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.

Order of Operations (continued)

• 2(2+4)-10+5x2= 2(6)-10+5x2= 12-10+5x2= 12-10+10= 2+10= 12

• 3(5+2)+15= 3(7)+15= 21+15= 36• 2(2+4)x6= 2(6)x6= 12x6= 72

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

Add Fractions and Mixed Numbers

• Convert the mixed numbers to improper fractions then add them together.

• 2 2/3 + 3 3/5= 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 8/12 11 3/8

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

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

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

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

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

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.

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 32/7 divided by 20/21

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

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

Solving Problems using percents

)3212(

)100375.0(

• 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 %

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%

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) -24+133) Take 13 out of 24 then put on the negative to the

answer.

Answer:11

Examples

1) -53-(-17) Answer:-36

2) 14-(-45) Answer:59

3) -8+(-3) Answer:-11

Multiplying and Dividing Signed Numbers

• Same signs: positive• Different signs: negative

182

218: Ex

9:Answer

Examples

1)-9 14

Answer: -126

Answer: 4

Answer: 352

2) -32/(-8)

3) -88 (-4)