8.6.1 Multiplying a Fraction by a Whole Number

There are different ways to think of how to multiply a fraction and a whole number:

• Use a diagram and model how the fractions fit together

1. Convert the multiplication to repeated addition

PreClass Assignment:

• Watch the Youtube Videos:
  • Modeling Multiplication using a diagram
  • Writing a multiplication as a repeated addition statement
• For each movie, think about what you would say if you were to narrate this video for someone else.

In Class Assignment

• P202 #5a #6, 7, 8, 9, 10, 11, 12 15, *16 *17

Things you should be able to do after today:

• Explain what a whole number x a fraction means as a repeated addition statement
• Multiply a whole number by a fraction and write the answer as an improper fraction or a mixed number
• Convert a word problem to a math statement using multiplication

8.6.2 Dividing fractions by a whole number

Resources

• Watch the youtube videos that explain the notes for todays class.  Watch the videos and have your notes completed for next day.
• Youtube videos.
  • modeling division
  • dividing a fraction by a whole without a diagram

Assignment

• p208 #4, 5, 6, 7, 8, 9, 10 12

8.6.3 Multiplying Proper Fractions

Resources

1. Watch the Youtube Videos and Copy down the notes.

• Don't have your notebook? Get the blank notes template here.
  • Video #1 How to multiply proper fractions
  • Video #2 How to cross reduce fractions before multiplying

Assignment

• P214 #3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, *16

Things you should be able to do after today:

• multiply two or more proper fractions and reduce the answer to lowest terms
• use the cross reducing method to help reduce the multiplication of proper fractions to lowest terms
• represent a word problem using a diagram and use that diagram to determine a multiplication of proper fractions

8.6.4 Multiplying Mixed Numbers and Improper Fractions

Proper fractions make up a very small set of numbers; many times, you will need to multiply mixed numbers or whole numbers.  It is basically the same as multiplying proper fractions with just a couple different steps that are very important:

1. Convert your mixed numbers or whole numbers to improper fractions
2. Cross reduce if possible
3. Multiply your numerators and multiply your denominators
4. Convert your answer back to a mixed number if necessary.

Resources

• Notes

Things you should be able to do after today:

• Convert a mixed number or whole number to an improper fraction
• Convert an imroper fraction to a mixed number
• Multiply improper fractions and proper fractions

Assignment:

• Worksheet examples
• p220 #10-16

Attachments:

File	Description	File size
8.6.4.multiplying.mixed.pdf	Worksheet	116 kB
8.6.4.notes.pdf	Notes for multiplying mixed numbers	335 kB

8.6.5 Dividing Fractions

Dividing fractions is an easy process if you think about changing the division to a multiplication question.  This is because we can make use of the reciprocal.

For example, we often think of dividing by 2 as taking  ½ as taking of something.  2 and ½ are reciprocal numbers.  In today's notes, find out how we can use reciprocals to help us divide by a fraction.

Resources:

• Notes

Things you should be able to do after today:

• Find the reciprocal of a fraction
• Change a division question into a multiplication question using reciprocals
• Divide using fractions

Assignment

• Worksheet
• p227 #7-11, 13, 15, 17, 20 *23

Attachments:

File	Description	File size
8.6.5.dividing.ws.pdf		192 kB
8.6.5.notes.pdf		532 kB

8.6.6 Applications of Fraction Operations

Fractions are just like regular numbers (decimals and whole numbers), so order of operations also applies when mixing operations with fractions. You need to remember the rules for BEDMAS, but also take special care when doing BEDMAS with fractions, because the rules for multiplying, dividing, adding and subtracting with fractions are sometimes different.

Some things you want to remember:

• changing all of your mixed numbers to improper fractions is a good idea (because any multiplying or dividing will require improper fractions anyways)
• adding and subtracting fractions requires common denominators, multiplying and dividing do not
• cross reducing may only be done when multiplying fractions
• dividing by a fraction can be changed into multiplying by a reciprocal

Resources:

• Notes

Assingment:

• p234 #4-8, 1-12 *15
• Sea Monster worksheet

Attachments:

File	Description	File size
8.6.6.notes.pdf		862 kB

8.6.7 Fraction Operations Review

Things you need to know how to do in this chapter:

1. How to add/subtract fractions (for the BEDMAS section)
2. How to make fractions to lowest terms
3. How to convert improper fractions and mixed numbers
4. How to multiply fractions
   • With whole numbers
   • Cross reducing
   • With Improper Fractions and mixed numbers
5. How to divide fractions
   • With whole numbers
   • With improper fractions and mixed numbers
6. Order of Operations (BEDMAS)
7. Mixed operations
   • How to show one step per line!
   • How to write an equation from a word problem
8. Solve problems involving “time and a half”

Assignment:

• Practice p236 #1-10, 13-17, 19-22, 24, 26