### All Algebra 1 Resources

## Example Questions

### Example Question #1 : Real Numbers

What is ?

**Possible Answers:**

**Correct answer:**

Divide the absolute values to get the magnitude of the answer.

Remember the following rules:

Positive divided by negative is negative.

Positive divided by positive is positive.

Negative divided by negative is positive.

Since we are dealing with two negatives, our answer will be positive.

### Example Question #1 : How To Divide Integers

**Possible Answers:**

**Correct answer:**

This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!

Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have

.

But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as

.

We can now divide into , which gives us

.

The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with because added to equals , and minus equals .

### Example Question #2 : Integer Operations

If a number is divisible by 9 and 12, it **must** also be divisible by...

I. 36

II. 48

III. 144

**Possible Answers:**

III only

I and II only

II only

III and II only

I only

**Correct answer:**

I only

For a number A to be divisible by another number B, A must share all of the prime factors of B. For example, 100 is divisible by 10 because the prime factors of 10 (5 and 2) are found in the prime factors of 100 (2, 2, 5, and 5).

In this problem, we have a number A that is divisible by 9 and 12. First, find the prime factors of 9 and 12. The factors of 9 are (3, 3). The factors of 12 are (2,2,3). So, to be divisible by 9 **and** 12, the number A **must** have the factors (2,2,3,3). Multiply those together, and we get 2*2*3*3= 36.

So, A **must** be divisible by 36. It could be divisible by the other answer choices, but since the question asked which choice **must** be right, we can only choose 36.

### Example Question #3 : Integer Operations

Rewrite 100 as a number in base six.

**Possible Answers:**

**Correct answer:**

One way to do this:

Divide 100 by 6. The remainder will be the last digit.

Now divide the quotient by 6. This remainder will be the second-to-last digit.

The quotient is less than 6, so it is the first digit. The base-six equivalent of 100 is .

### Example Question #1 : Real Numbers

Divide and express the quotient in scientific notation:

**Possible Answers:**

**Correct answer:**

All of these choices are equivalent to the correct answer. But only is in scientific notation.

### Example Question #1 : Real Numbers

Divide:

**Possible Answers:**

**Correct answer:**

Write the factors of the two numbers.

### Example Question #2 : Integer Operations

If a number is divisible by , which of the following is always true?

I. Divisible by

II. Divisible by

III. Divisible by

**Possible Answers:**

All true

I and II

II only

I only

None true

**Correct answer:**

I and II

If a number is divisble by some number , then it is also divisible by all of its factors. Hence, if a number is divisible by , it is also divisible by , and . Thus, I and II are both true.

### Example Question #1 : Integer Operations

Divide .

**Possible Answers:**

**Correct answer:**

Rewrite the expression in fraction form.

Write out the common factors of both the numerator and denominator.

We can then see that the fraction can be reduced to without having to conduct long division.

The answer is .

### Example Question #1 : Integer Operations

Divide:

**Possible Answers:**

**Correct answer:**

Rewrite the expression as a fraction.

Write out the multiples of the numerator and denominator.

The twos can be cancelled. Simplify what remains of the fraction.

The answer is:

### Example Question #1 : Integer Operations

Divide the integers:

**Possible Answers:**

**Correct answer:**

Rewrite the expression as a fraction.

Rewrite the fraction by common factors of two.

Divide and cancel the twos, which will become one.

The answer is: