Transcript multiplying and dividing fractions

Multiplying and
Dividing
Fractions
Your Focus
GPS Standard: M6N1. Students will understand the meaning
of the four arithmetic operations as related to positive rational
numbers and will use these concepts to solve problems.
e. Multiply and divide fractions and mixed numbers.
EU: Products may be larger, smaller, or equal to their factors.
EQ: When does multiplying produce a product smaller than the
factors?
Vocabulary: fraction, numerator, denominator, product
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
Of = Multiply
• When we see the word “of” in a problem involving
fractions, it means we need to multiply. Here is an
example:
– There are 8 cars in Michael’s toy collection. 1/2
of the cars are red. How many red cars does
Michael have?
• This problem is asking “What is 1/2 of 8?”
• A way to answer it is to put a multiplication sign in
place of “of.” You then get 1/2 x 8
Multiplying Fractions
• When multiplying fractions, they do NOT need to have a
common denominator.
• Option 1:
1. Multiply numerators
2. Multiply denominators
3. Simplify
• Option 2:
1. Cross cancel
2. Multiply numerators
3. Multiply denominators
4. Simplify
Multiplying Fractions by Whole
Numbers
Step 1: Make the whole number into a fraction
with a denominator of 1.
Step 2: Cross cancel or multiply across
Step 3: Simplify
Multiplying Fractions by Mixed Numbers
Step 1: Change mixed numbers into improper
fractions
Step 2: Cross-Cancel or Multiply as before
Step 3: Simplify
Dividing Fractions
• When dividing fractions, they do NOT need to
have a common denominator.
• To divide two fractions, change the operation to
multiply and take the reciprocal of the second
fraction (flip the second fraction). KeepChange-Change.
Change Operation.
2 9 2 2
  
5 2 5 9
Flip 2nd Fraction.
Dividing Fractions
• Finish the problem by following the rules for
multiplying fractions.
2 9 2 2
4
   
5 2 5 9 45