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# Fractions for Firefighter Exam Study Guide (page 6)

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Updated on Jun 30, 2011

### Multiplying Fractions

Multiplying fractions is actually easier than adding them. All you do is multiply the top numbers and then multiply the bottom numbers.

Example:

Sometimes you can cancel before multiplying. Cancelling is a shortcut that makes the multiplication go faster because you are multiplying with smaller numbers. It's very similar to reducing: If there is a number that divides evenly into a top number and bottom number, do that division before multiplying. If you forget to cancel, you will still get the right answer, but you will have to reduce it.

Example:
 1. Cancel the 6 and the 9 by dividing 3 into both of them: 6 ÷ 3 = 2 and 9 ÷ 3 = 3. Cross out the 6 and the 9. 2. Cancel the 5 and the 20 by dividing 5 into both of them: 5 ÷ 5 = 1 and 20 ÷ 5 = 4. Cross out the 5 and the 20. 3. Multiply across the new top numbers and the new bottom numbers:
Try these multiplication problems:

To multiply a fraction by a whole number, first rewrite the whole number as a fraction with a bottom number of 1:

Example: (Optional: Convert to a mixed number: )
To multiply with mixed numbers, it's easier to change them to improper fractions before multiplying.
Example:
1. Convert to an improper fraction:
2. Convert to an improper fraction:
3. Cancel and multiply the fractions:
4. Optional: Convert the improper fraction to a mixed number:
Now try these multiplication problems with mixed numbers and whole numbers:

Here are a few more real-life problems to test your skills:

1. After driving of the 15 miles to work, Mr. Stone stopped to make a phone call. How many miles had he driven when he made his call?
1. 5
2. 10
3. 12
2. If Henry worked of a 40-hour week, how many hours did he work?
1. 10
2. 20
3. 25
4. 30
3. Technician Chin makes \$14.00 an hour. When she works more than 8 hours in a day, she gets overtime pay of times her regular hourly wage for the extra hours. How much did she earn for working 11 hours in one day?
1. \$77
2. \$154
3. \$175
4. \$210
5. \$231

### Dividing Fractions

To divide one fraction by a second fraction, invert the second fraction (that is, flip the top and bottom numbers) and then multiply. That's all there is to it!

Example:
1. Invert the second fraction
2. Change the division sign (÷) to a multiplication sign (×)
3. Multiply the first fraction by the new second fraction:

To divide a fraction by a whole number, first change the whole number to a fraction by putting it over 1. Then follow the division steps above.

Example:
When the division problem has a mixed number, convert it to an improper fraction and then divide as usual.
Example:
1. Convert to an improper fraction:
2. Divide
3. Flip change ÷ to ×, cancel, and multiply:

Here are a few division problems to try:

Let's wrap this up with some real-life problems.

1. If four friends evenly split pounds of candy, how many pounds of candy does each friend get?
1. 4
2. How many -pound chunks of cheese can be cut from a single 20-pound piece of cheese?
1. 2
2. 4
3. 6
4. 8
5. 10
3. Ms. Goldbaum earned \$36.75 for working hours. What was her hourly wage?
1. \$10.00
2. \$10.50
3. \$10.75
4. \$12.00
5. \$12.25

1. 10
2. 6
3. 200
4. a.
5. b.
6. 15
7. c.
8. e.
9. c.
10. b.
11. d.
12. b.