Middle School Math Problems with Solutions

Math is a cumulative subject; as students advance from grade to grade, the concepts they learn in math class advance, too. If your child is struggling with middle school math, you can introduce sample problems and model how to solve them as a way to boost his confidence in his abilities.

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How Are Middle School Math Problems Different from Elementary Math Problems?

As your child enters middle school, he likely will be introduced to math concepts that are quite a big tougher than he's used to. While first through fifth grade generally are spent mastering basic skills in addition, subtraction, multiplication and division, middle school math typically requires more complex application of these skills in the form of ratios, proportions and statistical thinking.

If your child is struggling with a particular math concept, you might work through a sample question with him. Then, stand by while he attempts to solve a similar problem on his own, which can help him gain confidence in his math skills.

Middle School Math Problems and Solutions by Grade Level


1. If a car is traveling 45 miles per hour, how many miles will it travel in seven hours?

To solve, your child should create a proportional relationship: 45/1 = x/7. Then, he or she should cross multiply to reach the answer: x = 315 miles.

2. 4/5 ÷ 2/1

To divide fractions, your child first must turn the second fraction into a reciprocal fraction, so 2/1 becomes 1/2. Then, he or she should multiply across: 4/5 x 1/2 = (4 x 1)/(5 x 2) = 4/10, which can be reduced to 2/5.

3. -41 + 8

In middle school, students begin to work with negative numbers, which can be confusing at first. You might have your child use a number line to visualize the negative number system. The answer to this problem is -33.


1. On his quiz, John answered 12 out of 15 questions correctly. What percentage of questions did he get right?

First, your child should establish the fraction 12/15, which equals 0.80. The, he should multiply the decimal by 100 to find the percentage: 0.80 x 100 = 80%.

2. A building is 510 feet high. On a scale drawing, one inch equals three feet. How large would the building be on the drawing?

Your child should use proportional relationships to solve this problem. The first ratio is 1/3 because three feet are represented by one inch. The second ratio is x/510, with the variable representing the height of the building in the scale drawing. Next, your child can establish a proportional relationship like this: 1/3 = x/510. Then, cross multiply so that 3x = 510, and divide both sides by three. The building would be 170 inches on the drawing.


1. Solve for x: 23 = 4x - 1.

Your eighth-grader should add one to both sides, so that the problem looks like this: 24 = 4x. Then, he can isolate the variable by dividing both sides by four. The answer is x = 6.

2. In a right triangle, the base is three inches, and the height is four inches. Find the length of the hypotenuse.

For this problem, your child will have to use the Pythagorean Theorem, which is A^2 + B^2 = C^2. He should first insert the known values: (3)^2 + (4)^2 = C^2. Next, he should square the numbers so that 9 + 16 = 25 = C^2. Finally, your child must find the square root of 25, which is 5. The hypotenuse is five inches long.
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