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# Fraction Review for Armed Services Vocational Aptitude Battery (ASVAB) Study Guide (page 3)

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Updated on Jun 23, 2011

### 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 2 steps together:
Try these subtraction problems:

Now let's put what you have learned about adding and subtracting fractions to work in some real-life problems.

1. Manuel drove miles to work. Then he drove miles to the store.When he left there, he drove 2 miles to the dry cleaners. Then he drove miles back to work for a meeting. Finally, he drove miles home. How many miles did he travel in total?
2. Before leaving the warehouse, a truck driver noted that the mileage gauge registered 4,357 miles. When he arrived at the delivery site, the mileage gauge then registered 4,400 miles. How many miles did he drive from the warehouse to the delivery site?

### 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. Canceling is a shortcut that makes the multiplication go faster because you're 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: and . Cross out the 6 and the 9.
2. Cancel the 5 and the 20 by dividing 5 into both of them: and . Cross out the 6 and the 9.
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 Hamm makes \$13.00 an hour. When she works more than 8 hours a day, she gets overtime pay of times her regular hourly wage for the extra hours. How much did she earn for working 10 hours in one day?
1. 110
2. \$125.75
3. \$136.50
4. \$154.25
5. \$163.50

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