INTRODUCTION TO FRACTIONS

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

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

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Types of Fractional Numbers

• A proper fraction is a fraction whose value is
  less than 1 (numerator lt denominator)
• An improper fraction is a fraction whose value is
  greater than or equal to 1 (numerator gt
  denominator)
• A mixed number is a number whose value is greater
  than 1 made up of a whole part and a fraction part

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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

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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

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Ex Write 17 as an improper fraction

• 17 17 / ?
• 17 divided by what is 17?
• 1
• Therefore, 17 17 / 1

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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

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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 . . .
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10
11
This is what 11/8 looks like.
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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.
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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

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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
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Therefore 2 5/8 21/8
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Finding Equivalent Fractions

• Equal fractions with different denominators are
  called equivalent fractions.
• Ex 6/8 and 3/4 are equivalent.

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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

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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
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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
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so choose the form of the Magic One
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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
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so choose the form of the Magic One
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Simplest Form of a Fraction

• A fraction is in simplest form when there are no
  common factors in the numerator and the
  denominator.

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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
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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
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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.
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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.