Fraction Operations
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![Page 1: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/1.jpg)
Fraction Operations
Using Pattern Blocks
![Page 2: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/2.jpg)
Fractions CCSS
4.NF.3c Add and subtract mixed numbers with like denominators.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number
![Page 3: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/3.jpg)
Fractions CCSS 5.NF.1 Add and subtract fractions with unlike
denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
![Page 4: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/4.jpg)
Fractions CCSS
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
![Page 5: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/5.jpg)
Adding Fractions
Using Pattern Blocks
![Page 6: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/6.jpg)
Start Out Simple
6
2
6
1
6
1.1 +
To simplify:
=3
1
![Page 7: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/7.jpg)
Start Out Simple
4
2
4
1
4
1.2
+
To simplify:
=2
1
![Page 8: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/8.jpg)
Try
12
1
12
3.4
6
1
6
1
6
1.3
6
4
6
2.5
![Page 9: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/9.jpg)
Unlike fractions
4
3
4
2
4
1
+
Change to same denominator: =
2
1
4
1.1
+ =
4
2
2
1
Cannot make another shape (Simplified)
![Page 10: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/10.jpg)
Unlike fractions
2
1
6
3
6
2
6
1
+
Change to same denominator: =
3
1
6
1.2
+ = =
6
2
3
1
![Page 11: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/11.jpg)
Try
4
1
12
5.4
4
1
6
1.3
4
3
2
1.5
![Page 12: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/12.jpg)
Subtracting Fractions
Using Pattern Blocks
![Page 13: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/13.jpg)
Start Out Simple
6
2
6
3
6
5.1 -
To simplify:
=3
1
![Page 14: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/14.jpg)
Try
4
1
4
3.3
12
5
12
11.2
6
1
6
5.4
![Page 15: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/15.jpg)
Unlike fractions
4
1
-
Change to same denominator: =
4
1
2
1.1
- =
4
2
2
1
Cannot make another shape (Simplified)
![Page 16: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/16.jpg)
Simplifying
6
3
6
2
6
5.1 -
To simplify:
=2
1=
![Page 17: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/17.jpg)
Unlike fractions
6
1
6
1
6
2
-
Change to same denominator: =
6
1
3
1.2
- =
6
2
3
1
![Page 18: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/18.jpg)
Try
2
1
4
3.4
4
1
12
10.3
4
1
3
1.5
![Page 19: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/19.jpg)
Multiplying Fractions
Using Pattern Blocks
![Page 20: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/20.jpg)
Multiplying Fractions
½ X ½ means ½ of ½ which means: one of two equal parts of one-half.
Pictorially:
One-half ½ of one-half
?2
1
2
1
2
1
2
1of
4
1
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Multiplying Fractions
1/3 X ½ means 1/3 of ½ which means: one of two equal parts of one-half.
Pictorially:
One-half 1/3 of one-half
6
1
?2
1
3
1
2
1
3
1of
![Page 22: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/22.jpg)
Try
3
1
4
1.4 X
2
1
6
1.3 X
2
1
3
2.5 X
![Page 23: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/23.jpg)
Dividing Fractions
Using Pattern Blocks
![Page 24: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/24.jpg)
Dividing Fractions
6 2 can mean: In 6, there are how many groups of 2?
There are 3 groups of 2 in 6,
so 6 2 = 3
This is important for us when dividing fractions.
![Page 25: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/25.jpg)
Dividing Fractions
means: In one whole, there are how many halves?Pictorially:
2
11
needs how many to cover it?
Two cover a
22
11 therefore
![Page 26: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/26.jpg)
Dividing Fractions
means: In one-half, there are how many sixths?Pictorially:
6
1
2
1
needs how many to cover it?
Three cover a
36
1
2
1 therefore
![Page 27: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/27.jpg)
Dividing Fractions
means: In two-thirds, there are how many sixths?Pictorially:
6
1
3
2
needs how many to cover it?
Four cover
46
1
3
2 therefore
![Page 28: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/28.jpg)
Try-- handout
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Try-- handout
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Try-- handout
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Try-- handout
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Dividing Fractions
means: In one-half, there are how many thirds?Pictorially:
3
1
2
1
needs how many to cover it?
We need to think of this slightly differently because it is more than 1 but less than 2
![Page 33: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/33.jpg)
Dividing Fractions
![Page 34: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/34.jpg)
Try
3
1
6
5.3
2
1
4
3.2
![Page 35: Fraction Operations](https://reader035.fdocuments.us/reader035/viewer/2022070401/56813657550346895d9ddfdb/html5/thumbnails/35.jpg)