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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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Meaning of Greater Than, Less Than Symbols [11/07/2002]

Does the meaning of less than and greater than signs depend on location?

Meaning of Term in Algebra [09/16/2007]

Why is it that when you multiply or divide two numbers or variables they become one term (such as 2*x becoming 2x), but when you add or subtract two numbers or variables they are still two terms (such as 2 + x)?

Measuring the Length of a Moving Train [08/12/2003]

I was driving in the opposite direction from a moving train that had many cars behind the locomotive. It took me approximately 2-3 minutes from the time my car 'met' the front of the train until it passed me going the opposite direction. My speed was about 40 miles an hour. Is it possible to estimate the length of this moving train without actually measuring when it is not moving?

Mixed Operations [04/08/1997]

When calculating 839-319+200/20x15, I got 540. But, should I have first multiplied...?

Mixing Peanuts and Cashews [11/19/1999]

Peanuts sell for $3.00 per pound. Cashews sell for $6.00 per pound. How many pounds of cashews should be mixed with 12 pounds of peanuts to obtain a mixture that sells for $4.20 per pound?

Mixture Problem [11/11/1997]

How much pure antifreeze should be added to 3 gallons of a 30 percent antifreeze solution to get 65 percent antifreeze?

Monetary Conversions [01/27/2001]

Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2 mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya and for papaya to mango?

Monomial, Polynomials [11/14/1997]

What is a monomial?

Monomials, Polynomials [03/02/2001]

Can you explain monomials and polynomials to me?

More Variables Than Equations in a System [01/21/2002]

I have a problem that uses four variables but only two equations to relate them. I don't seem to have enough information to figure out the value of each variable or answer the question. Can you help?

Mother's Age in Terms of Daughter's [06/27/2001]

The sum of the ages of a father, a mother, and a daughter is 73. When the father is twice as old as the daughter, the sum of their two ages will be 132...

Mowing Half a Lawn [03/31/2002]

Chris and Lee are each responsible for mowing half of their 50-foot by 90-foot rectangular back yard...

Mr. Brown's Walk [09/09/1997]

One day Mr. Brown took the 4:00 p.m. train, arrived at the station one hour early, and started walking home... How long did Mr. Brown walk?

A Mule and a Donkey [04/08/1999]

A famous Euclidean brainteaser.

Multiplication and Division Equations [11/29/2001]

Solve for x: 17x = 85.

Multiplying/Adding Fractions Gives Same Answer [03/01/2002]

Find two fractions which, when multiplied and added, give the same answer.

Multiplying a Fraction by a Variable [08/17/2006]

How do I find the product of something like (1/3) times 'a'?

Multiplying and Dividing Fractions [8/18/1996]

Three hard problems, illustrated.

Multiplying Binomials and Other Polynomials [04/16/2004]

I have a hard time multiplying binomials properly, such as (2x + 5)(x + 7). I do not know what order the problem should be solved in.

Multiplying or Dividing by a Negative Number [04/08/1999]

When x(x-4) is less than 0...

Multiplying Polynomials [2/10/1996]

How do you multiply polynomials?

Names of Polynomials [05/22/1999]

Why is an equation having only two roots, one of which is raised to the second power, called a quadratic equation?

Natural Domain of a Function [03/12/1999]

Some inputs don't make sense for some functions.

Negative Exponents [10/23/1996]

I have to simplify this expression with non-negative exponents: x^5.

Negative Numbers Combined with Exponentials [03/09/2001]

Why in the order of operations is negation a multiplication done after exponentiation, rather than as a part of the base? What about polynomials?

Negatives and Inequalities [09/10/1998]

Why when we multiply or divide an inequality by a negative number do we reverse the inequality sign?

Negatives in Absolute Value Expressions and Equations [10/15/2005]

How do I solve an equation like |x - 3| - 4 = 0? How do I evaluate absolute value expressions with negatives, like |-7 - 3|?

Negative Squared, or Squared Negative? [10/18/2002]

In -3^2, isn't -3 actually a number, and not -1*3? If so, then shouldn't the value be -3*-3=9?

Nested Negative Exponents [8/2/1996]

How do I deal with nested negative exponents?

Net Result of Consecutive Percentage Increases [12/11/2003]

Suppose a quantity is increased by some percentage, and then is later increased again by another percentage. How can I calculate the overall percentage increase?

Nonlinear Factors [10/12/1998]

I have been told that factoring the sum of two squared numbers is not possible, but factoring x^4 + 4 is possible. Please explain.

Normalization [08/01/2001]

How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ?

Number Puzzle: 26, 70 [09/12/2001]

The sum of two numbers is 26; 4 times the first number plus 2 times the second number equals 70. What are the two numbers?

Number * Sum of Remaining Four Numbers [04/03/2003]

Find 5 numbers such that when each number is multiplied by the sum of the remaining 4 numbers, the following values will result: 152, 245, 297, 320, 360.

One Variable Equations [04/26/1997]

How do you solve 14 = 7d - 2 + d?

Operator Precedence [08/13/2003]

Since the following statement is true: (1+1)**(5-2) is 8, why is the following statement true and not false: 2**1+1 is 3 and not 4, and 3*1**3 is 3 and not 27...' ?

Orange and Grape Sodas [08/24/2002]

Douglas bought a total of 50 cans of orange and grape sodas. He bought 12 more cans of grape than orange. How many of each did he buy?

Ordering Exponents and Variables [04/08/2000]

Is there a rule for putting terms in descending order if the variables have the same exponent? What about negative exponents and descending order?

Order in Linear Expressions [11/20/2001]

Can you give me a convincing argument as to why, in an equation such as y=13-7x, where y is a function of x, it should be written as y=-7x+13?

Order of Addition, Subtraction [9/5/1996]

If an equation has both addition and subtraction in it, which do I solve first?

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