Dividing Fractions 2

Learning Goal We are learning to divide fractions using related multiplication.

When would you divide fractions? One example is when you are trying to figure out how many episodes of your favorite ½ hour tv program you could watch in the 1 ½ hrs you have available. 1½ ÷ ½ = 3 You could watch 3 episodes.

Dividing Fractions – Conceptual Understanding When you divide two fractions that are between 0 and 1, the quotient is going to be larger than at least one of your fractions. ½ ÷ ½ = 1 ½ ÷ ¾ = 2/3 Ok. Let’s look at how we can solve these problems…

Dividing Fractions: The Process 1) Change mixed numbers into improper fractions. 2) Invert and multiply. (You may choose to cancel before multiplying.) 3) Reduce your answer (if possible).

Example: 15/3 ÷ 2/9= Answer: 45/2

Example: 3 1/5 ÷ 1 2/8 = Answer: 64/25

Understanding the rules

Rule #1: Change mixed numbers into improper fractions Rule #1: Change mixed numbers into improper fractions. Which problem would you prefer to solve? This one: 3 ¾ ÷ 2 1/3 Or this one: 15/4 ÷ 7/3

Reciprocal  

Rule #2: Invert and Multiply Why invert and multiply? This is actually a short cut that helps us get to the answer more quickly. Dividing by a number is equivalent to multiplying by its reciprocal. After all, dividing by 1 is much easier than dividing by 3/8! Example: 6/7 ÷ 3/8 = ______ Answer: 16/7

Rule #3: Reduce Your Answer Reducing before multiplying helps simplify the equation early on, so that there is less work later.

Let’s try a few together: 5/8 ÷ 7/8 = 3/5 ÷ 2 = 15 ÷ 2 ½ =

What are the 3 steps in dividing fractions? Closing What are the 3 steps in dividing fractions?

Practice Pg. 319 #s 7, 10, 12, 13

Journal… Can you think of some word problems that would require division by fractions? Think about it, then in your journal, create a visual for your word problem.