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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Swimming Lengths [03/05/1997]

Together, Raoul, Tammy, and Nathan swam 39 lengths of the pool. If each swam the same number of lengths, how many lengths did each swim?

Swiss Chocolates, Lollipops, Gumdrops [02/10/2003]

You have $100 and must buy 100 pieces of candy...

Translating Words into Math [3/8/1995]

We are doing story problems. I need help on understanding them so that I can solve them by myself. I am stuck on one particular problem: The number is decreased by 1/3 of the number. The result is 62. Find the number.

Two Methods of Factoring Quadratics [04/14/1998]

Could you describe how to factor quadratic trinomials?

Two-Step Equations and Equations with Variables [5/17/1996]

I'm in pre-algebra and I suffer at 2-step equations and the ones with variables on both sides...

Undefined Slope and Zero Slope [04/11/1997]

What is the difference between an undefined slope and a slope of zero?

Understanding Variables [08/02/1999]

Why do we replace numbers with letters in algebra?

Upstream and Downstream Speed [08/16/1998]

It takes a ferryboat 2 hours to travel 30 miles going downstream and 3 hours for the return trip upstream. What is the ferryboat's speed in still water?

Variables: Connecting Letters and Numbers [12/06/2001]

Is there some sort of table you can use to show what letter is equal to what number?

What Does 'n' Mean? [09/25/2001]

In a pair of numbers, if n is the first number, what is the second?

What is a Quadratic Equation? [08/04/1997]

What is a quadratic equation? What is it used for? How can we use it to solve everyday problems?

What is Slope? [9/2/1996]

What is a slope, and if given a slope = n equation, how do you apply that slope number to another graph problem?

What is the Distributive Property? [3/4/1995]

A middle school student questions one of the most important introductory topics in algebra.

When do the Cars Meet? [01/23/1997]

Two cars are 635 kilometers apart. They start at the same time and drive toward each other. One travels at 70 km/h and the other travels at 57 km/hr. In how many hours do they meet?

Why does PEMDAS work? [7/9/1996]

Why does the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) order of operations really work?

Write in Slope-Intercept Form [11/06/1997]

Write and sketch x - y + 2 = 0 .

X greater than 25, OR less than 30 [8/17/1996]

x > 25 or x < 30. The "or" part of the problem bugs me. Is the answer {26, 27, 28, 29}?

10% Sodium + 30% Sodium [07/09/2003]

A group of chemists are conducting an experiment to produce a new liquid material. One chemical contains 15% sodium (Na) and the other chemical contains 30% sodium (Na). Once they mix the two samples the resulting chemical contains 22% sodium (Na). How many milliliters (ml) of each sample must be mixed to obtain 600 ml of the new chemical?

14b * 20x Rearranged [03/11/2002]

What is 14b times 20x ?

1/x = x% [04/16/2001]

For what value of x does 1/x = x% ?

25 Coins for a Dollar [02/13/2003]

I need 25 coins for my dollar. What are they?

300 Foul Shots [07/11/2001]

A basketball player shoots 100 foul shots on a given day, and increases the number he shoots by 10 per day...

3 Algebra Problems: Simplifying [8/18/1996]

35x+8-34x = 3-2; -12a-7+4a = 37-12; 10m+3-7m = 18+9.

4-Variable Systems of Equations [12/10/2002]

2w-x+5y+z=-3; 3w+2x+2y-6z=-32; w+3x+3y-z=-47; 5w-2x-3y+3z=49.

60 Eyes and 86 Feet [09/30/1997]

How many camels and ostriches were in the zoo?

9x^2 = 64 [03/22/2003]

I am trying to figure out what 9x^2 = 64 is.

Absolute Value As Statement about Distance [10/16/2002]

|x|+|x+2|+|x-4| < 5.

Absolute Value Equations [10/16/1998]

How do you make the set of numbers -3 < x < 11 into an equation using absolute values?

Absolute Value Equations [10/30/2002]

What is the answer to 'the absolute value of x-3 + the absolute value of 3-x = 12' ?

Absolute Value Inequalities [06/23/2004]

I have to solve |x| + 3 < 5 and I don't remember if it's 'and' or 'or'. Is there an easy way to remember, or another way to solve the problem?

Absolute Value (Real Numbers: Rational) [02/02/1999]

Find the solutions of |1/(x-2)| >= 4.

Adding Algebraic Fractions, Different Denominators [8/24/1996]

How do I solve 7/2x + (2-x)/(3x^2) + (3 + 5x)/(6x^3)?

Adding and Subtracting Algebraic Fractions [8/24/1996]

How do I add and subtract fractions with the same denominator?

Adding and Subtracting Inequalities [09/29/1998]

Can you explain the rules? What if two inequalities are in the same or opposite directions?

Adding Fractions in Algebra [2/9/1996]

A student needs help with adding fractions in equations.

Adding Fractions That Have Variables [03/24/2002]

9a/10 + 2/5. I have the answer in the back of the book but I don't know how to solve it.

Adding Fractions with Variables [03/21/1997]

How do I add 7/53 + 23/n ?

Adding or Dividing Letters [10/26/2002]

Solve for x: ax + bc = cx - df. I don't understand how you can divide and add and subtract letters.

Addition Property of Inequalities [8/29/1996]

If x > y, then x+z __?__ y+z ??

Algebra and Fractions [08/30/1997]

The sum of two-thirds and one-ninth of a number is 28. Find the number N.

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