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Exercises

Variables as Unknown Quantities

Sometimes we are given information about a number, and we need to figure out what the number is.Sample Problems1. Fill in the blank: 2 + ? = 10.The answer is 8, since 2 + 8 = 10. This solution may...

Variable Notations

Remember that mathematicians love to abbreviate things (RTMLTAT, for short). To write "3 multiplied by 4" in symbols, we could write 3 · 4, 3 × 4, or (3)(4). To write "3 multiplied by x" we coul...

Constants

Constants are quantities that do not change. They are like crotchety old curmudgeons who are stuck in their ways. 3, 57, 299, and  are constants. π and e are also constants. We can al...

Expressions and Equations

In the English language there are phrases and there are sentences, as you know. A phrase is a string of words that expresses a thought but does not form a complete sentence. A sentence is a grammat...

Combining Like Terms

You probably don't keep bananas in your sock drawer or toothpaste on your bookshelf. If you do, we can recommend a good therapist. Aside from it being an awful hassle to run from the bookshelf...

Independent and Dependent Variables

Let's take a closer look at how independent and dependent variables work by working through some examples:Sample ProblemJim gets paid $10 per hour. The amount Jim gets paid in a week depends on the...

Formulas

It is been a long time since you have needed to deal with formula on a daily basis. You probably transitioned to solid foods at around five months. But, now it is back.All right, this is a differen...

Evaluating Expressions by Substitution

Remember that a variable is like an empty box that is waiting for a number. It is a box, and it waits patiently. Have you ever seen a box wait? Those things have unbelievable staying power.We call...

Evaluating Formulas by Substitution

As we mentioned, a formula has a dependent variable on one side and an expression involving the independent variable(s) on the other side. To evaluate a formula, we evaluate the expression containi...

Temperatures

Let F be degrees Fahrenheit, a unit commonly used in the United States, and let C be degrees Celsius, used almost everywhere else. Oh, but ours is the right one. Sure... We can convert fr...

Weights

While some conversion formulas force you to round up or down, they're close enough for reliable estimates. In the previous exercise, for example, no one will ruin her cookies by being a single degr...

Distances and Speeds

Let M be miles, and let K be kilometers:K = 1.609MM = 0.6214KSince  (this is one of those important formulas you should probably commit to memory), in order to convert a speed f...

Money

At this website, you can figure out how much your dollar is worth in about any currency unit in the world. This site may be particularly useful to you if you do, in fact, have only one dollar. In t...
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