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INTRODUCTION TO FRACTIONS

INTRODUCTION TO FRACTIONS. MSJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur. Introduction to Fractions. A fraction represents the number of equal parts of a whole Fraction = numerator (up North) denominator (Down south)

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INTRODUCTION TO FRACTIONS

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  1. INTRODUCTION TO FRACTIONS MSJC ~ San Jacinto Campus Math Center Workshop Series Janice Levasseur

  2. Introduction to Fractions • A fraction represents the number of equal parts of a whole • Fraction = numerator (up North) denominator (Down south) = numerator/denominator • Numerator = # of equal parts • Denominator = # of equal parts that make up a whole

  3. Example: My husband and I ordered a large Papa John’s pizza. The large pizza is cut into 8 (equal) slices. If my husband ate 3 slices, then he ate • 3/8 of the pizza

  4. Types of Fractional Numbers • A proper fraction is a fraction whose value is less than 1 (numerator < denominator) • An improper fraction is a fraction whose value is greater than or equal to 1 (numerator > denominator) • A mixed number is a number whose value is greater than 1 made up of a whole part and a fraction part

  5. Converting Between Fraction Types • Any integer can be written as an improper fraction • Any improper fraction can be written as a mixed number • Any mixed number can be written as an improper fraction

  6. Integer Improper Fraction • The fraction bar also represents division • The denominator is the divisor • The numerator is the dividend • The original integer (number) is the quotient • To write an integer as a division problem, what do we divide a number by to get the number? • One . . . n = n/1

  7. Ex: Write 17 as an improper fraction • 17 = 17 / ? • 17 divided by what is 17? • 1 • Therefore, 17 = 17 / 1

  8. Improper FractionMixed Number • Denominator: tells us how many parts make up a whole • Numerator: tells us how many parts we have • How many wholes can we make out of the parts we have? • Divide the numerator by the denominator  the quotient is the whole part • How many parts do we have remaining? • The remainder (over the denominator) makes up the fraction part

  9. Ex: Write 11/8 as a mixed number. How many parts make up a whole? 8 Draw a whole with 8 parts: How many parts do we have? 11 To represent 11/8 we must shade 11 parts . . . But we only have 8 parts. Therefore, draw another whole with 8 parts . . . Keep shading . . . 9 10 11 This is what 11/8 looks like.

  10. Given the representation of 11/8, how many wholes are there? 1 Dividing 11 parts by 8 will tell us how many wholes we can make: 11/8 = 1 R ? The remainder tells us how much of another whole we have left: 1 R 3 Since 8 parts make a whole, we have 3/8 left. Therefore, 11/8 = 1 3/8.

  11. Mixed Number Improper Fraction • Denominator: tells us how many parts make up a whole. Chop each whole into that many parts. How many parts do we get? • Multiply the whole number by the denominator. • Numerator: tells us how many parts we already have. How many parts do we now have in total? • Add the number of parts we get from chopping the wholes to the number of parts we already have • Form the improper fraction: # of parts # of parts that make a whole

  12. Ex: Write 2 5/8 as an improper fraction. Draw the mixed number Looking at the fraction, how many parts make up a whole? 8 Chop each whole into 8 pieces. 8 + 8 + 5 How many parts do we now have? = 8 * 2 + 5 = 21 = parts from whole + original parts

  13. Therefore 2 5/8 = 21/8

  14. Finding Equivalent Fractions • Equal fractions with different denominators are called equivalent fractions. • Ex: 6/8 and 3/4 are equivalent.

  15. The Magic One • We can find equivalent fractions by using the Multiplication Property of 1: for any number a, a * 1 = 1 * a = a (magic one) • We will just disguise the form of the magic one • Do you agree that 2/2 = 1? • How about 3/3 = 1? • 4/4 = 1? • 25/25 = 1? 17643/17643 = 1? • 1 has many different forms . . . • 1 = n/n for any n not 0

  16. Ex: Find another fraction equivalent to 1/3 1/3 = 1/3 * 1 We can write 1/3 many ways just be using the Magic One = 1/3 * 2/2 = 2/6 or 1/3 = 1/3 * 1 = 1/3 * 3/3 = 3/9

  17. Ex: Find a fraction equivalent to ½ but with a denominator of 8 1/2 = 1/2 * 1 We can write 1/2 many ways just be using the Magic One. We want a particular denominator – 8. What can we multiply 2 by to get 8? = 1/2 * 4/4 = 4/8 Notice: 4 so choose the form of the Magic One

  18. Ex: Find a fraction equivalent to 2/3 but with a denominator 12 2/3 = 2/3 * 1 We can write 2/3 many ways just be using the Magic One. We want a particular denominator – 12. What can we multiply 3 by to get 12? = 2/3 * 4/4 = 8/12 4 so choose the form of the Magic One

  19. Simplest Form of a Fraction • A fraction is in simplest form when there are no common factors in the numerator and the denominator.

  20. Ex: Simplest Form Ex: 6/8 and 3/4 are equivalent The fraction 6/8 is written in simplest form as 3/4 = = = 1 x Magic one

  21. Ex: Write 12/42 in simplest form • First prime factor the numerator and the denominator: • 12 = 2 x 2 x 3 and 42 = 2 x 3 x 7 • Look for Magic Ones • Simplify = = = 1 x 1 x = Notice: 2 x 3 = 6 = GCF(12, 42)  factoring (dividing) out the GCF will simplify the fraction

  22. Ex: Write 7/28 in simplest form • What is the GCF(7, 28)? • Hint: prime factor 7 = 7 • prime factor 28 = 2 x 2 x 7 = 7 = = = 1 x = Dividing out the GCF from the numerator and denominator simplifies the fraction.

  23. Ex: Write 27/56 in simplest form • What is the GCF(27, 56)? • Hint: prime factor 27 = 3 x 3 x 3 • prime factor 56 = 2 x 2 x 2 x 7 = 1 There is no common factor to the numerator and denominator (other than 1) Therefore, 27/56 is in simplest form.

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