Fractions for Nursing School Entrance Exam Study Guide (page 4)

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems

Problems involving fractions may be straightforward calculation questions, or they may be word problems. Typically, they ask you to add, subtract, multiply, divide, or compare fractions.

Working with Fractions

A fraction is a part of something.

Example:

Let's say that a pizza was cut into 8 equal slices and you ate 3 of them. The fraction tells you what part of the pizza you ate. The following pizza shows 3 of the 8 pieces (the ones you ate) shaded.

Three Kinds of Fractions

Proper fraction:	The top number (numerator) is less than the bottom number (denominator):
	The value of a proper fraction is less than 1.
Improper fraction:	The top number is greater than or equal to the bottom number:
	The value of an improper fraction is 1 or more.
Mixed number:	A fraction written to the right of a whole number:
	The value of a mixed number is more than 1: It is the sum of the whole number plus the fraction.

Changing Improper Fractions into Mixed or Whole Numbers

It's easier to add and subtract fractions that are mixed numbers rather than improper fractions. To change an improper fraction, say , into a mixed number, follow these steps:

1. Divide the denominator (2) into the numerator (13) to get the whole number portion (6) of the mixed number:
2. Write the remainder of the division (1) over the old denominator (2):
3. Check: Change the mixed number back into an improper fraction (see steps that follow).

Changing Mixed Numbers into Improper Fractions

It's easier to multiply and divide fractions when you're working with improper fractions rather than mixed numbers. To change a mixed number, say , into an improper fraction, follow these steps:

1. Multiply the whole number (2) by the denominator (4):	2 × 4 = 8
2. Add the result (8) to the numerator (3):	8 + 3 = 11
3. Put the total (11) over the denominator (4):

4. Check: Reverse the process by changing the improper fraction into a mixed number. If you get the number you started with, your answer is right.

Reducing Fractions

Reducing a fraction means writing it in lowest terms, that is, with the smallest numbers possible. For instance, 50¢ is of a dollar, or of a dollar. Reducing a fraction does not change its value.

Follow these steps to reduce a fraction:

1. Find a whole number that divides evenly into both the numerator and the denominator.
2. Divide that number into the numerator, and replace the numerator with the quotient (the answer you got when you divided).
3. Repeat the same division step for the denominator.
4. Repeat steps 1–3 until you can't find a number that divides evenly into both numbers of the fraction.

For example, let's reduce . We could do it in two steps ; then . Or we could do it in a single step .

Shortcut: When the numerator and denominator both end in zeros, cross out the same number of zeros in both numbers to begin the reducing process. For example reduces to when you cross out two zeros in both numbers.

Whenever you do arithmetic with fractions, reduce your answer. On a multiple-choice test, don't panic if your answer isn't listed. Try to reduce it and then compare it to the choices.

Raising Fractions to Higher Terms

Sometimes before you can add and subtract fractions, you have to know how to raise a fraction to higher terms. This is actually the opposite of reducing a fraction.

Follow these steps to raise to 24ths:

1. Divide the old denominator (3) into the new one (24):
2. Multiply the answer (8) by the old numerator (2):	2 ×8 = 16
3. Put the answer (16) over the new denominator (24):
4. Check: Reduce the new fraction to see if you get back the original one:

Adding Fractions

If the fractions have the same denominators, just add the numerators together and write the total over the denominator.

Examples:

	Reduce the sum:
	Change the sum to a mixed number: ; then reduce: .

There are a few extra steps to add mixed numbers with the same denominators, say :

1. Add the fractions:
2. Change the improper fraction into a mixed number:
3. Add the whole numbers:	2 + 1 = 3
4. Add the results of steps 2 and 3:

Finding the Least Common Denominator

If the fractions you want to add don't have the same denominator, you will have to raise some or all of the fractions to higher terms so that they do; this number is then called the common denominator. All of the original denominators divide evenly into the common denominator. If it is the smallest number that they all divide evenly into, it is called the least common denominator (LCD).

Here are a few tips for finding the LCD, the smallest number into which all the denominators evenly divide:

• First, see if all the denominators divide evenly into the biggest one.
• Inspect multiples of the largest denominator until you find a number into which all the other ones evenly divide.
• When all else fails, multiply all the denominators together.

Example:

1. Find the LCD. Multiply the denominators:	3 × 5 = 15
2. Raise each fraction to 15ths:
3. Add as usual: