DIVIDING FRACTIONS.

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Presentation transcript:

DIVIDING FRACTIONS

There are 2 groups of 2 in 4, therefore Dividing Fractions What does 4 ÷ 2 mean in words? Justify your reasoning by using a model or a drawing. how many groups of 2 are in 4? ÷ Modeling this with tiles may be more effective. There are 2 groups of 2 in 4, therefore 4 ÷ 2 = 2

(How many groups of 2/3 are in 3/4)? Example 1 What does 3/4 ÷ 2/3 mean in words? (How many groups of 2/3 are in 3/4)? Modeling this with tiles may be more effective.

Model a 4 by 3 array for each fraction. Example 1 3/4 ÷ 2/3 When dividing fractions, the denominators are still the dimensions of the arrays! Model a 4 by 3 array for each fraction. Modeling this with tiles may be more effective. ÷

Example 1 3/4 ÷ 2/3 3/4 2/3 Find out how many groups of 2/3 (8 units) are in 3/4 (9 units) ÷ There is 1 whole group of 8 and one more left out of another group of 8 1 1/8 Count the number of units in 2/3 (8 units) and make groups from 3/4 Is equivalent to 9/12 Is equivalent to 8/12

3/4 ÷ 2/3 3/4 2/3 9/12 8/12 ÷ Is equivalent to Is equivalent to Count the number of units in 2/3 (8 units) and make groups from 3/4 Is equivalent to 9/12 Is equivalent to 8/12

Example 2 1/2 ÷ 1/3 1/2 1/3 Find out how many groups of 1/3 (2 units) are in 1/2 (3 units) ÷ Is equivalent to 3/6 Is equivalent to 2/6 There is 1 whole group of 2 and one more left out of another group of 2 1 1/2

1/2 ÷ 1/3 1/2 1/3 3/6 2/6 ÷ Is equivalent to Is equivalent to These fractions may need to be written as # over # instead of with the slash marks for the students to understand better.

There are only 8 out of a group of 9, so the quotient is 8/9 Example 3 2/3 ÷ 3/4 2/3 3/4 Find out how many groups of 3/4 (9 units) are in 2/3 (8 units) ÷ YOU CAN’T GET A WHOLE GROUP OF 9 UNITS! Is equivalent to 8/12 Is equivalent to 9/12 There are only 8 out of a group of 9, so the quotient is 8/9

2/3 ÷ 3/4 2/3 3/4 ÷ Is equivalent to 8/12 Is equivalent to 9/12

Guided Practice SKETCH and SOLVE by using area model arrays 1. 1/2 ÷ 1/4 2. 1/2 ÷ 2/3 3. 2/3 ÷ 1/2 4. 2/3 ÷ 1/4 5. 2/5 ÷ 5/6 6. 1/2 ÷ 1/5