Learn Fractions
A fraction , in general, is the expression of a number
divided by another and aproper fraction represents the parties took
a whole.
The classic example is a cheese that we break into portions. In the drawing, we made 8 servings, 3 Roses and 5 green.
 Taking 3 roses represent 3 servings of
eight which have divided the cheese, that is 3/8
of the cheese,and if we take the 5 green, representing 5 servings of eight which have divided the cheese is say 5/8 of the cheese. |
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The parts that we (3 or 5) are called the numerator and the parties that we divide the cheese (8) denominator . To read a fraction, the numerator is read normally but, as discussed below, the denominator is a special form of read .
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Denominator
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Reading
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Examples
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2
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media
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5/2 = five half
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3
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thirds
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2/3 = two-thirds
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4
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Quarter
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3/4 = three quarters
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5
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fifths
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4/5 = four-fifths
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6
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sixths
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5/6 = five sixths
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7
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sevenths
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6/7 = six sevenths
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8
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knockout
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7/8 = seven eighths
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9
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Ninth
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8/9 = eight-ninths
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10
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tenths
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9/10 = nine tenths
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greater than 10
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Number is added to
the end avos |
10/11 = ten eleven avos
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Sorting Fractions
Fractions can be classified in different ways; in the table below the characteristics of the most important is.
Fractions can be classified in different ways; in the table below the characteristics of the most important is.
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Type
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Features
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Examples
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Own
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The numerator is smaller than the denominator
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1/2, 7/9
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Improper
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The numerator is greater than the denominator
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4/3, 5/2
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Homogeneous
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Have the same
denominator
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2/5, 4/5
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Heterogeneous
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They have
different denominators
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3/7, 2/8
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Full
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The numerator equals the denominator
represent an integer |
6/6 = 1
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Equivalents
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When they have the same value.
Two fractions are equivalent if their cross products are equal |
2/3 and 4/6
2 x 6 = 3 x 4 |
If a fraction multiply or divide the numerator and denominator by the same number, we get an equivalent fraction to the first, as both have the same value. For example:
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1
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(1 x 4)
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4
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3
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(3: 3)
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1
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|||||||||
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-
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=
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---
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=
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-
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=
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0.5;
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-
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=
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---
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=
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-
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=
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0.2
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2
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(2 x 4)
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8
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15
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(15: 3)
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5
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Simplify or Reduce a fraction is to find the smallest possible fraction equivalent;for this, the first thing we do is find the largest number that divides evenly (remainder = 0) the numerator and denominator (greatest common divisor) and then divide the numerator and denominator by the greatest common divisor, since as we have seen before dividing the numerator and denominator of a fraction by the same number we get an equivalent fraction (of equal value). Example: Simplify 30/42numbers that divide exactly 30 (splitters) are: 2, 3, 5, 6 ., 10 and 15 which divide numbers exactly 42 (dividers) are:. 2, 3, 6, 7, 14 and 21 The common divisors . both are 2, 3 and 6 The greatest common divisor is 6, therefore , divide numerator and denominator by 6.
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30
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30/6
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5
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||
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-
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=
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---
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=
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-
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42
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42/6
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7
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When a fraction, the numerator and denominator have no common divisor, is said to be an irreducible fraction.
Adding and Subtracting
Fractions If the fractions have
the same denominator (homogeneous), add or subtract the numerators and put the
same denominator.
Example:
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3
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2
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(3 + 2)
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5
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5
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2
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(5-2)
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3
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|||||||
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-
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+
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-
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=
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---
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=
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-
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;
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-
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-
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-
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=
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---
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=
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-
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6
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6
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6
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6
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7
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7
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7
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7
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If the fractions have different denominators (heterogeneous), the first thing you have to do is match the denominators. To achieve this, we look at the given two equivalent fractions multiplying the numerator and denominator of each of them by the denominator of the other. Once obtained the same denominator, we proceed as in the previous case, we add the numerators and put the common denominator.Example:
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2
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3
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(2 x 7)
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(3 x 5)
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14
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15
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29
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||||||
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-
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+
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-
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=
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---
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+
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---
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=
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-
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+
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-
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=
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-
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5
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7
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(5 x 7)
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(7 x 5)
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35
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35
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35
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Fractions Multiplication
The product of several fractions is equal to another fraction whose numerator is the product of the numerators and denominator the product of the denominators.
Example:
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3
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4
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2
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(3 x 4 x 2)
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24
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2
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||||||
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-
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x
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-
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x
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-
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=
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----
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=
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-
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simplifying
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=
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-
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4
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5
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3
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(4 x 5 x 3)
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60
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5
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Fraction Of A Number
Calculate the fraction of a number is the same as multiplying the fraction by that number. Example: Calculate the 2/3 of 60 :
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2
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2
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(2 x 60)
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120
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|||||||||
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-
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of
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60
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=
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-
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x
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60
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=
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---
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=
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-
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=
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40
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3
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3
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3
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3
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Division of Fractions
The quotient of two fractions is another fraction whose numerator is the product of the first numerator by the denominator of the second, and the denominator denominator the product of the first by the numerator of the second. Example:
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4
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3
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(4 x 5)
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20
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|||
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-
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:
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-
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=
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---
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=
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-
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9
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5
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(9 x 3)
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27
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