Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.
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Transcript of Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.
![Page 1: Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.](https://reader030.fdocuments.in/reader030/viewer/2022012922/56649f345503460f94c5240e/html5/thumbnails/1.jpg)
Fractions
A Review of the Basics
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But First…We Remind You of…
• Factors and Multiples
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What are Factors
• Numbers that multiply together to make our “given” number
Greatest Common Factor (GCF)
• The greatest common factor is the largest factor that two numbers share.
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12 1 x 12
2 x 63 x 44 x 3
Factors of 12:
1, 2, 3, 4, 6,12
421 x 422 x 213 x 144 x ??5 x ??6 x 77 x 6
Factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
Example
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What is the GCF of 18 and 27?
18 271 x 182 x 93 x 6
4 x ?5 x ?
6 x 3
Factors of 18:
1, 2, 3, 6, 9, 181 x 272 x ?3 x 94 x ?5 x ?6 x ?7 x ?8 x ?9 x 3
Factors of 27:
1, 3, 9, 27
Common Factors: 1, 3, 9
GCF: 9
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What is the GCF of 48 and 60?
48 601 x 482 x 243 x 164 x 126 x 8
1 x 602 x 303 x 204 x 155 x 126 x 10
Factors of 48:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 60:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Common Factors: 1, 2, 3, 4, 6, 12
GCF: 12
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What are Multiples• A multiple is formed by multiplying a given
number by the counting numbers. Ex. “x” by 1, 2, 3, 4, 5, 6 etc.
Least Common Multiple (LCM)
• the smallest number that is common between two lists of multiples.
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EXAMPLE: Find the LCM of 12 and 18
The multiples of 12:
•12 x 1 = 12
•12 x 2 =24
•12 x 3 = 36
•12 x 4 = 48
•12 x 5 =60
The multiples of 18:
•18 x 1 = 18
•18 x 2 = 36
•18 x 3 = 54
•18 x 4 = 72
•18 x 5 = 90
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12, 24, 36, 48, 60
18, 36, 54, 72, 90
The first number you see in both lists is 36.
The least common multiple of 12 and 18 is 36.
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Example 2: Find the LCM of 9 and 10
9, 18, 27, 36, 45, 54, 63, 72
10, 20, 30, 40, 50, 60, 70, 80If you don’t see a common multiple, make each list go further.
81, 90, 99
90, 100, 110
The LCM of 9 and 10 is 90
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Example 3:Find the LCM of 4 and 12
4, 8, 12, 16
12, 24, 36Answer: 12
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Example 4:Find the LCM of 6 and 20
6, 12, 18, 24, 30, 36
20, 40, 60, 80, 100, 120
42, 48, 54, 60
Answer: 60
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What are Fractions?
• Parts of a whole.
• Numbers between two whole numbers
2
1Example
4
13
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Parts of a Fraction
4
1
Denominator: The WHOLE how many pieces the whole has been broken into.
Numerator: The PART how many of the whole we have
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Mixed Numbers and Improper Fractions
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Proper Fraction
• a numerator that is less than its denominator.
• Value is between 0 and 1
• Ex.
4
3
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Improper Fraction
• Numerator that is more than or equal to its denominator.
• Value is greater than 1 or less than -1.
• Ex.
3
4
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Mixed Number
• shows the sum of a whole number and a proper fraction.
• Ex.
4
32
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Writing Mixed Numbers as Improper Fractions
1. Multiply denominator by whole number.
2. Add the product and the numerator.
3. The resulting sum = numerator of the improper fraction.
4. The denominator stays the same.
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Example
24 3143
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Writing Improper Fractions as Mixed Numbers
1. divide the denominator into the numerator.
2. quotient = whole number
3. remainder = numerator of the fraction.
4. divisor = denominator of the fraction.
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Example
135 135
2
10 3
whole number
denominatornumerator
2 35
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Fractions that are the same amount, but with different numerators and denominators.
24
= 48
Equivalent Fractions
![Page 24: Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.](https://reader030.fdocuments.in/reader030/viewer/2022012922/56649f345503460f94c5240e/html5/thumbnails/24.jpg)
Creating Equivalent Fractions
• Multiply the numerator and denominator by the same number.
35
We can choose any number to multiply by. Let’s multiply by 2.
x 2x 2 =
610
So, 3/5 is equivalent to 6/10.
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If you have larger numbers, divide the numerator and denominator by the same number.
35
28Factors of 28
1 282 144 7
Factors of 35 1 355 7
Divide by a common factor.
÷ 7
÷ 7 5
4Is the same as
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Fractions in Simplest Form
Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1.
Examples of fractions that are in simplest form:
45
211
38
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Writing Fractions in Simplest Form.
1. Find the greatest common factor (GCF) of the numerator and denominator.
2. Divide both numbers by the GCF.
![Page 28: Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.](https://reader030.fdocuments.in/reader030/viewer/2022012922/56649f345503460f94c5240e/html5/thumbnails/28.jpg)
Example:
2028
201 x 20
2 x 10
4 x 5
281 x 28
2 x 14
4 x 7
20: 1, 2, 4, 5, 10, 20
28: 1, 2, 4, 7, 14, 28
Common Factors: 1, 2, 4
GCF: 4
We will divide by 4.
÷ 4÷ 4
= 57
Simplest Form
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Comparing and Ordering Fractions
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Strategy
1. Must make denominators the same.
2. Compare the numerators.
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Writing Equivalent Fractions
Easy way
56
34 6 x 4 = 24
24 24
x 4
20x 6
18
20 > 18
>
• Find a common denominator is to multiply the two original denominators.
![Page 32: Fractions A Review of the Basics. But First…We Remind You of… Factors and Multiples.](https://reader030.fdocuments.in/reader030/viewer/2022012922/56649f345503460f94c5240e/html5/thumbnails/32.jpg)
• Find the LCM of both denominators.
712
599, 18, 27, 36, 45
12, 24, 36, 48, 60
36 36
x 4 20x 3
21
20 < 21
<
Another way
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Ordering Fractions
1. Find the LCM of the denominators.
2. Use the LCM to write equivalent fractions.
3. Put the fractions in order using the numerators.
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Example - Order from Least to Greatest:
3 2 18 5 4
8, 16, 24, 32, 40, 48
5, 10, 15, 20, 25, 30, 35, 40
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
40 40 40
x 5 15x 8
16 x 1010
1/4 < 3/8 < 2/5