 ### Fractions

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This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

This lesson is for students in grades 6 and 7.  Students will learn to:

• Rename fractions in higher terms and lower terms
• Rename improper fractions as mixed or whole numbers
• Add and subtract fractions

Illinois States Standards - Mathematics Number 6

Identify Fractions

Because things in the real world don't always come in complete amounts, fractions are used to name parts of complete units.   For example, if there are 12 students in class and 10 students are present, 10/12 of the class is present.

To practice writing and identifying fractions go to:

Renaming Fractions

Any fraction can be renamed in higher terms.  For example, consider the fraction 5/6.  Multiply both terms by the same number:  5(2) = 10 and 6(2)=12; therefore 5/6 = 10/12

Many fractions can be renamed in lowest terms.  For example, the numerator and denominator in the fraction 15/18 have a common factor of 3. (A list of factors for numbers from 1 to 100 may be found at http://mathforum.org/library/drmath/view/58525.html.) Divide both the numerator and denominator by 3;  the resulting fraction is 5/6.  It is in lowest terms.  There is no common factor for the numerator and the denominator.

To practice renaming fractions go to:

Adding Fractions and Mixed Numbers

To add either fractions or mixed numbers, the fractions parts being added must be in the same terms.  You cannot add 2/3 and 3/4 because they represent different size parts.  The least common multiple for 3 and 4 is 12;  raise 2/3 to 8/12 and 3/4 to 9/12.  Now add:  8/12 + 9/12.  The sum is 17/12.  This is an improper fraction and should be renamed as a mixed number.  Divide the numerator 17 by the denominator 12.  There is one set of 12 in 17 with 5 parts left over. 17/12 is equal to 1 and 5/12.

To practice adding fractions and mixed numbers go to:

Subtracting Fractions and Mixed Numbers

To subtract either fractions or mixed numbers, the fractions must also be in the same terms as in addition.  Find a common denominator and raise the terms of the fractions.  5/8 - 1/6 = 15/24 - 4/26 = 11/26

When you are subtracting mixed numbers, it may be necessary to regroup.  For example, 12 2/3 - 7 7/8.  Find a common denominator and raise the terms:  12 16/24 - 7 21/24. Borrow 1 from 12 and rename it as 24/24; add the 24/24 to the 16/24. 12 16/24 = 11 40/24

Now you can subtract;  11 40/24 - 7 21/24 = 4 19/24.

For more information about subtraction of fractions and mixed numbers go to:

To practice subtracting fractions and mixed numbers go to:

To apply your skill in adding and subtracting fractions and mixed numbers, complete one of the following activities:

Take this test and assess your skill at adding and subtracting fractions and mixed numbers.

1. What is 3/7 + 2/7? Please click on the correct answer!

a) 5/14 b) c) 5/7

2. What is 7/12 + 1/12? Please click on the correct answer!

a) 8/24 b) 1/3 c) 2/3

3. What is 3/14 + 2/7? Please click on the correct answer!

a) 5/21 b) 1/2 c) 5/14

4. What is 5/6 + 4/9? Please click on the correct answer!

a) 11/9 b) 23/18 c) 9/15

5. What is 7/10 - 3/10? Please click on the correct answer!

a) 4/10 b) 2/5 c) 3/0

6. What is 13/18 -11/18? Please click on the correct answer!

a) 2/9 b) 1/9 c) 2/18

7. What is 13/14 - 5/7? Please click on the correct answer!

a) 3/14 b) 3/21 c) 3/7

8. What is 5/8 - 5/12? Please click on the correct answer!

a) 3/5 b) 3/4 c) 5/24

9. What is 13/15 - 7/10? Please click on the correct answer!

a) 5/30 b) 1/6 c) 6/5

10. What is 37 3/10 + 6 7/10? Please click on the correct answer!

a) 43 1/2 b) 43 10/20 c) 14 14/21

11. What is 11 13/14 + 3 1/7? Please click on the correct answer!

a)15 1/14 b) 14 2/3 c) 14 14/21

12. What is 9 9/17 - 3 15/17? Please click on the correct answer!

a) 4 11/17 b) 5 c) 5 6/17

13. What is 14 7/8 - 14 2/3? Please click on the correct answer!

a) 1 5/24 b) 5/24 c) 1

14. What is 20 1/2 - 12 3/4? Please click on the correct answer!

a) 7 3/4 b) 33 1/4 c) 8 3/4

15. What is 1 7/8 + 3 5/8? Please click on the correct answer!

a) 1 3/4 b) 5 1/2 c) 2 3/4