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# Fractions for Firefighter Exam Study Guide

By LearningExpress Editors
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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 pizza below shows this: 3 of the 8 pieces (the ones you ate) are shaded.

### Three Kinds of Fractions

 Proper fraction: The top number is less than the bottom number: 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 is 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 bottom number (2) into the top number (13) to get the whole number portion (6) of the mixed number:
2. Write the remainder of the division (1) over the old bottom number (2):
3. Check: Change the mixed number back into an improper fraction (see the following steps).

### Changing Mixed Numbers into Improper Fractions

It's easier to multiply and divide fractions when you are 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 bottom number (4). 2 × 4 = 8 2. Add the result (8) to the top number (3). 8 + 3 = 11 3. Put the total (11) over the bottom number (4). 4. Check: Reverse the process by changing the improper fraction into a mixed number. If you get back the number you started with, your answer is right.

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