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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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?

Why Does Long Division Work? [12/22/2006]

I'm curious why the standard long division algorithm works. How do all the "bringing down" and other steps lead to the right answer?

Why Does the Order of Square/Square Root Matter? [8/28/1996]

Why does the square root of x^2 equal absolute value of x, but the square of the square root of x equals just plain old x?

Why Do We Have the Order of Operations? [03/05/2006]

Why do we have the order of operations? Why can't we just calculate from left to right? That seems much easier and more logical to me.

Why do we Need Algebra? [9/13/1996]

Why do we need algebra?

Why Do We Use Variables in Algebra? [01/31/2004]

Why do we use letters to represent numbers in algebra?

Why Factor? [08/18/2001]

I've been explained the how's, the where's, the what's, but not the WHY. What is the practical use of factoring?

Why Flip the Inequality Sign? [10/26/2001]

Please tell me why you flip the inequality sign when dividing by a negative number.

Why FOIL? [11/21/2002]

How can I explain to the class the importance of learning FOIL?

The Why of Algebra [11/13/1998]

What is algebra for? Why do you need the letters and variables?

Why Order of Operations? [5/17/1995]

7th-graders wonder why we use the order of operations at all. Why not just set up problems to read from left-to-right? Can you suggest some "real-life" examples that show the necessity of using the order of operations?

Why Some Solutions to Absolute Value Equations are False [10/24/2004]

When solving equations involving absolute value, you sometimes get an answer that doesn't check in the original equation. What is it about absolute value that makes this happen?

Why Use Letters in Math? [12/01/1999]

Why do we need to use letters in math?

Why Use n for Any Number? [09/28/2002]

Why do people use n when any number can fit in or when they want to indicate position?

Why Use Variables? [06/01/1999]

What is the point of using variables when you could use numbers?

Why Use X and Y for Variables? [10/23/2002]

Why do we use x and y for variables in an equation?

Writing Equations for Word Problems [09/01/1998]

Can you help me convert the following word problems to equations and solve them? An oil painting is 16 years older than a watercolor ....

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