Question #1 : Negative Numbers

Solve for :

16-4x=x+6

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

$-\frac{18}{5}$

Correct answer:

Explanation:

Begin by isolating your variable.

Subtract from both sides:

16-4x-x=6 , or 16-5x=6

Next, subtract from both sides:

-5x=6-16 , or -5x=-10

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 x=2

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Example Question #41 : Integers

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

Possible Answers:

$\frac{9}{2}$

$-\frac{9}{2}$

$-\frac{19}{4}$

Correct answer:

$-\frac{9}{2}$

Explanation:

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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Example Question #1 : How To Divide Negative Numbers

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

Possible Answers:

$-\frac{4}{3}$

$-\frac{10}{3}$

$\frac{10}{3}$

$\frac{4}{3}$

$-\frac{2}{5}$

Correct answer:

$\frac{4}{3}$

Explanation:

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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SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Multiply Negative Numbers

Example Question #1 : How To Multiply Negative Numbers

Example Question #1 : Negative Numbers

Example Question #1561 : Sat Mathematics

Example Question #1 : How To Multiply Negative Numbers

Example Question #11 : Negative Numbers

Example Question #11 : Negative Numbers

Example Question #1 : Negative Numbers

Example Question #41 : Integers

Example Question #1 : How To Divide Negative Numbers

All SAT Math Resources

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