*Algebra can be used to solve different types of equations, but algebra is also many other things Modern algebra (or "higher", or "abstract" algebra) deals (in part) with generalisations of the normal operations seen arithmetic and high school algebra.*

We know that we can find the distance traveled by multiplying the speed and the time traveled at that speed (for instance, if we travel 2 hours at 30 miles per hour, we have gone 60 miles).

In addition, we know that Bill travels a third of the time ( The Celsius (C) and Fahrenheit (F) temperature scales are related by a linear function.

Furthermore, number theory interacts more specifically with certain areas of mathematics (e.g., analysis) than does algebra in general.

Indeed, number theory is traditionally divided into different branches, the most prominent of which are algebraic number theory and analytic number theory.

For instance, we can talk about 1 banana, 1 meter, 1 liter, 1 mile per hour, 1 ton, or a limitless variety of other things.

Units act in many ways like multiplicative constants: they multiply and divide like any other factor, and they can cancel each other out when they are the same.This problem illustrates the process of unit conversion; a year is the same as 525,600 minutes even though 1 ≠ 525,600.Bill takes a trip in which he drives a third of the time at 30 miles per hour, a third of the time at 50 miles per hour, and a third of the time at 70 miles per hour.The main difficulty is translation of the details of the word problem into the kinds of mathematical expressions that you have learned to handle. This step may seem obvious, but you will save yourself much time and difficulty if you take some time to carefully read what the problem says. A word problem may provide you with enough details to calculate all sorts of parameters, but the problem probably will only be asking for one or two. You don't need to be an artist to do this-just draw something that you can understand and that helps you organize your thoughts about the problem. The mathematical expressions that you glean from the word problem will involve an unknown value (or values) at some point (one of which may be the result from step 2 above); try to identify what this value is and assign it a variable symbol. Problems from the real world involve units, and you need to keep track of them. If you have carefully performed the preceding steps, you should be in good shape to write the correct expressions. The result should be a solution that fulfills the requirement you wrote down in step 2 (that is, whatever the problem is asking for). Does the problem ask for a speed but you've ended up with units of acceleration in your answer?Here are some steps that will help you organize the process of translating from words to mathematical expressions that you can solve. You may not be able to visualize all the details, but you should gain a mental picture of what is generally being discussed. Thus, figure out what you are trying to find and write it down. If the problem involves a moving automobile, for instance, you don't need to draw a professional rendition when a box or something similar (even marked "car" if necessary) will do. Write down this assignment for reference as you solve the problem (for instance, " = the velocity of the car"). You've probably gone astray somewhere along the line.You may be surprised at how far you can get by approaching the problem systematically.First, let's identify what the problem is asking for: a total trip time, which we can call , which is the value we want to calculate.Let's look at a couple quick examples (note that although these examples use plural and singular units for ease of reading, whether a unit is written in its plural or singular form has no bearing on the meaning or the math): This second example is actually a case of identity, because 12 inches = 1 foot. We can thus see how the presence of units has an effect on the math, but the same general principles that we have studied still hold. Let's multiply by factors with corresponding units that convert from years to seconds as follows.(Again, note that we are actually multiplying in each case by 1 because of the relationship of the units.) Thus, 1 year = 525,600 minutes, or (alternatively) there are 525,600 minutes in a year.Algebra revolves around the concept of the variable, an unknown quantity given a name and usually denoted by a letter or symbol.Many contest problems test one's fluency with algebraic manipulation.

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