# Rewriting Expressions Worksheets

This topic has a substantial impact on your ability to properly perform many different types of problems in algebra. Algebra can be used to help you make good decisions and track your progress in countless areas of everyday life. So, I would say this is a very important topic. Expression usually consists of three different possible types of terms: variables, coefficients, and constants. A variable is an unknown or missing value. A coefficient is a number that is used together with variables to indicate a proportional relationship of some type. We then have constants that are definite numeric values. All of these parts can be used together to move all three of terms around and state the expression in a different, but equivalent way. These worksheets and lessons will demonstrate how you do this and will help you master rewriting expressions.

### Aligned Standard: Grade 7 Expression & Equations - 7.EE.A.2

- Create an Expression Step-by-step Lesson- We need you to determine how much Madison will make next year based on his salary increase.
- Guided Lesson - These scenarios will require you to create expressions to work towards solving them.
- Guided Lesson Explanation - Remember, these are very basic expressions just meant to be introductory at this point.
- Practice Worksheet - When students complete this one, they should have a good handle on the skill.
- Matching Worksheet - Match the word problem to the expression that represents it.

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

### Homework Sheets

Use an expression to solve the word problems.

- Homework 1 - Allen gets a 4% raise every year. He made a salary of $40,000 this year. How much will he make next year?
- Homework 2 - All varieties of dogs are $50. Anna buys a pug and a pit bull. Write an expression that represents the total cost, T of the dogs if p represents the number of pug dogs and b represents the number of pit bulls.
- Homework 3 - Rachel sold 55 bears this week. The sale of bears grows by 5% every week. What will be the next sales of bears?

### Practice Worksheets

These are aimed at a more intermediate level.

- Practice 1 - Aiden wants to buy chocolates. All varieties of chocolates are $6.50 each. Aiden buys one dairy-milk chocolate and one Bourneville chocolate. Write an expression that represents the total cost, T, of the candy if d represents the number of dairy-milk chocolate and b represents the number of Bourneville chocolate.
- Practice 2 - Jacob gets an 8% raise every year. He made a salary of $70,000 this year. How much will he make next year?
- Practice 3 - Michael fills 3 pages in one hour. David fills 5 pages in one hour. This week Michael fills 2 pages extra. Write an expression that represents the weekly number of pages by both. M= the number of hours that Michael fills pages this week. D= the number of hours that David fills pages this week?

### Math Skill Quizzes

Make sure that you hone your decimal, fraction, percentage conversions before working on these.

- Quiz 1 - Denny eats 2 burgers per hour. John eats 3 burgers per hour. This week John eats an additional 3 burgers. Write an expression that represents the number of burgers they ate this week.
- Quiz 2 - The height of snake is 200cm. Every day it grows by 2%. What will be the snake height tomorrow?
- Quiz 3 - All varieties of burgers are $3.50. Justin buys veggie burgers and non-veggie burgers. Write an expression that represents the total cost, T, of the clocks if (a) represents the number of veggie burgers and (n) represents the number of non-veggie burgers.

### Rewriting Algebraic Expressions

There is more than one way to rewrite an algebraic expression. This can be really helpful because it allows us to put expression in a different format that makes it easier for us to solve. We can use this skill to our advantage to manipulate expressions and bend them to our needs. Rewriting an algebraic expression means that the equation needs to be rewritten in a relatively shorter and simpler format. For example, in an expression 2^{3} + 2^{5} = 2^{8}. The powers in this condition have been added with each other because the constant or the base term was the same. This is very similar to solving just straight up arithmetic.

1. We can apply the same tactic in algebraic expressions, as well. For example, x^{3} + x ^{5} = x^{8}.

2. When the expression involves division, then the powers need to be subtracted. The power of the denominator will be deducted from the power of numerator. For example, x^{5} / x^{3} = x^{2}. Using these two steps, you can easily rewrite your algebraic expressions in a much simpler and shorter format.

3. Now when it comes raising to the power of or algebraic expressions involving multiple powers. In that case, the powers will be multiplied with each other. Here is an example: (x^{3})^{5} = x^{15}

There also a few old math operation properties that can be applied to expressions to help us rewrite them. Just remember that if you can apply these properties to your standard integers, they also apply to variables as well. The distributive property is one of the more commonly used applications on this topic. To remind ourselves that states that if: a(b + c) it can be written as: ab + ac.

The last thing to keep in mind is that we can always combine like terms. This is usually our final step, but it can be used earlier in the problem to get a better ordering of the terms to make them easier to control. 2x^{2} + 3y - x^{2} can be rewritten by combining the like terms (x^{2}). When we compile: 2x^{2} and - x^{2}, we are left with: x^{2}.

We can use a variety of techniques that we have discussed in a stream with one another. Take a look where we use the distributive property and then combine like terms:

If we were asked to rewrite this expression: 2x + 4(x – 5) it can be by using a mixture of the techniques that we have discussed. Take a look:

2x + 4(x – 5)

2x + 4x – 20 (distributive property)

2x – 20 (combine like terms)

Something to be familiar with when working on these types of problems is the terminology used to understand what is expected of you in problems. A problem asks us to rewrite expressions when we are asked to reduce or simplify.