Multiplying Mixed Numbers 4 ½ x 3 ⅚ 12-6 GET EXCITED!!!!!

What does this photo show?

How much pizza do I have? You have 1 pizza and a half of a pizza Or 1 and ½ pizza Or a pizza that is represented as a mixed number.

Here are some other examples of mixed numbers: Cooking 1 ¼ cup of flour Measuring 2 ⅙ inches Calculating distance – For example, it is 9 ½ miles from Ms. Victoria’s house to Neil Armstrong Elementary every day.

What do you all already KNOW about Mixed Numbers? A whole number and a fraction of a whole number Mixed numbers cannot equal 2 You can change a mixed number an improper fraction an vice versa

What do you WANT to know about multiplying mixed numbers? Can you multiply mixed numbers as they are or do you have to change them to improper fractions Steps to solve Can we multiply mixed numbers

Mixed Numbers Guided Practice A clothing factory has machines that make jackets. These machines operate for 7 ½ hours each day. How many jackets can each machine make in one day? (Envision, 284) What mathematical operation are you going to use to find out how many jackets each can make in one day?

Guided Practice (Cont.) Total Jackets Per Hour Machine A Machine B 2 ¾ 3 1/3 Total jackets made in one day by machine A? Total jackets made in one day by machine B?

Solve Machine A Step one: turn the mixed number fractions into improper fractions Multiply the denominator by the whole number 2x4=8, then add the numerator to the answer 8+3=11/4. Do the same mathematical process for 7 ½ 7x 2= 14+1=15/2 Machine A 2 ¾ jackets per hour

Machine A cont. Step two: Now that you have improper fractions can you multiply the two fractions? Yes, because you all know how to multiply fractions by fractions. Step three: Now multiply. 11/4 x 15/2 = 165/8

Machine A – We’re almost done! Step four : Change the improper fraction back to a mixed number 165/8 Think how many times does 8 go into 165? Well, I know that 8 goes into 16 two times and it does not go into five. What does this tell me?? Put a zero there, since eight does not go into five 165÷8 = 20 5/8

Final Answer! Machine A can make 20 5/8 jackets per day. Questions? Concerns? Take out your math notebooks. Please.

Solve Machine B Step one: turn the mixed number fractions into improper fractions. 3x3=9 +1 =10/3 and we already converted 7 ½ into an improper fraction when were solving for machine A, which was 15/2. Step two: Now that you have improper fractions can you multiply the two fractions? Machine B 3 1/3 jackets each day

Machine B cont. Step two: Now that you have improper fractions 10/3 and 15/2 can you multiply the two fractions? Step three: Now multiply. 5x5 =25 and 1x 1=1, which gives us the fraction 25/1 or 25 Final answer: Machine B make 25 jackets each day.

Machine B cont. Yes, you all know how to multiply fractions by fractions. But, before you do this step. Do any of you know what step we can do that will make the multiplication easier? Cross cancel

Machine B continued Cross cancel the 3 and 15 3÷3=1 and 15÷3=5 now replace the 3 in the 10/3 with a one and 15 in the 15/2 with 5. Remember you can cross can the 2 and 10. 2÷2=1 replace the 2 with the 1 and 10÷2 =5 replace the 10 with the 5.

Machine B Final answer Step three: Now multiply. 5x5 =25 and 1x 1=1, which gives us the fraction 25/1 or 25 Final answer: Machine B make 25 jackets each day.

What have you LEARNED about multiplying mixed fractions? Exit Slip You have to change the mixed number into an improper fraction You don’t have to multiply the whole numbers You have to be careful about cross canceling You have to change the improper fraction into a mixed fraction You have to multiply the denomonators R.I.P