Fractions for Firefighter Exam Study Guide
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:
- Divide the bottom number (2) into the top number (13) to get the whole number portion (6) of the mixed number:
- Write the remainder of the division (1) over the old bottom number (2):
- 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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