Combining Like Terms - Grade 6 - Download 7 Worksheets Now

For a sixth-grade student, the world of mathematics begins to open up to a new language: algebra. One of the first and most fundamental concepts you’ll encounter is combining like terms. It’s a key skill that simplifies complex algebraic expressions and sets the foundation for more advanced math. So, what exactly does it mean to combine like terms, and how do you do it?

What is Combining Like Terms?

At its core, combining like terms means simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. Think of it like sorting a fruit basket. You can group all the apples together and all the oranges together, but you can’t add the apples and oranges to get a single, new kind of fruit. Similarly, in an algebraic expression, you can only combine terms that are “alike.”

What are “like terms”?

The variable must be raised to the same exponent. For instance, 3i² and i² are like terms, but 3i² and 3i are not.
They must have the exact same variable. For example, 5x and 2x are like terms. 5x and 2y are not.

combining like terms — Combining like terms – Fruit sorting example

How to Combine Like Terms: A Step-by-Step Guide

To combine like terms, follow these simple steps:

Identify Like Terms: Look at the entire expression and identify groups of terms that have the same variable and exponent. Be sure to include the sign (+ or -) that comes before each term. For example, in the expression 3u+t2−4t2−2u, the like terms are 3u and −2u, and t2 and −4t2.
Rearrange the Expression: For clarity, rearrange the expression so that the like terms are next to each other. This is a helpful visual step that can prevent mistakes. For the example above, you’d write it as 3u−2u+t2−4t2.
Combine the Coefficients: Add or subtract the numerical coefficients (the numbers in front of the variables) of each group of like terms.
- For the u terms: 3u−2u=1u, or simply u.
- For the t2 terms: t2−4t2=1t2−4t2=−3t2.
Write the Simplified Expression: Put the simplified terms back together to form the final expression. In our example, the simplified expression is u−3t2.

How to Combine Like Terms with Exponents

The process for combining like terms with exponents is the same as above. The key is to remember that the exponents must match exactly for the terms to be “like.”

Example 1: In the expression 3i2+3i+i2+i, the like terms are 3i2 and i2, and 3i and i.
- Combine the i2 terms: 3i2+i2=4i2.
- Combine the i terms: 3i+i=4i.
- The simplified expression is 4i2+4i.
Example 2: For the expression 7m2+8m2−2n2+n2, the like terms are 7m2 and 8m2, and −2n2 and n2.
- Combine the m2 terms: 7m2+8m2=15m2.
- Combine the n2 terms: −2n2+n2=−n2.
- The simplified expression is 15m2−n2.

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