Algebra in Real Life
We should always remember that algebra has a basis in real life. When we have all these variables and exponents and things, that's easy to forget. But the purpose of algebra is to help us find answers to real situations.
For example, let's say that you have a part-time job as a dog walker. You earn $15 each time you walk a dog. If d is the number of dogs you walk, your total income is $15d, or $15 times the number of dogs. That's an algebraic expression. And what if you had 6 walks scheduled this week? How much will you earn? That's where we get to evaluating algebraic expressions, our topic for this lesson.
Evaluating Algebraic Expressions
Evaluating algebraic expressions is when you substitute a number for each variable and then solve the expression. These types of problems typically look like this: Evaluate 15d when d = 6.
So this is our dog walking scenario. And you can see there are two parts to the question. First, there's an algebraic expression. This is a mathematical sentence of sorts that contains one or more variables. Here, it's 15d. Second, there's a sample value for the variable. In this case, we have d = 6.
To solve this problem, we take the value and plug it into our expression. So we'd replace the d in 15d with a 6. We complete the problem by multiplying 15 times 6, which gets us 90. That's our answer! You'll earn $90 this week - plus you'll get lots of exercise, which is kind of its own payment, right? Well, okay, the money's good, too.
Remember Parentheses
Ready to try some practice problems? Almost. First, a warning. It's critical that you always use parentheses. Did you ever go on a carnival ride where they tell you to keep your arms inside the ride? Parentheses are the ride, and minus signs are the numbers' arms. They even kind of look like arms, which is a bonus.
Here's why this matters. Let's say you have x2 - 3 and you want to evaluate it when x = 2. Okay, no problem. That's 22 - 3. Exponents are first, so I square the 2 and now I have 4 - 3. That's easy: 1. You might be thinking, 'I don't need parentheses. I solved that problem without them just fine.'
Okay, what if x = -2? So we have -22 - 3. Again, I square the 2 and I get -4 - 3. That will be -7. And that's wrong. You should have squared not just 2 but -2. Then you'd get 4 - 3 and again get 1.
That would've been easy to remember if you'd written the expression as (-2)2 - 3. So consider this a safety reminder: Always use parentheses. Don't let your numbers lose their arms.