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Beginning Algebra

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 :.

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Beginning Algebra

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  1. BeginningAlgebra Addition/SubtractionsofFractions

  2. Addition & Subtraction with Fractions

  3. Primes/Factors Number Line Fractions LCD/ Fractions Sums Add/Subtract Fractions .

  4. Prime Numbers and Factoring Prime Number: Positive Integer or Natural Numberdivisible only by itself and 1. Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Counting Numbers<121 not divisible by 2, 3, 5, 7 are Prime Numbers.

  5. Multiplying Product Factors 3 3 4 4   Factoring Prime Numbers and Factoring . =12 =12

  6. 60 = 4 15  2 60 = 2 5 3    60 3 5  =  2 2 Prime Numbers and Factoring Factors Prime Factors Exponent Form Prime Number: Positive Integer or Natural Numberdivisible only by itself and 1.

  7. 10  9) (2 (7 5)    7 2  3 3 5 2    3 5 2 7    Prime Numbers and Factoring 630 = 63 Factors Factors 630 = 630 = Prime Factors Exponent Form 630 = All divisors of 630: Note vertical pairs: 630, 315, 210, 126, 105, 90, 70, 63, 45, 42, 35, 30, 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21

  8. Negative direction Positive direction … - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 … Negative numbers Positive numbers Origin 1 1 -1 - 4.5 4.0 6.5 4 4 • • • • • … - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 … Coordinates of points NUMBER LINE

  9. -2 - 3 1 1 5 a 3 2 d c c d RECIPROCALS numbers with product of 1 × = 1 × = 1 5 × = 1 × = 1 a .

  10. a a Numerator Numerator b b Denominator Denominator 103 35 -8 1 43 5 2 8 … - 5 - 4 - 3 - 2 -1 0 1 2 3 4 5 6 7 8 9 … 28 7 5 -5 6 3 FRACTIONS English words Math symbols .

  11. an = bn a 0 b 0 1 2 3 4 4 7 1 6 1 2 5 3 2 8 =1 =1 =1 4 4 4 8 2 2 8 4 8 8 8 8 8 8 0 FRACTIONS Equivalent Fractions

  12. 7 7 3 3 3 3 2 2 5 5 630 630         = 240 240 2 2 2 2 2 2 5 5 2 2 3 3           Divide by 2 3 5   = = 7 3  2 2 2   21 = 8 Reduce Fraction to Lowest Terms Prime Factors Reduce fraction Reducedimproper fraction

  13. Multiply numerators times numerators    and denominatorstimesdenominators c a c a a ac = d b b  b d bd c d Multiply Fractions or Check the result to see if it will reduce to simpler form.

  14. or 1 7   8 Multiply numerators times numerators 2 7 4 4  1 7 7 = 8 9 9  9 2 18 and denominatorstimesdenominators Multiply Fractions [Ifnumeratorshavecommon factors with denominators, factor them outand reducebefore you multiply.] . Check the result to see if it will reduce to simpler form.

  15. To add fractions with common denominators, just add the numerators. a+ b = b a c + c c Add and Subtract Fractions: Check the result to see if it will reduce to simpler form.

  16. 1. = = 2+ 4 5 2. = 2– x 4 x 2 2 + – 3 5 3 6 5 3 5 Add and Subtract Fractions: In algebra some of the factors may be letters, or variables, which must be treated as prime factors. Letters will be left in the result as “literal sums”.

  17. 2 2 2 2 2 7 3 3 3 2 2         7  Least Common Denominator or LCD 24 = Prime Factors 42 = Prime Factors 24 LCD 168= 42 LCD:LeastCollection of Prime Factors.

  18. RAISEall fractions to havecommon denominators, then add the resulting numerators. = c a a b   + + missing factors d b b b c d = ad + bc ad + bc d d bd bd Add and Subtract Fractions: If the fractions do not have common denominators [Factor the denominators and find the LCD. ] Check the result to see if it will reduce to simpler form.

  19. 1 5 + 2 2 2 2 2 2 2 2 2 2 2 7 3 3 3 3 3 3 2 2 2 2 2                  missing factor missing factors 5 1    2 2 7 5 1 42 24 7 7 7 7     9 9 = 56 1 Add and Subtract Fractions: + = + = 7 + 20 27 = =

  20. 24 7 7 18 18 18 missing factor 1 missing factor 3 24 5 5 3 3 + + = = 1·72 = 2·2·2·3·3 24 24 18 missing factor 2 missing factor 2 missing factor 3 missing factor 1 3 ·72 - 7(2 ·2) + 5 ·3 216 - 28 + 15 203 = = 2 · 2 · 2 · 3 · 3 2 · 2 · 2 · 3 · 3 72 Adding mixed numbers – integers and fractions: 72 = 2 · 2 · 2 · 3 · 3 LCD LCD 

  21. THE END

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