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### Fraction Rules Review

Yes, you need to write it all down, including the examples.

You will be graded on your notes.

Why not just use decimals???

- Because you are doing Algebra. Converting every fraction to decimals makes working with variables REALLY, REALLY difficult….
- Especially when you start working with exponents (powers)….
- Or multiple variables….
- So learn to love fractions!

Adding Fractions

- Check for a common denominator (the bottom #). If the denominators are the same, just add the top numbers across.

1/6+4/6=5/6

2. If the denominators are different, find the least common denominator (LCD).

Least Common Denominator

- First find the Least Common Multiple of the two denominators.

1/6+3/4

LCM of 6 and 4 is 12, so the LCD of 1/6 and ¼ is 12

b. Then multiply BOTH the top AND the bottom numbers of the fraction (the numerator and the denominator) by whatever number is needed to make the denominator the LCD

1/6 * 2/2=2/12

¾*3/3=9/12

Finally, you can…

3. Add the top numbers (the numerators) across; leave the bottom numbers alone.

2/12+9/12=11/12

4. Simplify if possible.

Subtracting Fractions

- Follow the same process as adding fractions. Remember that once the denominators are the same, you only need to subtract the top numbers (the numerators).

Multiplying Fractions

- Line them up next to each other.
- Multiply top AND bottom (numerator and denominator) straight across.

1/6*3/4=3/24

3. Simplify.

3/24=1/8

***Simplify Before Multiplying

- A good idea; it saves time.
- Look for common factors to reduce by.

1/6*3/4

The six and the three have 3 as common factor, so you can reduce them:

½*1/4=1/8 same answer as before!

Dividing Fractions

- Reverse the second fraction (the divisor) top-to-bottom (use the reciprocal), and reverse the operation (multiply instead of divide).

1/6 1/6

¾ = * 4/3

2. Remember to simplify wherever you can before multiplying.

Reduce first: 1/3*2/3

Then multiply: 1/3*2/3=2/9

Adding Whole/Mixed Numbers

- Check for LCD. If they already have a common denominator, you can add the whole numbers together and add the fractions together. Remember to convert improper fractions into whole or mixed numbers before you stop.

2 2/3 +3 2/3=

2+3= 5, and 2/3 + 2/3=4/3

Add the results: 5+4/3= 6 1/3

2. If there is no LCD, convert BOTH numbers into improper fractions:

2 2/3 + 1 4/5

Multiply the denominator times the whole number; add the result to the top (numerator).

2 2/3: 2*3 +2=8, so 2 2/3=8/3

1 4/5: 5*1 +4=9, so 1 4/5=9/5

3. Find the LCD of the improper fractions.

8/3 and 9/5 LCD of 3, 5=15

4. Convert each fraction into an equivalent fraction, using the LCD.

8/3*5/5=40/15

9/5*3/3=27/15

5. Add the top numbers (the numerators) only.

40/15+27/15=67/15

6. Simplify the result.

67 divided by 15=4 7/15

Subtracting Whole/Mixed #’s

Follow the same process as for adding them.

IF there is a common denominator already, you may need to “borrow” from the whole numbers first. Sometimes, it’s easier to just use improper fractions anyway!

“borrowing” to subtract mixed numbers

10 1/6-2 3/6

The first fraction is smaller than the second, so you need to “borrow” from 10 (the whole number):

9 7/6-2 3/6 now you can subtract:

9-2=7 and 7/6-3/6=4/6

7+4/6=7 4/6

Simplify: 7 2/3

Multiplying Whole/Mixed #’s

***Remember that a whole # can be written as a fraction by writing itself over 1 (because any number divided by itself is still…itself.)

2=2/1

27=27/1

234=234/1

Convert both #’s to fractions.

3 1/3*4= 10/3*4/1

2. Multiply the top and bottom (numerator and denominator) straight across.

10/3*4/1=40/3

3. Simplify.

40/3=13 1/3

4. THINK. If you estimate, will you be close to the same answer?

3*4=12…which is close to 13 1/3

Dividing Whole/Mixed #’s

9 1/3

2/6 becomes 28/3

2/6

Use the reciprocal: 28/3*6/2

Simplify first: 14/1*2/1= 28/1 =28

Follow all the same steps as for multiplying, but reverse the second fraction (use the reciprocal) and the operation (multiply).

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