June 5, 2022 by

#### Introduction

One math skill that is introduced in the sixth grade is that of combining like terms. Like terms are mathematical terms that have the same variables and exponents. Like terms may have different coefficients that will be added together as in basic mathematical problems.

Combining like terms is the way in which a student simplifies a math problem and serves as the proper form for writing a polynomial. Though this skill may sound intimidating, students have built up to the ability to combine like terms for many years by the time they reach sixth grade.

For example, in kindergarten, a student may be asked to put all the red objects in a pile or all the square objects in a group together. In third grade, students may be asked to put all the even numbers in a column or all the multiples of five in a row. These are base skills for combining like terms.

Combining like terms meets the common core standard of “being able to write, read, and evaluate expressions in which letters stand for numbers.” However, some students begin to struggle with mathematics when letters are added as a component. That is why worksheets like the ones included on this page are of such importance.

Being able to combine like terms is a very basic skill in higher levels of math such as algebra, geometry, and calculus, so understanding is imperative. If using the worksheets on this page, start with the most basic.

Have students look for letters and subscripts (numbers in small writing above the letters). If students are struggling, allow them to circle like terms with the same colored pencil with different terms in different colors. This can help keep terms straight. A conversation may go as follows:

Teacher: Look at this problem that we will use to practice like terms 2b + b. Now, there is only one term here. What is it?

Student: b

Teacher: Great! We have 2b +b. If the letter is alone then we can say it is equal to 1 so 2b + b = 3b. Let’s try another one. 8i2 + 3h + i2 + 2h. What are the terms like?

Student: i and h?

Teacher: Very good, but that is not quite right. Look at the subscript beside the I, that is part of the equation, so we have i2 and h. Now we need to combine like terms. The easiest way to do this is rearrange the equation. So we have 8i2 + i2 + 3h +2h. What will our problem be if we combine like terms?

Student: 9i2 + 5h

Teacher: Wonderful job! We must remember that when we combine like terms, if we rearrange the equation to solve, we need to keep the sign that is in front of the number we are using. Try a few equations on your own.

As students work through each equation, check in to make sure they understand how to combine terms correctly. Keep in mind that the equation does not have to be solved, that is a separate skill for a later date.

#### FAQ – Combining Like Terms

##### Why am I struggling so much with this concept? I am usually good at math.

It is not uncommon for strong math

students to struggle with concepts such as combining like terms. When we

combine like terms we are moving into the realm of algebra which is more

detailed and adds letters to the numbers that are familiar in mathematics. It

will take time and practice to understand this skill, but it will be worth it.

##### What are like terms in math?

When a math problem refers to “like

terms” it is referencing the terms that are the same as far as letters or

exponents. For example, 3h and 4h are like terms, but 3h and 3h2

are not like terms because one is squared and the other is not. The same is

true of the terms 3rx and 5r. Both terms have r, but the other is rx meaning

they are not like terms. This concept can become confusing, but with practice

it does get easier.

##### Why do I need to combine like terms?

Combining like terms is a way to simplify a problem before solving. When first asked to simplify terms, the goal is just to properly combine like terms without solving, but in later lessons the entire problem will be solved.

##### How do I know whether to add or subtract when combining like terms?

It can be confusing when the goal is to combine like terms, but the signs are changing. Pay attention to the sign directly in front of the term. For example, 3h + 5r – 2h will be combined to h +5r because the5r comes after an addition sign and we are left with 3h – 2h which equals h because the 1 is assumed when a letter is alone.

Another example would be 8t + 2t – 4s + 6s. We begin to simplify by adding 8t + 2t which is 10t. We are then left with -4s +6s which equals 2s. The whole thing is then combined to be 10t +2s. The skill takes time to perfect, but watch letters, exponents, and signs.

##### What if there are multiple like terms in a problem?

As you build this particular skill, problems may become more difficult and diverse. If multiple like terms appear, the process is still the same. Several examples are offered below.

3r + 5s + 2t + 2r – 3t + 4s = 3r + 2r + 2t – 3t + 5s + 4s

Now combine like terms 5r – t + 9s. Make sure to watch your signs.

Or

2a + 6b2 + 3c – a + 7b + 2c = 2a – a + 7b +6b2 + 3c + 2c

Now combine like terms a + 7b + 6b2 + 5c. We cannot combine 7b and 6b2 because they are not like terms.

Or

6 – 9 + 3g – 2h + 6h = -3 + 3g + 4h

This problem is very straightforward. If numbers are alone, combine them as terms as in the 6 and 9 in the problem.

#### Description

These worksheets help students to write, read, and evaluate expressions in which letters stand for numbers. It includes exponents,  distributive property.

#### Curriculum snippet

Apply and extend previous understandings of arithmetic to algebraic expressions.