Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

Middle School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

This page:
  algebra checkmark

  Dr. Math

See also the
Dr. Math FAQ:
  order of operations

Internet Library:
  basic algebra

  algebra help


About Math

   factoring expressions
   graphing equations

   factoring numbers


     conic sections/
   3D and higher



Number Sense
   factoring numbers
   negative numbers
   prime numbers
   square roots

Word Problems

Browse Middle School Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Direct and indirect variation.
    Inequalities and negative numbers.
    Positive/negative integer rules.
    Solving simple linear equations.

Use Factoring to Find Two Consecutive Integers... [7/31/1996]
Find two consecutive integers whose product is 56.

Using Euclid's Algorithm with Three Numbers [11/05/2003]
How do I find the GCD of three integers using Euclid's Algorithm? I am not sure where you plug the third integer into the algorithm.

Using Guess and Check to Start an Algebra Problem [02/15/2008]
Laura is three times as old as Maria was when Laura was as old as Maria is now. In two years Laura will be twice as old as Maria was two years ago. Find their present ages. Dr. Ian shows that by first making a guess and checking it you can then easily write the algebraic equations needed to solve the problem.

Using Interval Notation to Express Answers [12/03/1996]
Solve for x in the inequality x/(x+3) >= 1/(x-1) and express the answer in interval notation.

Using Variables to Solve Word Problems [05/10/1998]
Susan puts only dimes and quarters in her coin bank ...

Variable Expressions with Parentheses [9/9/1996]
How do you solve 2(x-1)-3(2-3x)-(x+1) using the distributive property?

A Variable for Each Digit [11/28/2001]
A husband's age is the inverse of and greater than his wife's age... Some examples are 82,28 or 54,45. Is there a way to solve this without simple trial and error?

Velocity and Time [02/11/1999]
A car averages 30 km/hr the first half of a trip, and 50 km/hr the second half of the trip. What is the car's average velocity for the trip?

A Velocity-Time Problem [02/16/1999]
If you drive 40 mph instead of 30 mph, you save 30 seconds per mile, but if you make the same 10 mph increase from 70 mph to 80 mph, you only save 5.6 seconds per mile. Why?

Venn Diagram - Fast Food Restaurants [05/09/2002]
From a list of how many restaurants serve what kinds of food, deduce the total number of restaurants.

Verifying the Solution to an Inequality ... by Substituting? by Checking Boundaries? [04/28/2010]
A student is confused about how to verify work on a linear inequality in one variable, which also features fractions and sign changes. Doctor Peterson responds with an explanation of how to check a solution to an inequality: by testing its boundaries.

Water Main Section Lengths [01/09/2003]
A water main is being laid using pipe that comes in either 18-foot or 20-foot sections. The water main will require 14 fewer sections of 20- foot pipe than if 18-foot sections are used. Find the total length of the water main.

Weighted Average of the Velocities [01/30/2003]
Finding the average velocity for each of the three phases of the trip...

Weighted Averages [11/30/2001]
An advertisement for an orange drink claims that the drink contains 10% orange juice. How much pure orange juice would have to be added to 5 quarts of the drink to obtain a mixture containing 40% orange juice?

What are Like Terms? [11/20/2001]
Examples of like terms.

What Are Variables and How Do They Work? [06/29/2004]
I don't understand the meaning of even basic algebra, like what 2y or x means. What do variables mean?

What Are Variables For? [02/09/2001]
Why is it important to be able to figure out the values of variables?

What Does It Mean to Distribute [08/25/2007]
I understand the basics of the distributive property, but I'm confused about what the 'over' means, like in the distributive property of multiplication over addition or over subtraction.

What Do Input and Output Mean in Math? [04/09/2007]
What is the relationship between the input and output on a table? I'm not quite sure what an input or output is.

What Do Parentheses Mean? [08/15/2002]
Can you help me find ways to figure out what parentheses mean?

What Is a Coefficient? [01/29/2004]
What is a coefficient?

What is 'Algebra'? [8/6/1996]
What is the meaning of the word 'algebra'?

What is Algebra? [08/24/1997]
Could you explain algebra from the ground up?

What is Algebra? [07/20/2001]
Algebra is like arithmetic, but some of the numbers have names instead of values...

What is a Partial Fraction? [01/08/1999]
What do partial fractions have to do with polynomials?

What is the Value of K? [01/24/2003]
For positive integer walues on N, define N! to be the sum of integers 1 to N inclusive.

What is x? [01/07/2002]
Can you tell me how to work out 5x + 3 = 38 ?

What's the Value of x? [07/25/1997]
2x = x+18+27 and 3x = 2x+7+9.

What Time Did Ajay Start? [08/06/2003]
Three persons, Ajay, Bhanu, and Chandu, plan to travel from P and reach Q at 4.00 PM...

What Time Does She Get to Work? [04/30/2002]
Lillian drives to work at an average speed of 45 miles per hour. If she travels 30 miles to work and leaves at 8:00 A.M., what time does she get to work?

When Do You Flip an Inequality Sign? [12/19/2005]
What does it mean to change the sense of an inequality? When do you have to do that?

When FOIL Fails [03/22/2001]
Find the product - (2c-3)3rd power. I can do FOIL on a question to the second power, but I cannot figure out how to do a question to the third power.

When Hands of a Clock Meet [8/29/1996]
To the nearest second, what is the first time after 12:00 that the hour hand and the minute hand of a clock are together?

When Was King George Born? [08/23/2002]
King George died 180 years after King Alfred was born. Their combined age when they died was 73 years. King Alfred died in 315 A.D. In what year was King George born?

Which is more 'simple'? [09/24/2001]
Which is considered more simple (when simplifying): 2x+2y (two terms and three operations) or 2(x+y) (one term and two operations, but the higher operation of parentheses)?

Which Property? [10/11/2005]
A look at the general ideas of commutative, associative, and distributive properties with the goal of understanding them and being able to remember which one is being used in a math problem.

Who Picked the Most? [09/12/1998]
Arrange the names of the people in the order of the number of peaches that each picked, starting with the person who picked the most.

Who Will Win the Race? [11/26/2002]
Who will win the race and by how many meters?

Why Algebraic Expressions with Parentheses? [03/18/2003]
How would you write these algebraic expressions without parentheses? -(2x-3y-6) and -(5x-13y-1).

Why Does Cross Multiplication Work? [05/09/2002]
Why does the rule a/b = c/d also mean ad = bc? Why can we solve proportions by cross multiplying?

Page: [<prev]  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 [next>]

Search the Dr. Math Library:

Search: entire archive just Middle School Algebra

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994- The Math Forum at NCTM. All rights reserved.