Fractions A quick help for those who have forgotten how to work with them.
-
Upload
jasper-bryant -
Category
Documents
-
view
217 -
download
3
Transcript of Fractions A quick help for those who have forgotten how to work with them.
![Page 1: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/1.jpg)
FractionsA quick help for those who have forgotten how to work with them.
![Page 2: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/2.jpg)
Fraction Operations
• Addition• Subtraction• Multiplicatio
n• Division• Exit
![Page 3: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/3.jpg)
Adding Fractions
![Page 4: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/4.jpg)
Adding Fractions
In order to add fractions you must have common denominators and for the sake of this presentation you must also change all mixed numbers to improper fractions.
![Page 5: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/5.jpg)
Adding Fractions
Adding fractions with like denominators. When you have like denominators, you add the numerators, then reduce.
![Page 6: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/6.jpg)
Adding Fractions
8
3
8
1Example 1
![Page 7: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/7.jpg)
Adding Fractions
2
1
8
4
Example 1
![Page 8: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/8.jpg)
Adding Fractions
When fractions have uncommon denominators multiply the denominators together, then multiply the numerator by the same number you multiplied the denominator by. This will always give you a common denominator.
![Page 9: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/9.jpg)
Adding Fractions
Example 2
7
2
3
1
![Page 10: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/10.jpg)
7
2
3
17
7
3
Adding Fractions
Example 2
3
![Page 11: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/11.jpg)
21
6
21
7
Adding Fractions
Example 2
![Page 12: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/12.jpg)
21
13
Adding Fractions
Example 2
![Page 13: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/13.jpg)
Adding Fractions
When you have mixed numbers change the mixed number to an improper fraction then add as before. However, if you start out with a mixed number you need to convert your answer to a mixed number as well.
![Page 14: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/14.jpg)
Adding Fractions
Example 3
4
33
3
21
![Page 15: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/15.jpg)
Adding Fractions
Example 3
4
15
3
5
![Page 16: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/16.jpg)
4
15
3
544
3
Adding Fractions
Example 3
3
![Page 17: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/17.jpg)
12
45
12
20
Adding Fractions
Example 3
![Page 18: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/18.jpg)
12
55
12
65
Adding Fractions
Example 3
![Page 19: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/19.jpg)
Adding Fractions
Try these:
4
1
8
3. 1
9
2
12
5. 2
6
15
4
13. 3
![Page 20: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/20.jpg)
Adding Fractions
Answers:
8
5. 1
36
23. 2
12
58. 3
![Page 21: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/21.jpg)
Fraction Operations
• Addition• Subtraction• Multiplicatio
n• Division• Exit
![Page 22: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/22.jpg)
Subtracting Fractions
![Page 23: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/23.jpg)
Subtracting Fractions
In order to subtract fractions you must have common denominators and for the sake of this presentation you must also change all mixed numbers to improper fractions.
![Page 24: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/24.jpg)
Subtracting Fractions
Subtracting fractions with like denominators. When you have like denominators, you subtract the numerators, then reduce.
![Page 25: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/25.jpg)
Subtracting Fractions
8
3
8
1Example 1
![Page 26: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/26.jpg)
Subtracting Fractions
4
1
8
2
Example 1
![Page 27: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/27.jpg)
Subtracting Fractions
When fractions have uncommon denominators multiply the denominators together, then multiply the numerator by the same number you multiplied the denominator by. This will always give you a common denominator
![Page 28: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/28.jpg)
Subtracting Fractions
Example 2
7
2
3
2
![Page 29: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/29.jpg)
7
2
3
27
7
3
Subtracting Fractions
Example 2
3
![Page 30: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/30.jpg)
21
6
21
14
Subtracting Fractions
Example 2
![Page 31: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/31.jpg)
21
8
Subtracting Fractions
Example 2
![Page 32: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/32.jpg)
Subtracting Fractions
When you have mixed numbers change the mixed number to an improper fraction then subtract as before. However, if you start out with a mixed number you need to convert your answer to a mixed number as well.
![Page 33: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/33.jpg)
Subtracting Fractions
Example 3
4
33
3
21
![Page 34: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/34.jpg)
Subtracting Fractions
4
15
3
5Example 3
![Page 35: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/35.jpg)
4
15
3
544
3
Subtracting Fractions
Example 3
3
![Page 36: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/36.jpg)
12
45
12
20
Subtracting Fractions
Example 3
![Page 37: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/37.jpg)
4
5
12
15
Subtracting Fractions
Example 3
![Page 38: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/38.jpg)
4
11
4
5
Subtracting Fractions
Example 3
![Page 39: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/39.jpg)
Subtracting Fractions
Try these:
4
1
8
3. 1
9
2
12
5. 2
6
15
4
13. 3
![Page 40: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/40.jpg)
Subtracting Fractions
Answers:
8
1. 1
36
7. 2
12
111. 3
![Page 41: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/41.jpg)
Fraction Operations
• Addition• Subtraction• Multiplicatio
n• Division• Exit
![Page 42: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/42.jpg)
Multiplying Fractions
![Page 43: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/43.jpg)
Multiplying Fractions
When multiplying fractions we don’t care about having common denominators. We just multiply straight across.
![Page 44: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/44.jpg)
Multiplying Fractions
8
3
8
1Example 1
![Page 45: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/45.jpg)
Multiplying Fractions
64
3Example 1
![Page 46: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/46.jpg)
Multiplying Fractions
Example 2
7
2
3
1
![Page 47: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/47.jpg)
21
2
Multiplying Fractions
Example 2
![Page 48: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/48.jpg)
Multiplying Fractions
When you have mixed numbers change the mixed number to an improper fraction, then multiply as before. However, if you start out with a mixed number you need to convert your answer to a mixed number as well.
![Page 49: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/49.jpg)
Multiplying Fractions
Example 3
4
33
3
21
![Page 50: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/50.jpg)
Multiplying Fractions
4
15
3
5Example 3
![Page 51: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/51.jpg)
4
15
3
5
Multiplying Fractions
Example 3
![Page 52: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/52.jpg)
4
25
12
75
Multiplying Fractions
Example 3
![Page 53: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/53.jpg)
4
16
4
25
Multiplying Fractions
Example 3
![Page 54: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/54.jpg)
Multiplying Fractions
Try these:
4
1
8
3. 1
9
2
12
5. 2
6
15
4
13. 3
![Page 55: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/55.jpg)
Multiplying Fractions
Answers:
32
3. 1
54
5. 2
24
1916. 3
![Page 56: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/56.jpg)
Fraction Operations
• Addition• Subtraction• Multiplicatio
n• Division• Exit
![Page 57: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/57.jpg)
Division
![Page 58: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/58.jpg)
Dividing Fractions
We never really divide fractions. We take the first fraction and multiply it by the reciprocal of the second fraction.
![Page 59: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/59.jpg)
Dividing Fractions
Hint for dividing fractions:
To get the right answer, flip the fraction on the right.
![Page 60: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/60.jpg)
Dividing Fractions
8
3
8
1Example 1
![Page 61: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/61.jpg)
Dividing Fractions
3
8
8
1Example 1
![Page 62: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/62.jpg)
Dividing Fractions
3
1
24
8
Example 1
![Page 63: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/63.jpg)
Dividing Fractions
Example 2
7
2
3
2
![Page 64: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/64.jpg)
Dividing Fractions
Example 2
2
7
3
2
![Page 65: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/65.jpg)
3
7
6
14
Dividing Fractions
Example 2
![Page 66: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/66.jpg)
Dividing Fractions
When you have mixed numbers change the mixed number to an improper fraction, then divide as before. However, if you start out with a mixed number, you need to convert your answer to a mixed number as well.
![Page 67: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/67.jpg)
Dividing Fractions
Example 3
4
33
3
21
![Page 68: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/68.jpg)
Dividing Fractions
4
15
3
5Example 3
![Page 69: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/69.jpg)
Dividing Fractions
15
4
3
5Example 3
![Page 70: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/70.jpg)
9
4
45
20
Dividing Fractions
Example 3
![Page 71: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/71.jpg)
Dividing Fractions
Try these:
4
1
8
3. 1
9
2
12
5. 2
6
15
4
13. 3
![Page 72: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/72.jpg)
Dividing Fractions
Answers:
2
3. 1
8
15. 2
62
39. 3
![Page 73: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/73.jpg)
Fraction Operations
• Addition• Subtraction• Multiplicatio
n• Division• Exit
![Page 74: Fractions A quick help for those who have forgotten how to work with them.](https://reader036.fdocuments.us/reader036/viewer/2022062517/56649f1f5503460f94c37b6a/html5/thumbnails/74.jpg)
The End