Fraction Operations

Using Pattern Blocks

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

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.

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.

Adding Fractions

Using Pattern Blocks

Start Out Simple

6

2

6

1

6

1.1 +

To simplify:

=3

1

Start Out Simple

4

2

4

1

4

1.2

+

To simplify:

=2

1

Try

12

1

12

3.4

6

1

6

1

6

1.3

6

4

6

2.5

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)

Unlike fractions

2

1

6

3

6

2

6

1

+

Change to same denominator: =

3

1

6

1.2

+ = =

6

2

3

1

Try

4

1

12

5.4

4

1

6

1.3

4

3

2

1.5

Subtracting Fractions

Using Pattern Blocks

Start Out Simple

6

2

6

3

6

5.1 -

To simplify:

=3

1

Try

4

1

4

3.3

12

5

12

11.2

6

1

6

5.4

Unlike fractions

4

1

-

Change to same denominator: =

4

1

2

1.1

- =

4

2

2

1

Cannot make another shape (Simplified)

Simplifying

6

3

6

2

6

5.1 -

To simplify:

=2

1=

Unlike fractions

6

1

6

1

6

2

-

Change to same denominator: =

6

1

3

1.2

- =

6

2

3

1

Try

2

1

4

3.4

4

1

12

10.3

4

1

3

1.5

Multiplying Fractions

Using Pattern Blocks

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

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

Try

3

1

4

1.4 X

2

1

6

1.3 X

2

1

3

2.5 X

Dividing Fractions

Using Pattern Blocks

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.

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

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

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

Try-- handout

Try-- handout

Try-- handout

Try-- handout

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

Dividing Fractions

Try

3

1

6

5.3

2

1

4

3.2