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Problem Solving
Jim,Ken, Len and Max have a bag of miniature candy bars from trick-or treating together. Jim took 1/4 of the bars, and ken and len took 1/3 of all the bars. Max got the remaining 4 bars. How many bars were in the bag originally?
Max 4 bars
Jim 1/4= 3/12
Ken 1/3= 4/12
len 1/3
All: 12x4= 48
Jim: 3x4=12
Ken: 4x4=16
Len 4x4=16
*go look at your notes for the examples
3/4 class is girls, 2/3 have dark hair what fraction of the class is g+dh?
2/3x3/4=6/12=1/2
Meaning
Part of a whole
Quotient -----> 3/4 = 3/4
Ration -----> 20 students
15 girls
5 boys
Ratio Part of a whole
Ratio+fraction
Models
1 whole "pie"
Hexagon
1/2
Trapezoid
2/4
Rhombus
1/3
Triangle
1/6
Mixed #: a number that has a whole and fractional part
If you add fractions with the same shaped blocks!
Turn into an improper fraction
3 1/2
3x2=6+1=7---> 7/2
Adding
GCF: 4,8,12,16,20,24
LCM: 6,12,18,24
1/4+1/6= 24
2/12+3/12= 5/12
Prime factorization
24
2 12
3 4
2 2
2= 2x2x2x3
Greatest Common Factor( GCF)
Least Common Multiple (LCM)
List Method
Factors
24: 1,2,3,4,6,8,12,24
36: 1,2,3,4,6,9,12,18,36
GCF is (24,36)= 12
Multiple
24,48,72
36,72
LCM(24,36)=72
GCF (24,36)= 2x2x3=12
LCM (24,36)= gcfx2x3
=12x2x3=72
Divisibility rule
A number is divisible by a number if there is another number that meets this requirement
BxC=A
Ex.
10 divisible by 5 because 5x2=10
5x2=10
Factor
5 is a factor of 10
2 is a factor of 10
10 is divisible by 5
10 is divisible by 2
Ending Sum of Digits
by 2: 0,2,4,6,8 by 3: 120
by 5: 0,5 by: 7,038
by 6: If it is divisible by both 2 and 3
Last 2 Digits
72,744 <---- yes because 44 goes into 4
824<-------- 24 goes into 4
Last 3 Digits
by 8
7,239 <----- take the last 3 digits
by 7:
826 <----- Double the 6
By 11? "chop off
Adding
American Standars
Partial Sums
Partial Sum w/place value
Left- To- Right
Expanded notation
Subtraction
American Standard
European/Mexcian
Reverse Indian
Left to Right
Expanded notation
Interger Subtraction
Campare >,<,=
are used to make comparisons in mathematics and programming.
a) 34(base5) __<__34(base6)=
(3x5)+4x5)
15+4=19
b) 4(base7)_=__4(base8)=
(4x7)=28 (4x8)=32
c) 43(base5)___25(base6)=
(4x5)+(3x5) (2x6) x (5x6)
20+3=23 12+5= 17
Division
15 cookies
3 on each plate
15 cookies
5 plates
15/5
15 cookies
xxx= 15-3 =12
xxx= 12-3=9
xxx= 9-3=6
xxx=6-3=3
xxx=3-3=0
Atternative algnithm
16/197
160-----------> 10 boxes
37
-16 ------------> 1 box
--------
21
-16 --------> 1box
Base -10
system
or
Decimal
Base -5: 0,1,2,3,4
One= 5
Five=5
25= 5(square)
125= 5 times 3
221(base 5)= (2x25)+(2x5)+(1x1)
= (2x5(2))+(2x5(1))+(1x5(0))
= 50+10+1
Use expanded notation
In the expanded notation of a number, each digit is separated and written with its corresponding place value
Example: 452 written in expanded notation as:
4x100+5x10+2x1
4= 400
5= 5 tens
2= 2 units
1) 111 base 2 = (1x2(2))+(1x2(1))+(1x2(0))
= (1x4)+ (1x2) + (1x1)
= 4+2+1=7
4 ways to solve a problem
Device a plan
Carry out the plan
