Dividing Fractions Investigations
Read the following statement. Decide whether you agree or disagree with the statement. Then explain in one to two sentences why you agree or why you disagree with the statement.
1. ÷ =
Investigation 1: If you are dividing two fractions, can you divide the numerators and divide the denominators to get your answer?
Divide the following fractions using the method above:
÷ ÷ ÷
2. Explain in one to two sentences what you discovered and any difficulties you had.
3. Let’s revisit the third problem. ÷ Brainstorm ways you could solve this problem.
4. Explain in one or two sentences a new strategy you could use when solving problems that do not divide across evenly, like the problem in number three.
Discuss different methods that could be used to solve this as a whole class. Use this space to record any method that you did not discover in question 4.
5. Now solve the following problems. You may use any of the methods that have been discussed.
÷ ÷ ÷ ÷
6. These methods all work, but some take longer or can be more complicated than others.
If you have a division problem with whole numbers, can you multiply the dividend and the divisor by the same number and still get the same answer?
Try it: Do 49 ÷ 7 = _____
Now multiply 49 x 2 and 7x2 and divide again.
(49 x 2) ÷ (7 x 2) = ______
Do you get the same answer?______
Look at the following new method for dividing fractions:
( x ) ÷ ( x ) (you are just multiplying both sides by the same number )
Does multiplying the dividend and the divisor by the same number change the value of the problem?______
x = 1
÷ 1 (any number multiplied by its reciprocal is 1)
What property is shown in that step?______
= 1 = 1
Does this method have the same result as the method you used in question five?______
Let’s practice using the new method (Just follow the steps we used above):
÷ ÷ ÷
7. Now write an algebraic rule showing what is happening in question 6. (Remember that an algebraic rule uses only variables)
8. Solve ÷ using three different methods.
9. Explain in one or two sentences which method you prefer.
10. Use your preferred method to solve:
11. Look at your answer to question #1. Were you correct? ______. If you chose no as your answer what have you learned in this investigation?
12. Summarize in three to five sentences what you have discovered about dividing fractions.