GRE - Fractions Refresher
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GRE
Fractions Refresher
Equivalent Fractions
•Equivalent fractions can be created by multiplying/dividing the numerator and denominator by the same number.
Examples:
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1×3 Å Multiply by 3 |
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×3 Å Multiply by 3 |
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Å 1 = |
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Practice: Fill in the blank
a)21 = 12
b)23 = 24
c)94 = 16
d)53 = 60
e)41 = 7
f)56 = 42
g)78 = 49
h)29 = 108
i)157 = 135
j)51 = 245
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Å Multiply by 5 |
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Å Multiply by 5 |
= 1535 Å37 = 1535
Answers:
a)21××66 = 126
b)23 ××88 = 1624
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9 ×4 |
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3 ×12 |
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e)41××77 = 278
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5 ×7 |
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6 ×7 |
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g) |
7 ×7 |
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8 ×7 |
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2 ×12 |
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9 ×12 |
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15 ×9 |
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j)1×49 = 49
5 ×49 245
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GRE
Fractions Refresher
numerator Æ
Simplifying Fractions
denominator Æ
•To simplify a fraction, divide the numerator and denominator by the same number until the numerator and denominator can be simplified no further.
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Examples:
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Å Divide by 8 |
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56 ÷8 |
Å Divide by 8 |
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Cannot be |
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simplified further
Practice: Simplify each fraction
a) 1520 =
b) 1827 =
c) 4048 =
d) 137 =
e) 15060 =
f) 3952 =
g) 135215 =
h) 154121 =
i) 10872 =
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Å Divide by 2 |
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Å Divide by 2 |
=2721 Å Can be simplified further
=21÷3 Å Divide by 3
27 ÷3 Å Divide by 3
= 79 Å Cannot be simplified further
Answers:
a)1520 ÷÷55 = 34
b)1827 ÷÷99 = 23
c)4048 ÷÷88 = 56
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d) 13 (already simplified)
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f)3952 ÷÷1313 = 34
g)135215 ÷÷55 = 2437
h)154121÷÷1111 = 1411
i)72 ÷36 = 2
108 ÷36 3
2
GRE
Fractions Refresher
Converting Fractions
•Let’s look at converting entire fractions to mixed fractions and converting mixed fractions to entire fractions
Entire fractions |
Mixed fractions |
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Converting an entire fraction to a mixed fraction:
1)Determine how many times the denominator divides into the numerator (this becomes the whole number)
2)The remainder becomes the numerator of the new fraction
3)The denominator remains the same
Examples: |
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325 = 6 52
The denominator (2) divides into the numerator (7) three times, with a remainder of one
The denominator (5) divides into the numerator (32) six times, with a remainder of two
Converting a mixed fraction to an entire fraction:
1)Multiply the whole number by the denominator and add the product to the numerator
2)The result becomes the new numerator and the denominator remains the same
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Examples: |
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The whole number (5) multiplied by the denominator (4) equals 21. The denominator (4) remains the same
The whole number (3) multiplied by the denominator (7) equals 22. The denominator (7) remains the same
Practice questions on the next page
3
GRE
Fractions Refresher
Practice: Convert each entire fraction to a mixed fraction
a)94 =
b)195 =
c)352 =
d)407 =
e)6811 =
f)596 =
Practice: Convert each mixed fraction to an entire fraction
a)3 41 =
b)8 53 =
c)2 94 =
d)11511 =
e)3 209 =
f)30 31 =
Answers:
a)2 41
b)3 54
c)17 21
d)5 57
e)6 112
f)9 56
Answers:
a)13
4
b)435
c)22
9
d)1526
e)6920
f)91
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4
GRE
Fractions Refresher
Adding and subtracting fractions
(1)Create equivalent fractions with the same denominator (a.k.a. common denominator)
(2)Add/subtract the numerators, and keep the denominator the same
Examples:
Practice:
a)38 + 121 =
b)1415 − 107 =
c)167 − 38 =
d)81 + 23 =
e)121 − 56 =
f)56 + 109 =
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Å Create equivalent fractions with the same denominator (12) |
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Å Add the numerators; keep the denominator the same |
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8 ×4 |
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9 ×4 |
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Å Create equivalent fractions with the same denominator (36) |
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= 17 |
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Å Subtract the numerators; keep the denominator the same |
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Fractions Refresher |
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GRE |
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Multiplying fractions |
numerator Æ |
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• Multiply numerator by numerator, and denominator by denominator. |
denominator Æ |
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Examples: |
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112 × 57 = 1077
56 × 71 = 425
• Whenever possible, “cross simplify” beforehand.
Cross simplifying
Method 1: 169 ×154 = 24036 = 24036 ÷÷1212 = 203
Cross simplify: 169 ×154 = 169 ÷÷34 ×154 ÷÷43 = 34 × 51 = 203
Practice: Find each product and write answer in simplest terms
a)53 × 79 =
b)3221 ×1635 =
c)247 ×149 =
d)158 × 34 =
e)1611 × 334 =
f)12572 × 2596 =
Answers:
a) 7
15
3 b) 10
c) 3
16
2 d) 5
e) 1
12
3 f) 20
6
GRE
Fractions Refresher
Dividing fractions
• Multiply by the reciprocal of the divisor.
Examples:
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Practice: Find each quotient and write answer in simplest terms |
Answers: |
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