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Below are some questions and answers from our archive of questions sent via e-mail by K12 students and teachers to Ask Dr. Math. You may also browse the entire Middle School Level Archive by category.

- About Rational Numbers
- Can you explain 'rational numbers' to me? How do you express them? What kind of operations can you perform on them?
- Different Types of Numbers
- I don't understand how to tell the difference between the different kinds of numbers. i.e. reals, integers...
- Questions about .999...
- Is 0.999... a rational number? Can .999... ever be equal to one?
- Factoring Fractions
- A student asks how to divide (12ax + 16x) by (4x).
- Factor and Simplify
- How would you simplify the following problem:
(1/x^2-1/y^2)/ (1/x^2+2/xy+1/y^2) ? - Fraction Equation Problem
- Let 1/a = a + 1/b = b + 1/c = c + 1/d = 2. What is the value of abcd?
- Fraction Problems
- I am having trouble with some fractions and fractional equations.
- Solving an Equation with Fractions
- A student asks how to work the problem: (x + 5)/4 =
(x-4)/(2/5). - Solving for x
- I need help on this problem: x/x+4 = x+1/x+8.
- Solving Another Equation with Two Variables
- 6y = 3D = 54. I am supposed to solve the equation, but I don't even understand it!
- Solving Equations
- A student has a number of 'word problems' that require solving equations.
- Solving an Equation with Fractions
- v = 6 - 5/4 v. I don't know if this question is asking
6 minus 1 1/4 or 6 * 1 1/4. - Algebra using Fractions
- Please show me how to solve this equation: (5/8)X = 9.
- Algebra Test Questions
- 1. Find 3 consecutive integers such that the sum of the first and third
is 84. 2. The length of a rectangle is 5 less than twice the width, the perimeter of the rectangle is 80; find the dimensions of the rectangle.3. Solve these equations:c + 2/5 = 3/7 and1/6 = a + 3/a - 4. - Adding Fractions in Algebra
- A student needs help with adding fractions in equations.
- Fractional Coefficients
- x-4/8 - 5-2x/3 = 7/12 ?
- Simplifying Fractional Equations
- am supposed to perform the indicated operations and express results in lowest terms:
1: ((x^2 - 2xy + y^2) / 6xy) * ((3x^2y^2) /(x^2 - y^2)) = ? - Simplifying: Put it Together
- I am supposed to perform the indicated operations and express the results in lowest terms. Here's the problem: (5/x-1) - (4x/x-1) -
(2-x/x-1) = ? - Order of Algebraic Operations
- How do I solve: (9*4-7*5+6*7-10) /
( 6/6+7*3-4*3-9) and2+2*3-(2/2)*(4-3)+1 ? - Another Order of Operations Problem
- (1+1*8-9*4) / (8*9+7*2) = ?
- Sierpinski Gasket
- What is the area of a Sierpinski gasket?
- Dimes and Quarters Puzzle
- Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica has. They both have the same amount of money. What coins does each have?
- Combinations of Coins
- If I had 6 coins in my pocket, how many combinations could I have?
- Trains and Fractions
- A non-stop train leaves city A for city B at 60 m.p.h.... If to the numerator and denominator of the fraction 1/3 you add its denominator... A train moving at 45 m.p.h. meets and is passed by a train moving at 36 m.p.h...
- Speed, Distance, and Time
- If you drive one mile in 45 seconds, how fast are you driving?
- Rates and Fractions
- Find each rate as a fraction in simplest form: 1) 24 laps in 12 minutes, 2) 180 miles with 15 gallons...
- Using Improper Fractions in a Word Problem
- Mr. Smith owns 1/4 of the stock of a business. Mrs. Smith owns 5/6 as much as Mr. Smith. How much do they not own of the stock?
- Word Problem with Fractions
- Jack can finish a job in 5 days, and Richard can finish the same job in 7 days. A job is to be done by Jack and Richard together. How long will it take them to finish it?
- Proportions of Men to Women
- In a certain village 2/3 of the men are married to 3/5 of the women. What proportion of the population as a whole is married?
- Solve for x in a Percentage Equation
- Express as a function of x. 1) The volume of water that must be added to 5L of antifreeze to make a solution that is x% antifreeze...
- Why Divide Fractions?
- Where, in this wide world of ours, would one divide fractions? For example: 3 2/5 / 7/8. Can you give me a real life example?
- How to Divide Fractions?
- When dividing fractions, for example: 3/11 divided by 5, I know that you reciprocate the '5' and multiply, but I don't understand why except that it works! Can you explain it?
- A Fraction Divided By a Fraction
- What is 18/6 divided by 2/3?
- Inverting and Multiplying When Dividing Fractions
- I have always been taught that to divide fractions I must invert and multiply. Why does this algorithm work? Is there any other way to divide fractions?
- Dividing Fractions
- Tell me a shortcut for dividing fractions.
- Multiplying Fractions
- x over 2y multiplied by 4y over 2 = ?
- Can You Have Zero in the Denominator?
- My (seventh grade) math teacher and I are in the midst of an argument over whether any number can be placed over zero in a fraction. I know that when you take a fraction like 10/5, it equals 2, and 5 * 2=10, and that works out for all fractions where the numerator is larger than the denominator, but it doesn't work out for n/0. I know that you'll probably say that it isn't a legitimate fraction, but.. I still say that it is. :)
- Zero as an Exponent
- 2^3 is 2 times itself 3 times or 2x2x2. But 2^0 isn't 2 times itself 0 times, is it? Can you explain 2^0 in those terms?
- Division by Zero
- Why can't you divide a number by 0?
- Factorials
- One day when I was playing on a calculator, I found that 1 and 0 both have a factorial of 1. Can you explain this?
- Converting Decimals to Fractions
- A certain fraction is converted to a decimal and the decimal representation is 0.6428571428571428571... What is the fraction?
- Writing Repeating Decimals as Fractions
- When you are expressing a repeating decimal as a fraction, why do you use 9, 99, 999, or 9999 etc. in the denominator? For example, 0.5555...(5 repeating) equals 5/9.
- Prime Factors in Unit Fractions
- Why does the denominator of a unit fraction have to have prime factors of 2 and/or 5 in order to terminate?
- Reduced fraction
- Write as a reduced fraction: -------/.428571
- History of Fractions
- How did the Babylonians, Ancient Chinese, Egyptians, Greeks, or Hindus use fractions?

*Mara Landers*

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