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Rational Numbers
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The Rational Numbers
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Proper Fractions
Improper Fractions
and
Mixed Numbers
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Prime Factorization
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Prime Number
A natural number,
greater than 1,
which has unique natural number factors 1 and itself.
Ex: 2, 3, 5, 7, 11, 13
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Composite Number
A natural number,
greater than 1,
which is not prime.
Ex: 4, 6, 8, 9, 10
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Prime Factorization
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Prime Factorization
To write a natural number as the product of prime factors.
Ex: 12 = 2 x 2 x 3
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Factor Rules
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10. Decide if 2, 3, and/or 5 is a factor of42
310
987
4950
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11. Building a factor tree for 205 4 2 2
The prime factorization of 20 is 2 x 2 x 5.
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15. Find the prime factorization of 24
The prime factorization of 24 is 2 x 2 x 2 x 3.
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16. Find the prime factorization of 315
The prime factorization of 315 is 3 x 3 x 5 x 7.
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17. Find the prime factorization of 119
The prime factorization of 119 is 7 x 17.
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18. Find the prime factorization of 495
The prime factorization of 495 is 3 x 3 x 5 x 11.
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19. Find the prime factorization of 945
The prime factorization of 945 is 3 x 3 x 3 x 5 x 7.
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Prime Factorization
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Reducing Fractions
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Reducing Fractions
A fraction is reduced when the numerator and denominator have no common factors other than 1.
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Reducing Fractions
A fraction is reduced when the numerator and denominator have no common factors other than 1.
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25. No “Gozinta” method allowed
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26. No “Gozinta” (Goes into) method allowed
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27. Simplify using prime factorization
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28. Simplify using prime factorization
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29. Reduce using prime factorization
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30. Reduce using prime factorization
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31. Reduce using prime factorization
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32. Copyright Scott Storla 2015
Reducing Fractions
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33. Multiplying Fractions
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34. No “Gozinta” method allowed
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35. using prime factorization Multiply
Procedure – Multiplying Fractions
1. Combine all the numerators, in prime factored form, in a single numerator.
2. Combine all the denominators, in prime factored form, in a single denominator.
3. Reduce common factors
4. Multiply the remaining factors in the numerator together and the remaining factors in the denominator together.
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36. using prime factorization Multiply
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37. Copyright Scott Storla 2015
Procedure – Multiplying Fractions
1. Combine all the numerators, in prime factored form, in a single numerator.
2. Combine all the denominators, in prime factored form, in a single denominator.
3. Reduce common factors
4. Multiply the remaining factors in the numerator together and the remaining factors in the denominator together.
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38. Multiply using prime factorization
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39. Multiply using prime factorization
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40. Multiply using prime factorization
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41. Multiply using prime factorization
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42. Multiplying Fractions
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43. Copyright Scott Storla 2015
Dividing Fractions
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Reciprocal
The reciprocal of a number is a second number which when multiplied to the first gives a product of 1.
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Procedure – Dividing Fractions
To divide two fractions multiply the fraction in the numerator by the reciprocal of the fraction in the denominator.
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Procedure – Dividing Fractions
To divide two fractions multiply the fraction in the numerator by the reciprocal of the fraction in the denominator.
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47. Divide using prime factorization
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48. Divide using prime factorization
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49. Divide using prime factorization
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50. Divide using prime factorization
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51. Copyright Scott Storla 2015
Dividing Fractions
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