Fraction Rules Review

1. Fraction Rules Review Yes, you need to write it all down, including the examples. You will be graded on your notes.

2. 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!

3. 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

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

5. 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

6. 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

7. 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.

8. 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).

9. 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

10. ***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! 

11. 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

12. 2. Remember to simplify wherever you can before multiplying. Reduce first: 1/3*2/3 Then multiply: 1/3*2/3=2/9

13. Whole & Mixed Numbers

14. 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

15. 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

16. 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

17. 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

18. 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!

19. “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

20. 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

21. 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

22. 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

23. 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).