# Variables in Expressions and Equations Worksheets

We begin to real spend a good bit of time chasing after those pesky unknown values in math expressions and equations called variables. These little placeholders are often signified through use of letters as symbols. The two most commonly used letters are x and y. We need to remember that any symbol can be used to define a variable as long as it is consistently used throughout the problem. I had a College Physics professor that was known for using the most unique symbols to define variables. I remember that we were trying to determine the speed at which a football travelled on the school field. He used a car with screeching tires to define speed, a meter stick to define distance, and a clock to define time. These worksheets and lessons will help students understand the purpose and uses of variable in equations and expressions.

### Aligned Standard: Grade 6 Expressions and Equations - 6.EE.B.6

- Variables In Word Problems Step-by-step Lesson- We give you a whole paragraph to sift through. We give you the variables and ask you to complete the thought.
- Guided Lesson - Write expressions from word problems and solve a premade expression.
- Guided Lesson Explanation - It will really help you, if you outline the thoughts behind this one before you proceed with it.
- Practice Worksheet - The variables are presented in the word problems and we ask you to solve them midstream.
- Matching Worksheet - Match the word problems to the expressions.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

These problems are all about find differences in a situation.

- Homework 1 - Max went to the market. There he saw 7 puppies. X puppies lost their way. 5 puppies were left at the market. How many puppies lost their way?
- Homework 2 - There were two fish ponds. Each pond has 50 fish. But f fish die due to environmental pollution. Now only 24 fish are left. How many fish past away?
- Homework 3 - A company ships 10 boxes of flip flops across the country. The total number of pairs of flip flops was 100. How many pairs of flip flops did the company put in each box?

### Practice Worksheets

The use of variables here is directly implied to help students grasp the concept.

- Practice 1 - There were two packs of match boxes. Each box has 100 match sticks. But m match sticks were damaged. Now only 67 sticks are left. How many total sticks were damaged?
- Practice 2 - Winnie has 10 kitties. Nina gives her d more kitties. Write the expression that shows the total number of kitties Winnie has.
- Practice 3 - Ed has 8 burgers. He ate x numbers of burgers. Write the expression that shows the number of burgers left.

### Math Skill Quizzes

Each quiz tends to focus on one area of the skill. Make sure to look at them all.

- Quiz 1 - Write the expression that shows p is added to 40?
- Quiz 2 - Write the expression that shows 650 is subtracted from m.
- Quiz 3 - Joy has 6 lollipops. Matt gives her d more lollipops. Write the expression that shows the number of lollipops Joy has.

### Why Would You Use Variables to Represent Numbers?

You will find variables (symbols designated most often by letters) in many mathematics topics, so understanding why they are used in the first place is essential. Variables are those letter symbols that are used to represent unknown values in a problem. It often seems like the more difficult a problem becomes; the more unknown numbers that are present.

Variables allow us to state that we have an unknown and to specify where it lies within the expression, statement, equation, or inequality. While that does not seem like it carries a lot of weight, it is the perfect place to define a set unknown value because it allows us to track it and determine the value, if we so choose to do so. With the help of variables, you can easily convert a word problem into an equation, which is the first step for solving it. Let us consider an example:

12x + 3 = 8x + 7

Here, you need to find the value of x, which makes the above equation true.

So, the first step consists of determining the value of the variable (with its numbers) on one side of the equal sign. While the constants (numbers) should be placed on the other side of the equal sign.

By changing the sign, the signs before moving variable or number will be changed oppositely. That means, here the plus sign will change to the minus sign.

12x - 8x = 7 - 3

Now, we will simplify the above equation. 4x = 4. This is where it gets tricky; we know that we want the value of x and not 4x. So, we want to keep x alone on one side and place the constants on the other. Now, the number with the variable is basically multiplied to it. So, when you take 4 on the other side then, it will change from a multiplying number to a dividing number. Let us look at the example.

x = 4/4. Now, 4 divided by 4 is equal to 1. So, the value of x is 1. x = 1.

In algebra, variables are the primary quantity that we are often spending most of our time determining. Understanding how to properly rearrange equations, inequalities, and expressions is often more than half the battle. If we think of variables as placeholders, it often makes it very simple to work through. Just as the name indicates, the end value of variables can vary based on the situation that they find themselves in.