# Algebraic Expressions Exercises

#### Variables as Unknown Quantities

Sometimes we're given some tantalizing information about a number, and we need to figure out what the number is.Sample ProblemFill in the blank: 2 + ? = 10.The answer is 8, since 2 + 8 = 10. Th...

#### 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 c...

#### Constants

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

#### Expressions and Equations

In the English language, we've got phrases and we've got sentences. A phrase is a string of words that expresses a thought but doesn't form a complete sentence. A sentence is a grammatically corr...

#### 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 t...

#### 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...

#### Formulas

Here's video to help illustrate a few formulas.
It's been a loooong time since you've needed to deal with formula on a daily basis. You probably transitioned to solid foods at around five mont...

#### Evaluating Expressions by Substitution

Remember that a variable is like an empty box that's waiting for a number. Have you ever seen a box wait? Those things have unbelievable staying power.We call it substitution when we pu...

#### 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 contai...

#### 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 from o...

#### Weights

While some conversion formulas force you to round up or down, they're close enough for reliable estimates. If you're cooking, for example, you probably won't ruin your cookies by being a single d...

#### Distances and Speeds

Let's talk kilometers and miles for a sec. If you're an American and you ever visit Canada, you might be thrown off by the speed limit signs. We know we were. That's because everything is in kilo...

#### 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...