Education.com
Try
Brainzy
Try
Plus

# Fractions for Firefighter Exam Study Guide (page 3)

By
Updated on Jun 30, 2011

If the fractions have the same bottom numbers, just add the top numbers together and write the total over the bottom number.

 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 bottom numbers, say

2. 2. Change the improper fraction into a mixed number:
3. 3. Add the whole numbers: 2 +1= 3
4. 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 bottom number, you will have to raise some or all of the fractions to higher terms so that they all have the same bottom number, called the common denominator. All of the original bottom numbers 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 that all the bottom numbers evenly divide into:
• See if all the bottom numbers divide evenly into the biggest bottom number.
• Check out the multiplication table of the largest bottom number until you find a number that all the other bottom numbers evenly divide into.
• When all else fails, multiply all the bottom numbers together.
Example:
 1. Find the LCD. Multiply the bottom numbers: 3 × 5 = 15 2. Raise each fraction to 15ths: 3. Add as usual:

### Subtracting Fractions

If the fractions have the same bottom numbers, just subtract the top numbers and write the difference over the bottom number.

Example:

If the fractions you want to subtract don't have the same bottom number, you will have to raise some or all of the fractions to higher terms so that they all have the same bottom number, or LCD. If you forgot how to find the LCD, just read the section on adding fractions with different bottom numbers.

Example:
 1. Raise each fraction to 12ths because 12 is the LCD, the smallest number that 6 and 4 both divide into evenly: 2. Subtract as usual:
Subtracting mixed numbers with the same bottom number is similar to adding mixed numbers.
Example:
1. Subtract the fractions:
2. Subtract the whole numbers: 4 – 1 = 3
3. Add the results of steps 1 and 2:

Sometimes there is an extra borrowing step when you subtract mixed numbers with the same bottom numbers, say

1. You can't subtract the fractions the way they are because is bigger than . So you borrow 1 from the 7, making it 6, and change that 1 to because 5 is the bottom number:
2. Add the numbers from step 1:
3. Now you have a different version of the original problem:
4. Subtract the fractional parts of the two mixed numbers:
5. Subtract the whole number parts of the two mixed numbers: 6 – 2 = 4
6. Add the results of the last two steps together:
Try these subtraction problems:
1. Now let's put what you've learned about adding and subtracting fractions to work in some real-life problems.

2. Officer Peterson drove miles to the police station. Then he drove miles to his first assignment. When he left there, he drove 2 miles to his next assignment. Then he drove miles back to the police station for a meeting. Finally, he drove miles home. How many miles did he travel in total?
3. Before leaving the fire station, Firefighter Sorensen noted that the mileage gauge on Engine 2 registered miles. When she arrived at the scene of the fire, the mileage gauge registered miles. How many miles did she drive from the station to the fire scene?