1. Order Of Operations Parentheses Multiply or Divide
Addition or Subtraction
Start out using parentheses, then move on to multiplication or division, then add or subtract, and perform these actions in order.

2. Order of Operations (continued)
2(2+4)-10+5x2= 2(6)-10+5x2= x2= = 2+10= 12
3(5+2)+15= 3(7)+15= 21+15= 36
2(2+4)x6= 2(6)x6= 12x6= 72

3. Change Mixed Number to Improper Fractions
To change a mixed number to an improper fraction you multiply the whole number times the denominator plus the numerator. The new number become the numerator, and placed over the denominator.
5 2/3=17/3
3 2/3=11/3
2 25/2=29/2

4. Add Fractions and Mixed Numbers
Convert the mixed numbers to improper fractions then add them together.
2 2/ /5= 8/3+18/5= 26/8= 3 2/8
¾+ 2 6/7= 3/4+ 20/7= 23/11= 2 1/11
5 5/8+ 5 3/4= 45/8+ 23/4= 68/12= 5 8/ /8

5. Subtracting Fractions and Mixed Numbers
In order to subtract fractions, as in adding fractions, the denominators must be the same.
¼ + ¼ = 2/4 or simplified, ½
However, when denominators are not the same, they must be multiplied to the lowest common denominator, or LCD

6. Subtracting Fractions and Mixed Numbers
¼ - 1/5 = ?
¼ and 1/5 do not have the same denominator, so you multiply to the lowest number they both have in common. In this case, that number is 20.
5/5 X ¼ = 5/20
4/4 X 1/5 = 4/20

7. Subtracting Fractions and Mixed Numbers
With our new numbers now having the same denominator we can subtract them
5/20 – 4/20 = 1/20
Also, if needed, you can reduce

8. Multiplying Fractions and Mixed Numbers
To multiply fractions, the simplest way is to “cross simplify.” this means simplifying by the opposite diagonal number. Then, you simply multiply straight across. (numerator times numerator, denominator times denominator
Lets say or problem is 15/21 X 2 1/3 or 7/3

9. Multiplying Fractions and Mixed Numbers
15/21 X 7/3 simplifies to 3/3 X 1/1
Then you simply multiply across
3X1 = 3 and 3X1 = 3
Turns out to 3/3 or 1

10. Dividing Fractions and Mixed Numbers
To divide fractions and mixed numbers, you follow the same steps as multiplying fractions and mixed numbers, except that when you multiply, you multiply one fraction by the other’s reciprocal.

11. Dividing Fractions and Mixed Numbers
You set it up the same as multiplying, except that you take one of the fractions, and switch the numerator and denominator.
Then, you simplify, and multiply across
Say our problem is 4 4/7 or 32/ divided by 20/21

12. Dividing Fractions and Mixed Numbers
First, you switch one of the fractions to it’s reciprocal.
For this problem lets switch 20/21
32/7 X 21/20
This simplifies to 8/1 X 3/5
Turns out to 24/5 or 4 4/5

13. Adding, Subtracting, Multiplying, and Dividing fractions to solve problems
A pitcher of lemonade contains 64 ounces of lemonade. If you have 2½ pitchers left after a cookout, how many ounces of lemonade do you have left?
2½ pitchers= 75 ounces
64 ounces=2 quarts
75 – 64
Answer: 11 ounces

14. Solving Problems using percents
12kg is what percentage of 32 kg?
Divide the first number by the second
Multiply the answer by 100
Round to the nearest unit (37.5)
Add the percent sign to the end
Answer: 38 %

15. Examples
1) 75 is what percent of 300? Answer:25% 2) 6 is what percent of 50? Answer:12% 3) 7 is what percent of 280? Answer:2.5%

16. Adding and Subtracting Signed Numbers
1) EX: -24-(-13)
When two negatives are next to each other, you can change them into one positive. 2)
3) Take 13 out of 24 then put on the negative to the answer.
Answer:11

17. Examples
1) -53-(-17) Answer:-36 2) 14-(-45) Answer:59 3) -8+(-3) Answer:-11

18. Multiplying and Dividing Signed Numbers
Same signs: positive
Different signs: negative

19. Examples Answer: -126 1)-9 14 Answer: 4 2) -32/(-8) 3) -88 (-4)
1)-9 14
Answer: 4
2) -32/(-8)
3) (-4)
Answer: 352