Algebra for 6th Grade: Concepts and Problems

Algebra Concepts for 6th Grade

Evaluating Expressions

One of the first algebra skills you'll learn is evaluating an expression when different values are given for the variable. For instance, you might be given the expression 4x + 2 and asked to evaluate it for x = 5. This means you'll replace the 'x' in the equation with a five, and then do the math, like this:

4x + 2

4(5) + 2

20 + 2

22

Then, you might be asked to evaluate the same expression with a different variable value, like seven. Here's how you would solve that problem:

4x + 2

4(7) + 2

28 + 2

30

Equivalent Expressions

You might not realize it, but you already know how to identify equivalent expressions when there are no variables involved. For example, you know that 3 x 4 = 4 x 3 because of the commutative property of multiplication (a * b = b * a). In algebra, you'll use the distributive property to identify equivalent expressions. This property states that a(b + c) = ab + ac. For example, 2(3 + 4) = (2 * 3) + (2 * 4) = 6 + 8 = 14.

You don't have to use the distributive property to solve that problem, since you could just add together three and four to get seven, and then multiply seven by two to get 14. However, this property is very helpful for simplifying algebra expressions with variables, like 2(x + y). Since you don't know the values of x and y, you can't add them together, but the distributive property tells you that 2(x + y) = 2x + 2y.

Solving Equations

Solving an equation means figuring out the value of the variable in that equation. Since you know both sides of an equation are equal, you can find the variable's value by getting it on one side of the equation by itself (isolating it). Here's how to do this:

1. Identify an inverse operation that will undo the part of the equation with the variable. For example, if the equation is 3(x - 7) = 12, you will choose division because it's the inverse of multiplication. You cannot solve the subtraction problem yet because it's inside the parentheses.

2. Perform that operation on both sides of the equation. It's always essential to do the same thing to both sides so that the equation remains true. For 3(x - 7) = 12, you'll get x - 7 = 4 if you divide both sides by three.

3. The next inverse operation will be addition, since x - 7 contains subtraction. Adding seven to both sides of the equation gives you x = 11, which is the solution to the equation.