Fractions for Nursing School Entrance Exam Study Guide
The practice quiz for this study guide can be found at:
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.
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 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:
- Find a whole number that divides evenly into both the numerator and the denominator.
- Divide that number into the numerator, and replace the numerator with the quotient (the answer you got when you divided).
- Repeat the same division step for the denominator.
- 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.
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