Rational numbers are numbers that can be represented as a fraction whose numerator and denominator are both integers.

The numerator is located in the top portion of a fraction, and the denominator is located in the bottom portion of a fraction. The denominator cannot be zero, as any number divided by zero is considered undefined, but the numerator may be zero.

An improper fraction contains a numerator that is larger than the denominator, and a mixed number contains a fraction paired with an integer.

To reduce a fraction, find the greatest common factor of the numerator and the denominator, and then divide both by this factor.

You can also find which fraction is greater using this method as well. Since the denominator will be the same in both numbers, simply multiply one fraction’s denominator to the other fraction’s numerator. The results will let you know which fraction is greater.

You can use the common denominator to find which fraction is greater as well. Since the denominator will be the same in both numbers, simply compare the numerators by multiplying them by the opposite fraction’s denominator. The results will let you know which fraction is greater.

As a speed tip, however, you can also quickly compare fractions by splitting the fractions into two groups, bigger than a half and smaller than a half.

To do this, divide the denominator of the fraction by two, and see if the numerator is larger or smaller than the halved denominator.

If you want to add or subtract fractions, all of the fractions must share a common denominator (a number that each fraction’s denominator can be a factor of).

The simplest method of finding the common denominator is multiplying the denominators together.

Remember, you must perform the same action to the numerator that you perform to the denominator!

To divide fractions, you simply find the reciprocal of the divisor (usually the second number) and multiply it to the dividend (usually the first number).

While addition and subtraction of decimals are a game of lining up the place values, multiplying and dividing decimals involve a little more work.

For multiplication, you multiply the values with decimals just as you would regular integers without worrying about the decimal place values.

However, the product from multiplying the values this way is not the correct answer. You must still move the result’s decimal place to the left the same number of times as the total number of decimal places contained in all of the multiplied values with decimals.

An easy way to do this is count how many total decimal places there are in the values, mark the amount to the side of the values (ex. 4 dcp.), and then multiply the values.

To divide decimals, you are still moving the decimal place. However, the movement occurs before you divide.

- Set up the values in long division, with the dividend underneath the long division symbol and the divisor to the left of the long division symbol.
- Move the decimal place of the divisor to the right until it is just to the right of the last digit.
- Move the decimal place of the dividend to the right the same number of times you moved the divisor’s decimal place.
- Perform long division on the new values to achieve the correct answer.

Review these fractions and their decimal equivalents to save time on calculations (remember the ISEE does not allow calculators):

**Answers to Practice Problems**

Answers:

- ⅓
- 1 13/19
- 24.9466
- 35
- 2/9 < 4/13 < 6/19
- 1/21
- D
- D

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