Sometimes the answer explanation suggests that I clear fractions by multiplying an entire equation by a common denominator. Sometimes the answer explanation suggests that I manipulate just one side of an equation. How do I know which is better?

This is a surprisingly subtle question. It turns out that the answer is partly “Do what’s mathematically sound,” but mostly “Do what’s useful.” It’ll take me 6 posts to show what that means:

Manipulating Algebraic Equations and Expressions with Fractions 1: A Quick Quiz

Manipulating Algebraic Equations and Expressions with Fractions 2: Expressions

Manipulating Algebraic Equations and Expressions with Fractions 3: Another Example

Manipulating Algebraic Equations and Expressions with Fractions 4: Equations

Manipulating Algebraic Equations and Expressions with Fractions 5: A Word Problem

Manipulating Algebraic Equations and Expressions with Fractions 6: Systems of Equations

Let’s begin with a quick quiz. I’ll give you a link to an answer key at the end of the quiz, and I’ll use these questions as the basis for the rest of the posts in this series.

4. Little Texas Drilling Company has three wells, each producing oil at a constant rate. Well A produces one barrel every two minutes. Well B produces one barrel every three minutes. Well C produces one barrel every four minutes. How many hours does it take Little Texas Drilling Company to produce 165 barrels of oil?

(A) 2
(B) 3
(C) 4
(D) 18
(E) 180

(A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

(B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question

(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

(D) each statement alone is sufficient

(E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

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