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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Order of Algebraic Operations [5/25/1995]

How do I solve: (9*4-7*5+6*7-10)/( 6/6+7*3-4*3-9) and 2+2*3-(2/2)*(4-3)+1 ?

Order of Operations [05/19/1999]

Given a, b, x, and y, find ax/by.

Order of Operations and Square Roots [10/09/2009]

At what step in the order of operations (PEMDAS) does one work out a square root? Is it an exponent?

Order of Operations Dispute [09/26/2000]

The problem reads: N divided by (division sign)ml where n=12, m=6, and l=3. I believe the correct answer should be .6666, as 12 divided by 18 equals this...

Order of Operations for Solving Equations [10/12/1995]

How would you multiply a question like this: -2(x-y)^2?

Order of Operations in an Equation [9/13/1995]

Let c = 4. Find: 16 divided by 2c. Is the answer 2, since 16 divided by 8 is 2, or is it 32 because order of operations tells us to multiply or divide from left to right?

Order of Operations: Negative Sign, Parenthesis [8/25/1996]

How do I explain why (-2)^2 = 4 and -2^2 = -4?

Order of Operations: Polynomials and Exponents [9/10/1996]

I'm stuck on 3*5-4^2, (3*5-4)^2, -6^2*2, (-6*2)^2 .

Order of Operations without Parentheses [8/3/1996]

How do you solve a problem like 21+82-59+29*86*66/50*7/87?

Order of Operations with Parentheses [08/04/2001]

I know the answers to the problems but not how to get the answers.

Order of Operations with Percentages [04/05/2001]

Why does the order of operations exclude percentage, square roots, etc.?

Origin of the word Quadratic [04/07/1998]

Why is a second degree polynomial called quadratic?

Parallel and Perpendicular Lines [01/14/1999]

How do you tell without graphing whether the graphs of these equations are parallel, perpendicular, or neither?

Parallel Lines [12/31/1998]

What are some ways of proving lines parallel - geometrically and algebraically?

Parallel Lines [9/3/1996]

The lines y=kx+4 and 3y=(k+3)x-5 are parallel. Find k.

Parentheses from the Inside Out [03/03/2003]

I don't understand order of operations and evaluating expressions.

Pascal's Triangle Pattern [04/22/1999]

What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order, and adding the products yield?

Passing Cyclists [08/31/2003]

Two cyclists ride on the same road in opposite directions, passing each other twice...

Percentage Increase in Cost of Eggs [8/4/1996]

When eggs went from 17 to 39 cents, by what percent did the price increase?

Plus or Minus Sign [03/08/2002]

What does this equation mean: y = +- k ? The - sign is directly under the + sign.

Polynomial Factoring Rules [04/02/1997]

How do I apply the polynomial factoring rules to t^21+1 and 25y^2-144 = 0?

Polynomials with x [9/10/1996]

How do I solve problems like 3x-x(3-5x)=(5x-2)(x+4)?

Population and Percentage [03/07/1999]

Given population data, find the number of women in two different years.

Positive Domains [5/19/1996]

What are the values for x in x > -2 when the domain is positive?

Pre-calculus Extra Credit Projects [6/5/1996]

A high school pre-calculus student asks for suggestions for an extra credit project.

Precedence of Unary Operators [09/01/99]

The PEMDAS rule for order of operations ignores unary operators. Can you explain the proper precedence for them, and give an example showing how not knowing the rule can cause an incorrect result?

Price Plus 1/2 Price [12/05/2001]

A puzzle book costs $5.00 plus one-half of its price. How much does the puzzle book cost?

Probate Puzzle [12/15/2003]

A will specifies that every son should receive three times as much as a daughter and every daughter should get two times as much as their mother. What is the mother's share?

Problem about Rain [09/20/2000]

During a recent span of time, 11 days had some rain... How many days had no rain at all?

Problem Solving and Mental Process [10/03/2002]

Two numbers add up to 19. The difference between the two numbers is 3. What are the numbers?

Proof That All Numbers Are Equal? [12/06/2005]

I saw a proof that all numbers are equal, which makes math pointless. There must be something wrong with the proof. Can you tell me what?

Quadratic Equation [6/22/1996]

What is a quadratic equation used for?

Quadratic Equation [8/28/1996]

What is the formula for the quadratic equation?

Quadratic Equation [04/08/1997]

The sum of two numbers is 15 and their product is 54. Find the numbers...

Quadratic Equations [3/19/1996]

How are quadratic equations used in the real world?

Quadratic Equations [6/25/1996]

Solving quadratic equations using the zero-factor property, the square root property, and the quadratic formula.

Quadratic Formula [5/11/1995]

Could you give me the quadratic formula?

Quadratic Formula, Distributive Property [06/02/1997]

Who invented the quadratic formula?

Quadratic Function: Definition [8/6/1996]

What is a "quadratic function"?

Quadrilateral Patterns [03/06/1997]

What is the formula that gives the number of quadrilaterals within a square grid when you increase the square grid by one unit on each side?

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