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 parts by this factor. Notice that dividing both the numerator and denominator keeps the fraction the same, it just looks different now.

To determine the greatest fraction, you should find the least common denominator. To find the least common denominator of two fractions, you can count multiples of each denominator until you find the same number. Once you find the common denominator, you can compare the fractions.

If you cannot easily find a common multiple, there are a couple speed tips that can also help you. One method is to multiply each fraction by the other fraction’s denominator, since the resulting denominators will be the same. You can then determine the greatest fraction by the result of multiplying each fraction’s denominator to the other fraction’s numerator.

As a final 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!

For multiplication, you simply multiply across.

The product’s numerator will be the product of the factors’ numerators.

The product’s denominator will be the product of the factors’ denominators.

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).

To add and subtract decimals, simply line up the decimal points and solve. You can add zeros after the last decimal to line up the numbers. For example:

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. Then, you must move the decimal place of the result (to the left) to account for the total number of decimal places contained in all of the multiplied values.

In the problem below, 5.2 has one decimal place, and 4.11 has two decimal places; after multiplying 52 and 411, you must move the decimal point three places.

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, and then multiply the values.

To divide decimals, you also must move 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 gets rid of any pesky decimals in the divisor.
- 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**

- ⅓
- 94/77
- 7.14
- 7
- 2/9, 4/13, 10/19
- 12/56 → 3/14

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