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# Fractions for Nursing School Entrance Exam Study Guide (page 4)

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### Subtracting Fractions

If the fractions have the same denominators, just subtract the numerators and write the difference over the denominator.

Example:

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

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 denominator 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 denominators, 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 denominator: 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:

### Multiplying Fractions

Multiplying fractions is actually easier than adding them. All you do is multiply the numerators and then multiply the denominators. You do not need to find a common denominator.

Examples:

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 the numerator and denominator, 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 and replace with the reduced numbers: 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 and replace with the reduced numbers: 3. Multiply across the new numerators and the new denominators:

To multiply a fraction by a whole number, first rewrite the whole number as a fraction with a denominator 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:

### Dividing Fractions

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

Examples:
 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.

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

The practice quiz for this study guide can be found at:

Mathematics for Nursing School Entrance Exam Practice Problems

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