We have great news for you!
You already know how to do all of the basic math necessary for
successfully solving many algebraic equations!
Algebra takes the basic math you already know and simply adds
things to it so that you can use those skills to solve increasingly difficult problems.
During this exam prep seminar we will take a look how you can use what you already
know to solve and simplify complex math expressions.
Here, let me show you:
Solve the following 4 math problems:
1)16 ÷ 2 =
2) 18 + 7
3) 25 + 3 =
4) 8 + 28=
Easy right?
Next you will combine those steps in the right order to solve a more
complicated math problem:
(16 ÷ 2 ) + ((18 + 7 ) + 3)
((10 - 2 ) x 7 ) - 9 + 8
(8)
+ ((25) +3)
((8) x 7) - 9 + 8
(8)
+ (28)
(56) - 9 + 8
8+28 = 36
36
47 + 8
55
(20 ÷ 10) + ((15 + 3 ) + 5 )
(2) + ((18)+ 5)
2 + 23
25
PEMDAS Parentheses First Exponents (powers/roots) Mul ply or Divide Add or Subtract what’s le Helpful HINT for Naviga ng Nega ves Two like signs become a posi ve sign Two unlike signs become a nega ve sign +(+) 3+(+2) = 3 + 2 = 5 −(−) 6−(−3) = 6 + 3 = 9 +(−) 7+(−2) = 7 − 2 = 5 −(+) 8−(+2) = 8 − 2 = 6 3 +( 5 + ( 9 - 5 )) + 9
((14 - 7 ) +(18 ÷ 3 )) + 2
3+ (5 + (4)) + 9
((7) + (6))+2
3 + (9) + 9
(13) + 2
12 + 9
15
21
( 7 +(16 ÷ 2 - 8 )) - 9
((17 + 4 ) +(10 ÷ 2 )) x 7
-2
182
((11 +2 ) + 2 ) - 7 - 6
((16 - 3 ) +(20 ÷ 2 )) + 2
2
25
(13 +(20 ÷ 4 - 3 )) + 4
((17 + 2 ) +(16 ÷ 8 )) + 3
19
24
Now for the Exponents
It’s the “E” in PEMDAS, and it does not make the expression exponentially more
difficult to solve, but you do need to know what to do with those raised numbers. You
will only be dealing with squares
and cubes right now, however an exponent basically means, “How many times to
multiply a number by itself.”
For example:
22= 4
23= 8
24= 16
102= 100 103=1000 104=10,000
105=100,000
25= 32
As you can see, the exponent can make a big difference!
Now lets take a look at some expressions that use exponents.
10 x (10 x 4 - 82) - 3
4 x (11 x 9 + 82 ) + 5
(20 + 2 ) x (14 + 4 ) - 52
(10 + 3)2+ (11 +20 ÷ 5 )
Try a Digital Challenge!
Work through more sample problems at this website:
https://www.khanacademy.org/math/arithmetic/multiplicationdivision/order_of_operations/e/order_of_operations
( 9 +67 - 42 ) ÷( -4 + 6 )
(13 +27 - 4 ) ÷ 3 + 42
( 4 + 3 )2 + (16 - 14 ÷ 2 )
(( 3 +3 ) 2 x 4 ) - 2 + 8
(15 ÷ 5 ) 2 + ((17 - 3 ) + 52 )
7 +( 2 + ( 3 + 4 ) 2 ) - 2
((13 - 3 ) +(12 ÷ 3 ) 2 ) x 52
8 +( 3 x (10 - 4 ) 2 ) + 7
Solving complex word problems: Using the word key below, construct an expression and then solve. EXAMPLE: Simon began the day with 4 collector cards, Pat has 3, and Mary had 6. Mark gave Simon the difference between Mary’s and Pat’s cards mes the number of cards Simon had to begin with. Simon went to the store and purchased Twice the difference between his cards and Pat’s cards. At the end of the day how many cards did Simon have? Simon: 4 cards Mary: 6 cards Pat: 3 cards Cards from Mark: (Mary’s Cards ‐ Pat’s cards) X Simon’s Cards Purchased Cards: (Simon’s cards—Pat’s cards) X 2 Expression: 4+((6—3) x 4 + (4 ‐ 3) x 2) = # of Simon’s cards at the end of the day Solve: P ‐ 4 + ((6‐3) x 4) + ((4‐3) x 2) E ‐ 4 + ((3) x 4) + ((1) x 2) M/D ‐ 4 + (12) + (2) A/S ‐ 16 + 2 18 Addition
Subtraction
Equals
Add
Subtract
Equals
Sum
Take Away
is
Increased By More
Difference
are
Combined Together
Decrease By
were
Plus
Fewer
will be
And
Minus
Multiplication
Division
Multiple
Quotient
Parenthesis
Words
Times
Per
Times the difference of
Product
Ratio
Twice the sum of
Twice
Divided By
Plus the difference of
Sample Word Problems: 1. A grocery store makes a fruit basket consisting of 4 pears, 6 apples, 8 oranges, and 2 bananas. If the
store receives 11 orders for gift baskets on a certain day, how many pieces of fruit are they using all together? (4 + 6 + 8 + 2) x 11 = 220 pieces of fruit Or (4 x 11) + (6 x 11) + (8 x 11) + (2 x 11) = 220 pieces of fruit 2. Suppose two classes are going on a field trip to the zoo. There are 28 people in one class and 22
people in the other class. The teachers want to order lunch for all of the students, and in each lunch,
they want there to be 2 packages of crackers. How many packages of crackers should the teachers order?
100 Packages of Crackers
3. Travis gained 9 pounds during the holidays. He dieted and lost 14 pounds, gained 3 pounds , but gained 3 more when he went on vaca on. By the end of the year he lost another 7 pounds. How much and in what direc on was the net change in weight? Travis lost 6 pounds. 4. Emily had 30 cookies to bring to school for her birthday. Three students wanted two cookies each. Then, a new student came to the school that day and he wanted three cookies. Then, one of the three kids gave their two cookies back. Emily was s ll passing out cookies. How many cookies did Emily have le to pass out a er the stu‐
dent gave her his back? Emily had 23 cookies le .