Fractions

High School Questions: Ask Dr. Math

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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 High School Level Archive by category.

Fractions and Algebra

Algebra: Common Denominators
I am having problems working out two problems because I don't know how to get all of them to have equal denominators.
Calculating the Diameter of a Carpet Roll
How do you calculate the diameter of a carpet roll when you have the length and the thickness?
Simplifying Equations
Simplifying a fractional equation.
Simplifying Equations
I need to solve this by factoring, finding the lowest common denominator, then multiplying by the reciprocal. Simplify: (1+(1/x-1))/(1+(1/x^2-1)).
Simplify this equation: (x+y)/(y^2-xy-y+x) + (y+1)/(xy-x-y+1) + (x+1)/(x^2-xy-x+y)
A rare "live" talk session with Dr. Math about factoring an equation.
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 times 1 1/4.
A Trick for Solving Equations with Fractions
Help solving an equation with fractions.
Value Excluded from the Domain
f(x) = 3x^3 + x^2 - 2x/(9x^2 - 4).

Rational and Irrational Numbers

Did Pi Ruin Socrates' Career?
Is it true that Socrates is believed to have been imprisoned for teaching the existence of pi? I understand that the belief in, or the teaching of, the existence of pi was considered heresy in his day.
Does point nine repeating equal one?
When I learned how to convert repeating decimals to fractions, we were given an example in which .9 repeating equalled one. I can't logically believe this is true, and I don't see an error with the math, so what am I missing or forgetting?
Infinity, Zero
You can't divide by zero, but no one can actually prove why. We learned in trig that you can't raise zero to the zero-th power because zero would equal one. I realize infinity is not so much a number as an endless amount, but if there are an infinite number of numbers between 1 and 2, and an infinite number of numbers between 1 and 50, wouldn't the second infinity be bigger than the first?
Weird Fraction Behavior
If you look at the fractions (16/64) and (19/95), you may notice that if you cancel out the second number in the numerator with the first number in the denominator the fraction remaining is equivalent to that of the original equation. The only restrictions are that the numbers canceling must be the same number, as in the above example (a 6 for a 6), and that the numbers for the original fraction are restricted to two digits. How many more of these numbers can you find?

Fractions and Limits

Finding the Limit
I have a question about the limit of a sequence ...
Limit Problem
Find the limit of (x^2 + 2x) / (5x - 5) as x tends to infinity.
L/Hospital's Rule and Limits
Find the limit of [sin 3x / tan (x/3)] as x -> 0.

Fractions in Trigonometry and Calculus

Asymptotes
I have a question about the oblique asymptote of the function: F( X ) = ( X^3 - 3X^2 + 2X - 8 ) / (X^2 + 4X + 4 )...
De Moivre's Theorem
What is the usefulness of de Moivre's theorem?
Finding Integrals Using Trigonometric Substitutions
What is the integral of 1/(x(1-x))^(1/2)? How can I integrate this function using only the derivative of arcsin or arctan?
Integral Using Substitution
Evaluate: xdx / (x^2+1)^(1/2), given u^2 = x^2+1.
Simplifying Trigonometric Expressions
A student asks for help simplifying and solving trigonometric expressions.

Fractals

Fractals
We are doing a project on fractals. Is there any way that you could help us understand what they are about? We have read all types of books and don't understand what they are saying. Could you explain them in regular English for us?
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Mara Landers

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