Algebra 1 : Integer Operations

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #81 : Integer Operations

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Example Question #82 : Integer Operations

Solve 

Possible Answers:

Correct answer:

Explanation:

First, distribute the exponents to the numerators and denominators:

.

Then, rewrite the problem in expanded form:

Next, rewrite the problem so that you only have prime factors in both numerators and denominators: 

.

Last, simplify by "canceling out" like terms, leaving you with

and multiply across both numerators and denominators, which will give you .

Example Question #83 : Integer Operations

Possible Answers:

Correct answer:

Explanation:

Example Question #84 : Integer Operations

Multiply and express the product in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Use your power properties to multiply these numbers.

This is not in scientific notation, so adjust as follows:

Example Question #85 : Real Numbers

Multiply and express the product in scientific notation:

Possible Answers:

Correct answer:

Explanation:

Use your power properties to multiply these numbers.

This is not in scientific notation, so adjust as follows:

Example Question #83 : Integer Operations

Rewrite as a number in base ten: 

Possible Answers:

Correct answer:

Explanation:

Example Question #87 : Real Numbers

Rewrite as a number in base ten: 

Possible Answers:

Correct answer:

Explanation:

 

Example Question #88 : Real Numbers

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

In this problem, you need to use the proper order of operations to find the correct answer: PEMDAS (Parentheses, Exponents, Multiplication-Division, Addition-Subtraction).

Exponents show up first in this problem, so the first step is to simplify:

This results in:

The next step is the multiplication:

This results in:

The next step is to do the remaining addition and subtraction from left to right.

499 is your final answer.

Example Question #1 : Mathematical Relationships

Evaluate the expression.

Possible Answers:

Correct answer:

Explanation:

Follow the correct order of operations: parenthenses, exponents, multiplication, division, addition, subtraction.

First, evaluate any terms in parenthesis.

Next, evaluate the exponent.

Divide.

Finally, add.

Example Question #11 : Proportionalities

The quantity x varies directly with y. If x is 26 when y is 100, find x when y is 200.

Possible Answers:

104

26

52

13

6.5

Correct answer:

52

Explanation:

We must set up a proportion. Since x varies directly with y, when y is multiplied by 2, x is also multiplied by 2. 26 times 2 is 52.

Direct variation:

Learning Tools by Varsity Tutors