Math Problems: Expressing Answers in the Simplest Form

What is the Method for Simplifying Answers?

Over the course of their math education, students have to solve many math problems by reducing them to their simplest forms. The two most common types of problems that have to be reduced are fractions and radicals. In both cases, the trickiest aspect is simply remembering to do it.

When you reduce fractions, you have to divide the numerator and denominator by the greatest common factor (GCF) to reach the simplest form. For example, when you simplify 6/10, you need to recognize that two is the GCF of six and ten. When you divide both the numerator and denominator of 6/10 by two, you get 3/5.

To simplify radicals, you'll generally be using either the product rule of radicals or the quotient rule of radicals. Use the product rule to simplify the square root of a large number. For example, the square root of 600 can be broken down into the square root of (100 x 6). As a result, you can take the square root of 100, which is 10, and the square root of 6. The final answer is 10 square root of 6.

The quotient rule of radicals is used to simplify a fraction that includes square roots, such as the square root of (2/9). This can be rewritten like this: (square root of 2) / (square root of 9). Because you can only solve for the square root of nine, which is three, your final answer should look like this: (square root of 2)/3.

Problems by Concept

Fractions

1. 25/30

Remember that you must divide both the numerator and the denominator by the same number. To simplify this fraction, you need to divide both by five. The answer is 5/6.

2. 60/80

The GCF is 20, which makes the answer 3/4.

3. 75/90

The GCF is 15. The answer is 5/6.

4. 33/66

The answer is 3/6 with a GCF of 11.

Radicals

1. Square root of 3300

The answer to this problem is 10 square root of 33. Begin by breaking down 3300 into 33 x 100, so the problem should look like this: square root of (33 x 100). Then, you can take the square root of 100, which is 10. As a result, the answer is 10 times the square root of 33.

2. Square root of 54

Simplified, this radical is 3 square root of 6. The product of 9 and 6 is 54, so you can think about the problem like this: square root of (9 x 6). Because you can take the square root of 9, the problem can be simplified to 3 times the square root of 6.

3. Square root of (5/49)

Rewrite this problem by taking the square root of the numerator and the denominator separately. It should look like this: (square root of 5) / (square root of 49). You can leave the numerator in this form; however, take the square root of 49, which is 7. As a result, the answer is (square root of 5) / 7.

4. Square root of (25/100)

Similar to the above problem, take the square root of 25 and the square root of 100 separately, like this: (square root of 25) / (square root of 100). Both the numerator and the denominator can be simplified: square roof of 25 = 5 and square root of 100 = 10. As a result, the simplified answer to this problem is 5/10, or 1/2.