beginning algebra
DESCRIPTION
Beginning Algebra. Addition/Subtractions of Fractions. Addition & Subtraction. with Fractions. Primes/Factors. Number Line. Fractions. LCD/ Fractions Sums. Add/Subtract Fractions. Prime Numbers and Factoring. Prime Number :. - PowerPoint PPT PresentationTRANSCRIPT
BeginningAlgebra
Addition/Subtractions of Fractions
Addition & Subtraction
with Fractions
Add/Subtract Fractions
Fractions
Number Line
.LCD/ Fractions Sums
Primes/Factors
Prime Numbers and Factoring
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ...
Prime NumbersPrime Numbers::
Counting Numbers < 121 not divisible by 2, 3, 5, 7 are Prime NumbersPrime Numbers.
Positive Integer or Natural Number divisible divisible only by itself and 11.
Prime NumberPrime Number:
Prime Numbers and Factoring
= 124 3 = 124 3Factors Product
Factoring
Multiplying
.
Prime Numbers and Factoring
Factors
Prime Factors
Exponent Form
60 = 4 15
60
= 2 32 5
32
2= 560
Positive Integer or Natural Number divisible divisible only by itself and 11.
Prime NumberPrime Number:
630 =
Prime Numbers and Factoring
63 10 Factors
Prime Factors
Exponent Form
Factors9)(7 (2 5)
2 3 537
52
3 72
All divisorsdivisors of 630:
630, 315, 210, 126, 105, 90, 70, 63, 45, 42, 35, 30, 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21
630 =
630 =
630 =
Note vertical pairsNote vertical pairs::
… - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 …
NUMBER LINE
OriginNegative numbers Positive numbers
Negative direction Positive direction
• … - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 …
• • • •
- 4.5 6.54.041-1 4
1
Coordinates of points
RECIPROCALSnumbers with product of 1numbers with product of 1
5 = 115
a = 11a
-23
- 32
= 1
cd
dc
= 1
.
Denominator b
English words Math symbols
… - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 …
.
Numerator aNumerator
Denominator
FRACTIONS
ba
728
3- 5
2- 8
65
81
43103
535
4
104
2
4
3 = 14
4
0 = 12
2
2
1
= 18
808
1
8
2
8
3
8
4
8
5
8
6
8
7
ab
a nb n
=Equivalent Fractions
FRACTIONS
Reduce Fraction to Lowest Terms
Prime Factors630240
= 2 3 537
2 2 322 5
= 2 3 537
2 2 322 5Divide by 2 3 5
= 37 222
= 218
Reduce fraction
Reduced improperimproper fraction630240
ba c
d or a
bcd
Multiply Fractions
Check the result to see if it will reduce to simpler formreduce to simpler form.
ac a c
Multiply numerators numerators timestimes numerators numerators
= bdb d
and denominatorsdenominators times denominatorsdenominators
94 7
8
Multiply Fractions
Check the result to see if it will reduce to simpler formreduce to simpler form.
or 49
78
1
2
[If numerators have common factors with denominators, factor them out and reducereduce before you multiply.]
7 1 7Multiply numerators numerators timestimes numerators numerators
18=
9 2and denominatorsdenominators times denominatorsdenominators
.
Check the result to see if it will reduce to simpler formreduce to simpler form.
just add the numeratorsadd the numerators.
a + b=
To add fractions with common denominatorscommon denominators,
ca b
c+ c
Add and Subtract Fractions:
= 2 + 45
65=
52 4
5+1.
2.32 x
3– = 2 – x3
In algebra some of the factors may be lettersletters, or variables, which must be treated as prime factors. Letters will be left in the result as “literal sums”.
Add and Subtract Fractions:
Prime Factors
LCD
LCDLCD: LeastLeast CollectionCollection of Prime FactorsPrime Factors.
32 7
Least Common Denominator or LCD
42 =
Prime Factors 22 2 324 =
168 = 22 2 3 7
24
42
Add and Subtract Fractions:
ba c
d+
If the fractions do do notnot have common denominators have common denominators
= ab
dd
cd
bb
+
RAISERAISE all fractions to have common denominatorscommon denominators,[Factor the denominators and find the LCDLCD. ]
ad + bcbd
missing factorsmissing factors
= ad + bcbd
then add the resulting numeratorsadd the resulting numerators.
Check the result to see if it will reduce to simpler formreduce to simpler form.
Add and Subtract Fractions:
=241
+ 425
22 2 31
+5 32 7
+ 22 2 3 75
22 2 3 71
569
=
22 2 3 727= =
7missing factormissing factor
22missing factorsmissing factors
7 + 20 22 2 3 7=
9
1
Adding mixed numbers – integers and fractionsintegers and fractions:
20372
=3 · 72 - 7( 2 · 2) + 5 · 3
2 · 2 · 2 · 3 · 3
missing factor 1
missing factor 2missing factor 3
72 = 2 · 2 · 2 · 3 · 3
18
24
LCD
missing factor 1
missing factor 2
missing factor 3
1 ·72 = 2 · 2 · 2 · 3 · 3
24
18
LCD718
+ 524
=3
216 - 28 + 15 2 · 2 · 2 · 3 · 3
=
718
+ 524
=3
THEEND