Dividing Fractions

Strategies and Examples

Using the one grid model (fraction divided by a whole number)

1. Draw a rectangle. Divide it into as many parts as your denominator (e.g. 3)

2. Shade in the number of parts you have in the numerator (e.g. 2)

3. Each part will now be divided into four equal parts (because you're dividing by 4)

4. Circle one fourth from each third

5. You now have two parts circled out of the total 12

6. The answer is 2/12 = 1/6 (LT)

Using the two grid Model (fraction divided by a fraction)

1. Draw two rectangles and show the first denominator (4 floors or rows) in the first rectangle and the second denominator (5 rooms or columns) in the second rectangle

2. Shade in the numerator for the first fraction (3) in the first rectangle (to get 3/4) and shade in the second numerator (4) in the second rectangle (to get 4/5)

3. Divide the first rectangle into 5 rooms (make 5 columns). Divide the second rectangle into 4 floors (make four rows)

4. You should notice that BOTH rectangles are now divided into 20 pieces

5. The first rectangle now has 15 shaded pieces and is being divided by the second rectangle which has 16 shaded pieces. This gives you 15 divided by 16 or 15/16

6. This strategy is also based on common denominators, as you are essentially dividing both rectangles into the common portion of 20. Then you are dividing each portion within the 20.

7. Reduce if necessary.

Using common denominators

1. Identify your two denominators (e.g. 6 and 5)

2. Multiply both parts of the first fraction (4/6) by the second denominator (5)

3. Multiply both parts of the second fraction (2/5) by the first denominator (6)

4. You will notice that both new denominators are now the same (the products are both 30). This will always happen because by multiplying the two denominators together, you are making the product the common denominator

5. The division in the denominator cancels our to 1 because we know that a number divided by itself always equals one (e.g 30 divided by 30)

6. The numerator is now 20 divided by 12 which can be re-written as 20/12 because we know that the line in a fraction is actually division

7. You are left with 20/12 = 5/3 = 1 2/3 (LT) --> show both improper and mixed fraction when necessary

Using the reciprocal (standard algorithm)

If you used this strategy, keep the first fraction the same and flip the second one. Don't forget to change the operation to multiplication.
Dividing Fractions with Fraction Models

Learning Goal

Learn various methods to solve division problems using fractions

Success Criteria

- a one grid model is used when you are dividing one fraction by a whole number (e.g. 2/3 divided by 8)

- a two grid model is used when you are dividing a fraction by a fraction (e.g. 1/2 divided by 2/3)

- changing both fractions to be out of a common denominator can be used in any division question

-using the reciprocal strategy is a short cut

Homework

One Grid Strategy:
1) 2/7÷4
2) 1/3÷8
3) 7/12÷5

Two Grid Strategy:
4) 2/3÷7/8
5) 3/5÷1/4
6) 11/15÷2/3

Common Denominator Strategy:
7) 5/7÷8/3
8) 11/9÷1/2
9) 5/6÷1/3

Reciprocal Strategy:
10) 2 1/3÷4/5
11) 6 1/4÷1/2
12) 3/4÷8/9