Fractions, Decimals,

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Fractions, Decimals, Percents

• Users Guide to

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Fractions

• Denominator- the number on the bottom of a
  fraction
• Represents how many equal pieces something is
  being cut into
• Numerator- the number on the top
• Represents the number of equal pieces

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Example two fifths 2/5

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Equivalent Fractions

• Equivalent Fractions are fractions that are equal
  to each other.
• For instance 1/2 2/4
• To find equivalent fractions, just multiply the
  numerator and denominator by the same number.
• Example 1 x 2 2
• 2 x 2 4

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Simplifying Fractions

• Simplifying Fractions means to change the
  fractions into their simplest form
• Example 5/10 1/2
• You can make this change easily by looking at the
  factors of both the numerator and denominator.
• Factors of 5 1, 5
• Factors of 10 1, 2, 5, 10

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Simplifying Fractions cont

• Factors of 5 1, 5
• Factors of 10 1, 2, 5, 10
• The common factors between both numbers are one
  and five. Five is the Greatest. So it is the
  Greatest Common Factor. Most mathematicians call
  this the GCF.
• Find out how many times the GCF goes into both
  the numerator and denominator.
• 5 goes into 5, 1 time
• 5 goes into 10, 2 times
• therefore. 5/10 1/2

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Adding Subtracting Fractions

• When adding and subtracting fractions, you must
  first have the same denominators for both
  fractions.
• Example 1/4 2/4
• Keep the denominator the same- add or subtract
  the numerators.
• 1/4 2/4 ¾
• (again, the denominator stays the same, the
  numerators get added together.)

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Common Denominators

• Before you can add fractions, you must make the
  denominators the same. This is called having
  common denominators.
• You can make common denominators by looking at
  the multiples of both denominators. The smallest
  common multiple (least common multiple-LCM)
  becomes your new denominator.

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Example

• 1/5 2/3

Look at the denominators and find the LCM (least
common multiple)
Multiples of 5 5, 10, 15, 20, 25, 30
Multiples of 3 3, 6, 9, 12, 15, 18, 21, 24, 27,
30

• 15 is the smallest multiple that both numbers
  have in common therefore, that is the number
  that should be used. Although, 30 and any other
  common multiples will also work.

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Example continued

• 1/5 2/3

10/15
3/15











The answer is 13/15.
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.. Answer

• 1/5 2/3
• 1/5 3/15
• 2/3 10/15
• 3/15 10/15
• 13/15

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Multiplying Fractions

• When multiplying fractions or should I say when
  finding the product of fractions
• You simply multiply across.
• Step 1- Multiply the Numerators
• Step 2- Multiply the Denominators
• Step 3- Simplify
• Please note that in most cases, you must
  simplify the fraction after multiplying.

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Example continued

• 2/5 x 3/8
• (2 x 3) / (5 x 8) 6/40
• 6/40 3/20
• 2/5 x 3/8 3/20

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Decimals
Tenths Hundredths Thousandths Ten-thousandths Hundred- thousandths Millionths

• Think about place value and think about money
• .55 means
• Fifty-five hundredths
• Or
• Five tenths plus five hundredths

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0.75 ¾ 75/100 75










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Percents

• Percent form tells how many per every hundred.
  
• 50 50/100
• Also equal to ½ or
• 100/200 or 200/400

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Benchmark Fractions

• These are the fractions that are the most
  commonly used. Memorize these benchmark
  fractions and their percent and decimal
  equivalents to make working with fractions
  easier.

½ 50 0.50
1/3 33 0.333
¼ 25 0.25
1/5 20 0.20
1/6 16.7 0.167
1/8 12.5 0.125
1/10 10 0.10
2/3 67 0.667
¾ 75 0.75