1. Multiplying and Dividing Fractions

2. Lesson Overview: After going through this lesson you will:
Understand the concepts of multiplying and dividing fractions
Understand the algorithms of multiplying and dividing fractions
Be able to apply your new knowledge to solve multiplication and division problems involving fractions

3. A Quick Review:
When multiplying or dividing fractions, change a mixed number into an improper fraction, but when reducing, change an improper fraction back into a mixed number.

4. Why Multiply and Divide Fractions?
There are many reasons why we may need to multiply and divide fractions in real-life settings, such as:
To calculate a grade in a class
To calculate money while grocery shopping, running errands, etc.
To become better problem-solvers
To be able to get correct measurements while measuring things such as an area of a room
To ration portions of food equally among friends
To get through your math classes!

5. Multiplying Fractions:
You may find that multiplying fractions is easier than adding or subtraction because you don’t need to find common denominators.
Instead, you multiply straight across. Multiply numerators together. Multiply denominators together.

6. Algorithm-Multiplication:
Set up the fractions side-by-side.
1/2 X 3/4
Multiply the numerators of the fractions and write the product as the numerator of the new fraction
½ X ¾ = 3/-- (1X3=3)
Multiply the denominators of the fractions and write the answer as the denominator of the new fraction
½ X ¾= 3/8 (2X4=8)
Remember to write your answers in lowest terms!

7. A Few Examples: Proper Fraction: 2/3 X 4/5
Answer: 8/15 (2X4=8, 3X5=15)
Improper Fraction: 9/2 X 3/7
Answer: 27/14=1 13/27 (9X3=27, 7X2=14)
Mixed Number: 2 1/6 X 3/2
Answer: 39/12=3 3/12=3 1/4 (13/6 X 3/2=
13X3, 6X2)
Whole Number: 5 X 2/7
Answer: 10/7=1 3/7 (5X2=10, 1X7=7)

8. Dividing Fractions:
What does 8/2 mean? It means you are dividing 8 of something by 2 of something else. You could think of it as giving 8 pieces of candy to 2 friends. They would each get 4 pieces, right?
What does 2 ½ / ¼ mean? The same as dividing with whole numbers. For instance, “Jack split 2 ½ pizzas with ¼ of his brothers.”

9. Rules for Dividing Fractions
Change the "÷" sign to "x" and find the reciprocal (flip-flop the numerator and denominator) of the divisor then multiply the numerators.
Multiply the denominators. 
Re-write your answer as a simplified or reduced fraction, if needed.
Example: ¼ / ½ changes to ¼ x 2/1
1/4 x 2/1=2/4=1/2

10. More on “Why do We Invert?”:
To make the problem easier, we want to get rid of the denominator (1/3). So, we multiply by its reciprocal (3/1) to get 1. Remember, though, if we multiply the denominator by a number, we must multiply the numerator by the same number.

11. Algorithm: Dividing Fractions
Set up the fractions side-by-side as you would when multiplying fractions. (3/4 / 1/2)
Now, you must find the reciprocal of the second number (called the divisor). Example: Change 1/2 to 2/1.
Next, multiply straight across as you would when multiplying fractions
Multiply numerators together
Multiply denominators
So, ¾ X ½ becomes ¾ X 2/1 , which equals 6/4 or
1 ½ in lowest terms

12. Some Examples: Proper Fraction: 3/4 / 5/6 Improper: 8/3 / 2/4
Answer: 18/20=9/10 (3/4 x 6/5)
Improper: 8/3 / 2/4
Answer: 32/6=16/3=5 1/3 (8/3 x 4/2)
Whole Number: 5 / 1/3
Answer: 15 (5/1 x 3/1)
Mixed Number: 2 1/4 / 2/3
Answer: 27/8=3 3/8 (9/4 x 3/2)