Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is...
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Transcript of Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is...
![Page 1: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/1.jpg)
Fractions
![Page 2: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/2.jpg)
Fractions
Numbers such as ½ and -¾ are called fractions.
The number above the fraction line is called the numerator.
The number below the fraction line is called the denominator.
![Page 3: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/3.jpg)
Reducing Fractions
When both the numerator and denominator have a common divisor, we can reduce the fraction to its lowest terms.
A fraction is said to be in its lowest terms (or reduced) when the numerator and denominator are relatively prime (have no common divisors other than 1).
![Page 4: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/4.jpg)
To reduce a fraction to its lowest terms, divide both the numerator and the denominator by the GCD.
The fraction 6/10 is reduced to its lowest terms as follows.
5
3
210
26
10
6
![Page 5: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/5.jpg)
You Try…
Reduce to its lowest terms 90
54
![Page 6: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/6.jpg)
Mixed Numbers and Improper Fractions The number 2¾ is an example of a mixed
number. It is called a mixed number because it is made up of an integer and a fraction.
2¾ means 2 + ¾ An improper fraction is a fraction whose
numerator is greater than its denominator.
![Page 7: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/7.jpg)
The figure shows improper fractions and mixed numbers….
![Page 8: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/8.jpg)
How do you convert mixed numbers to improper fractions?
![Page 9: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/9.jpg)
Example: Convert to Improper Fractions.
![Page 10: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/10.jpg)
How do you convert improper fractions to mixed numbers?
![Page 11: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/11.jpg)
Example: Convert to a mixed number.
5
8
3
____
5
185
5
31
![Page 12: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/12.jpg)
Example: Convert to a mixed number.
8
225
![Page 13: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/13.jpg)
Multiplication of Fractions
Multiply the numerators and multiply the denominators together then reduce if necessary.
![Page 14: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/14.jpg)
Examples
32
74
32
135
4
9
8
15
4
12
8
71
27
8
93
42
9
4
3
2
40
21
85
73
8
7
5
3
or
![Page 15: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/15.jpg)
Reciprocal The reciprocal of any number is 1 divided by
that number. The product of a number and its reciprocal
must equal 1.
![Page 16: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/16.jpg)
Division of Fractions
To find the quotient of two fractions, multiply the first fraction by the reciprocal of the second fraction.
![Page 17: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/17.jpg)
Example: Evaluate .4
3
7
5
21
20
3
4
7
5
![Page 18: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/18.jpg)
Addition and Subtraction of Fractions Before we can add or subtract fractions,
the fractions must have a lowest common denominator.
![Page 19: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/19.jpg)
![Page 20: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/20.jpg)
Adding or Subtracting Fractions with Unlike Denominators
Use prime factorization to find the LCD for the denominator.
Example:
60
7
60
18
60
25
6
6
10
3
5
5
12
5
10
3
12
5
![Page 21: Fractions. Numbers such as ½ and -¾ are called fractions. The number above the fraction line is called the numerator. The number below the fraction line.](https://reader036.fdocuments.us/reader036/viewer/2022062305/5697bfd01a28abf838caa5b9/html5/thumbnails/21.jpg)
Addition Example
NowReduce!