Ask Dr. Math

Middle School Archive

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.

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2a/5 or 2a Divided by 5? [12/13/2001]

Why, when writing a division problem, do you write 2a over 5 instead of 2a divided by 5?

Absolute Value and Inequality [8/23/1996]

Show that |a+b| = |a| + |b| iff ab is greater than or equal to 0.

Acid Concentration, Heating Bill [7/6/1996]

1) A pharmacist has 8 liters of a 15 percent solution of acid. How much distilled water must she add.... 2) By installing a $120 thermostat, a family hopes to cut its annual heating bill...

Adding and Subtracting Polynomials [12/08/1996]

How do you add and subtract polynomials?

Algebra: Common Denominators [5/14/1996]

I am having problems working out two problems because I don't know how to get all of them to have equal denominators.

Algebra Problem [2/7/1995]

If 10y=1 and 10x=1, what is the value of x+y?

Algebra problem [6/10/1996]

How do you solve 27x + 123 = 177?

All About Functions [11/06/1996]

Could you please explain functions?

Associative, Distributive Properties [9/5/1996]

Please explain the associative and distributive properties.

Basic Tips on Solving for X [11/16/2000]

I've tried several times to solve problems like 2x - 7 = 3 + x, but I still can't get the answers. Can you help?

Blending Seed [09/27/1998]

How much of $0.65/lb seed does a dealer need to combine with 200 lbs of $0.45/lb seed to make a $0.55/lb blend?

Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003]

All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?

Diagonals and Tiles [11/17/2001]

Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through?

Distributive Property [04/25/2002]

What's the best and simplest way to teach pupils that a-b = -(b-a)?

Distributive Property, Illustrated [09/28/2001]

How can I show (12*2) + (12*3) using the distributive property?

Doubling Sequence [8/24/1996]

On Jan 1st it snowed one centimeter; on Jan 2, 2cm; on Jan 3, 4 cm...

Equation of a Line Parallel to an Axis [06/19/2003]

How can I get the equation of a line if the line passes through a point and is parallel to the x- or y-axis?

Equations of a Line given Two Points [8/31/1996]

How do you find the equation of a line going through two points if you only know the two points?

Equations: the "Elimination" Method [11/20/1996]

Is there an easier way to solve a system of two equations than by the substitution method?

Equations with Variables [9/23/1996]

Solving equations with variables on both sides, like 6 - 2y = 7y + 13.

Expand Binomial [6/13/1996]

Expand (2x + 3)(x - 5)

Explaining Algebra Concepts and FOIL [08/04/1998]

Some ideas for learning algebra that may help prevent frustration.

Explaining Fractions [11/06/2001]

I am a practicum student in a 8th grade math class. The teacher and I don't know how to explain to the students why you can do this manuever. c=d/g; c/d=g; d/c=g.

Factoring Fractions [12/7/1995]

A student asks how to divide (12ax + 16x) by (4x).

Factoring Polynomials [11/07/2001]

Factoring polynomials like 12x^3y^9 + 20x^5y^4.

Finding the Equation of a Line [01/08/1997]

Given either a point and a slope or two points, how do you find the equation of a line in both point-slope and standard form?

FOIL Procedure [8/13/1996]

Can you help me remember the F.O.I.L concept when dealing with negative and positive numbers?

Geometric Objects and Properties using Algebra [06/29/1998]

Why does y = mx+b, and what does it mean?

Graphing Coordinates [1/15/1997]

How can you tell if you have a straight line just by looking at the numbers?

How Many Chickens and Ducks? [8/16/1996]

A man bought 20 chickens and ducks, with a $2 discount per chicken and 50 cent discount per duck...

How Many People? [06/11/2001]

There are three more people in front of Clancy than in front of Nancy, and twice as many in front of Mary Ellen as in front of Nancy. The total people in front of the girls is 11. How many people are in front of each of the girls?

How much is the dagger worth? [10/12/1996]

A sword and dagger are together worth 300 copper pieces. The sword is worth 200 copper pieces more than the dagger. How much is the dagger worth?

How Old are Ben and Kris? [10/17/1999]

Five years ago Ben was 2/3 as old as Kris. Ten years from now he will be 5/6 as old as Kris. How old are they now?

How Old is Chris Now? [12/26/2001]

Pat is twice as old as Chris was when Pat was as old as Chris is now. If Pat is 24 now, how old is Chris now?

How to do a Problem with Multiple Exponents [1/21/1995]

Could you explain how you do this type of question? - [(5a^2 * b^3)(-2a^4 * b^7)]/[(a*b^2)^2]

How to Turn Word Problems into Algebra Equations [6/6/1996]

Where do you put the letters and numbers when setting up algebra equations from word problems?

Inequality Sign Switch [01/13/2003]

How do you solve the inequality (-1/8)w < 3 ?

Isolate the Variable [9/9/1996]

Simplifying equations: what are the steps to solve 4c + 23 = 9c -7?

Linear Expressions [08/17/1999]

What are linear expressions, and how will I use them in my life?

Math Age Word Problem [03/20/2001]

Bob is as old as John will be when Bob is twice as old as John was when Bob's age was half the sum of their present ages...

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