H OW TO M ULTIPLY AND D IVIDE F RACTIONS By Frank Wang

M ULTIPLICATION AND D IVISION W ITH F RACTIONS You know adding and subtracting fractions, right? This PowerPoint is about the other two operations: multiplication and division! Although it is very hard to show it with real life items, it is very simple with regular numbers.

P ART ONE :

M ULTIPLICATION Here is a rule for whole number multiplication: the product of the two numbers will be greater than the two factors. Well, multiplication with fractions is the complete OPPOSITE of that rule. When you multiply fractions, the product is LESS than the two factors. This happens because a fraction is LESS than one, and anything multiplied by one is itself.

H OW TO This is very easy. There are only two steps to multiplying fractions. First, Multiply the numerators together and multiply the denominators together.

S TEP 1 EXAMPLE 4/6 x 7/8 = ? 4x7= 28 6x8= 48 ANSWER: 28/48

S TEP 2 EXAMPLE So, your answer is 28/48, right? NO! You have to simplify the fraction. To do this, you have to first find the GCF*. 28: 4, 7, 28, 1, 2, 14 48: 6, 8, 48, 1, 2, 24, 4, 12, 16, 3 * If 1 is the GCF, it is already in simplest form!

GCF After that, divide the numerator and the denominator by the GCF. 28 ÷ 4 = 7 48 ÷ 4 = 12 So, the answer is 7/12.

C HECKING To check if you did this step correctly or not, see if the numerator and denominator still have a common GCF. Let’s say when I wrote out the factors, I didn’t realize that 4 was there, so I chose 2. I would have gotten 14/24. I would then list the factors of these two numbers to check. 14: 7,2,1,14 24: 6, 4, 8, 3, 12, 2, 24, 1 14 ÷ 2 = 7 24 ÷ 2 = 12 So, the answer is 7/12.

P ART 2:

D IVISION For dividing whole numbers, the quotient is less than the dividend and divisor. Well, if you do it with fractions, the quotient is greater than the dividend and divisor. This is because of the reason that the multiplication works.

H OW TO Division is pretty much the same as multiplication. The first thing you have to do is flip one of the fractions around* and change the division sign to a multiplications sign. Then, you just have to regularly multiply like you would if they were normal fractions. *Numerator to denominator, denominator to numerator.

S TEP 1 E XAMPLE 4/6 ÷ 7/8 = 4/6 ÷ 8/7 x 4/6 x 8/7

S TEP 2 E XAMPLE 4/6 x 8/7 4x8=32 6x7=42

S TEP 3 E XAMPLE Put it in SIMPLEST FORM like you did with multiplication. Make sure you check! A: 16/21

C HECK Do you understand the concept of multiplying and dividing fractions now? Good. Check if you know with these problems. 5/6 x 7/9 2/5 ÷ 3/5

M ULTIPLICATION A NSWER The answer is 35/54. Here is how. 5 x 7 = 35 6 x 9 = 54

D IVISION A NSWER The answer is 2/3. Here is how I got it. 2/5 ÷ 3/5 = 2/5 x 5/3 2 x 5 = 10 5 x 3 = 15

F INAL REVIEW Last question: What is the fraction of the questions that you got correct divided by the amount you got wrong?

A NSWER There are different answers depending on the amount you got right and wrong. The possibilities are : 0 ( 4/0 ) 1 ( 2/2 )

T HANK YOU FOR P ARTICIPATING !!! Presentation by Frank Wang PowerPoint by Frank Wang Examples by Frank Wang Everything else ( except the methods) by Frank Wang