HOW TO DECOMPOSE A FRACTION IN DIFFERENT WAYS

Find three ways to decompose each fraction into a sum of other fractions with the same denominator.

Problem 1 :

3/4 = 1/4 + 1/4 + ___

3/4 = 2/4 + ___

3/4 = 1/4 + ___

Solution :

3/4 = 1/4 + 1/4 + ___

3/4 = 1/4 + 1/4 + 1/4

= (1 + 1 + 1)/4

= 3/4

3/4 = 2/4 + ___

3/4 = 2/4 + 1/4

= (2 + 1)/4

= 3/4

3/4 = 1/4 + ___

3/4 = 1/4 + 2/4

= (1 + 2)/4

= 3/4

Problem 2 :

7/8 = 6/8 + ___

7/8 = 5/8 + ___

7/8 = 4/8 + ___

Solution :

7/8 = 6/8 + ___

7/8 = 6/8 + 1/8

= (6 + 1)/8

= 7/8

7/8 = 5/8 + ___

7/8 = 5/8 + 2/8

= (5 + 2)/8

= 7/8

7/8 = 4/8 + ___

7/8 = 4/8 + 3/8

= (4 + 3)/8

= 7/8

Problem 3 :

6/5 = ___ + 3/5

6/5 = 2/5 + ___ + ___

6/5 = 2/5 + 2/5 + ___ + ___

Solution :

6/5 = ___ + 3/5

6/5 = 3/5 + 3/5

= (3 + 3)/5

= 6/5

6/5 = 2/5 + ___ + ___

6/5 = 2/5 + 2/5 + 2/5

= (2 + 2 + 2)/5

= 6/5

6/5 = 2/5 + 2/5 + ___ + ___

6/5 = 2/5 + 2/5 + 1/5 + 1/5

= (2 + 2 + 1 + 1)/5

= 6/5

Problem 4 :

5/6 = ___ + 3/6

5/6 = 1/6 + ___ + ___

5/6 = 1/6 + 1/6 + ___ + ___ + ___

Solution :

5/6 = ___ + 3/6

5/6 = 2/6 + 3/6

= (2 + 3)/6

= 5/6

5/6 = 1/6 + ___ + ___

5/6 = 1/6 + 2/6 + 2/6

= (1 + 2 + 2)/6

= 5/6

5/6 = 1/6 + 1/6 + ___ + ___ + ___

5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6

= (1 + 1 + 1 + 1 + 1)/6

= 5/6

Problem 5 :

9/12 = ___ + 5/12

9/12 = 3/12 + 3/12 + ___ + ___ + ___

9/12 = ___ + ___ + ___

Solution :

9/12 = ___ + 5/12

9/12 = 4/12 + 5/12

= (4 + 5)/12

= 9/12

9/12 = 3/12 + 3/12 + ___ + ___ + ___

9/12 = 3/12 + 3/12 + 1/12 + 1/12 + 1/12

= (3 + 3 + 1 + 1 + 1)/12

= 9/12

9/12 = ___ + ___ + ___

9/12 = 3/12 + 3/12 + 3/12

= (3 + 3 + 3)/12

= 9/12

Problem 6 :

8/10 = ___ + 4/10

8/10 = 2/10 + 3/10 + ___ + ___ + ___

8/10 = ___ + ___ + ___

Solution :

8/10 = ___ + 4/10

8/10 = 4/10 + 4/10

= (4 + 4)/10

= 8/10

8/10 = 2/10 + 3/10 + ___ + ___ + ___

8/10 = 2/10 + 3/10 + 1/10 + 1/10 + 1/10

= (2 + 3 + 1 + 1 + 1)/10

= 8/10

8/10 = ___ + ___ + ___

8/10 = 4/10 + 2/10 + 2/10

= (4 + 2 + 2)/10

= 8/10

Problem 7 :

Complete the following: 3/5 = ___ + ___

Solution :

3/5 = 1/5 + 2/5

= (1 + 2)/5

= 3/5

Problem 8 :

Ethan needs to plant three types of vegetables in 4/5 of his garden. Help him decompose his part of the garden into three fractions.

Solution :

4/5 = 2/5 + 1/5 + 1/5

= (2 + 1 + 1)/5

= 4/5

Problem 9 :

Using the given cherry model, find the missing fraction.

Solution :

Problem 10 :

Use the fraction strip to write 2/9 as a sum of unit fractions.

Solution :