8th Grade Math: Problems with Answers

In 8th grade, students further their studies of algebra and begin to graph equations. If your 8th grader needs extra practice with these concepts, you can create your own practice problems at home, using the samples below as examples.

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How Can I Emphasize the Importance of Learning 8th Grade Math?

Many 8th grade pre-algebra and algebra textbooks have answers in the back. It may be tempting for your son or daughter to check the answer to a problem before attempting to solve it by him- or herself. To emphasize the importance of doing the problem first, you might point out to your child that teachers often give students partial credit for showing their work. You also might remind your child that he or she won't be able to solve problems on a test if he or she is copying answers out of the back of a book instead of learning the concept.

When practicing math at home with your 8th grader, have him or her explain each step of his or her solution aloud to you. That way, if it's wrong, you can reinforce the correct steps.

Sample Problems With Solutions

Simplify

3 (3x - 5) + 2 (x - 4)

To simplify this problem, your child first should use the distributive property to clear the parentheses. To do this, he or she should multiply the number outside the parentheses by the numbers inside. In other words, (3 x 3x) and (3 x -5) for the first expression, and (2 x x) and (2 x -4) for the second expression, so the equation becomes 9x -15 + 2x - 8. Then, your child should combine the like terms, resulting in a final answer of 11x - 23.

1/2 (8x + 4) - 1/3 (3 - 9x)

As with the previous problem, your child should begin by distributing. The resulting equation should be 4x + 2 - 1 - 3x. The solution is x +1.

Solve for the Variable

7 (x + 1) + 4 (2x - 3) = 40

Your child should first distribute the numbers outside the parentheses - 7x + 7 + 8x - 12 = 40 - and then combine the like numbers - 15x - 5 = 40. To isolate x, he or she should add 5 to both sides, so that 15x = 45. Finally, your child should solve for x by dividing both sides by 15. The answer is x = 3.

Lines and Graphs

If a line has a slope of 2 and passes through the point (4,3), what is the equation for the line?

To solve this problem, your child should begin by inserting the given coordinates into the slope equation (y = mx +b). It should look like this: 3 = 2(4) + b. Now, he or she can solve for b, which is -5. Finally, your child should insert the slope and the b variable back into the slope equation, so that y = 2x - 5.
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