2.3 Multiplying and Dividing Fractions 1 Next, multiply
numerator by numerator and denominator by denominator. Cross
Reducing is the necessary step in multiplying fractions where you
look to see if any number in any numerator will reduce with any
number in any denominator. Cross Reducing and Multiplying Example
1a. Will any number in any numerator reduce with any number in any
denominator? Answer: 9 and 15 will reduce by 3. Divide 3 into both
these numbers, cross the numbers out and write the result next to
each number. 3 5 Next, multiply numerator by numerator and
denominator by denominator. Will any number in any numerator reduce
with any number in any denominator? Answer: 15 and 25 will reduce
by 5. Divide 5 into both these numbers, cross the numbers out and
write the result next to each number. 3 5 Example 1b. 3 4 12 and 16
will reduce by 4 Divide 4 into both these numbers, cross the
numbers out and write the result next to each number.
Slide 2
2.3 Multiplying and Dividing Fractions 2 Prime Factorization
Method for Multiplying Fractions Some students prefer the prime
factorization method because it is more procedural. You dont have
to be thinking what number divides evenly into these two numbers?
Procedure: To Multiply Fractions using Prime Factorization 1.
Rewrite the fraction using the prime factorizations. 2.Reduce the
common factors. (line out one on top with one on the bottom).
3.Multiply the remaining factors. Step 1. Rewrite using the prime
factorization of each number. Step 2. Reduce the common factors.
(line out one on top with one on the bottom). Line out a 7 on top
with a 7 on the bottom, a 5 on top with a 5 on the bottom, and two
3s on top with two 3s on the bottom. Step 3. Multiply the remaining
factors. Your Turn Problem #1 Multiply the following: Answer
Slide 3
2.3 Multiplying and Dividing Fractions 3 Step 1. Rewrite using
the whole number as a fraction. Multiplying a Fraction by a Whole
Number When multiplying a fraction and a whole number, write the
whole number as a fraction by writing it with a denominator of 1.
Step 2. Reduce and multiply using either method. Your Turn Problem
#2 Answer
Slide 4
2.3 Multiplying and Dividing Fractions 4 Multiplying Mixed
Numbers If one or more of the fractions are mixed numbers, convert
them to improper fractions. Reduce and multiply. Then convert the
answer back into a mixed number. Step 1. Rewrite any mixed numbers
as improper fractions. Step 2. Reduce and multiply using either
method. Your Turn Problem #3 Answer 5 2 3 1
Slide 5
2.3 Multiplying and Dividing Fractions 5 Multiplying With More
Than Two Fractions or Mixed Numbers If one or more of the fractions
are mixed numbers, convert them to improper fractions. Reduce any
numerator with any denominator and multiply. Convert answer into a
mixed number if possible. Step 1. No mixed numbers to rewrite. Step
2. Reduce. Your Turn Problem #4 Answer 1 2 5 9 8 divides into 8 and
16. 3 divides into 15 and 27. 3 divides into 3 and 9. 1 3 5 divides
into 5 and 5. 1 1 Step 3. Multiply. Prime Factorization Method:
Find the prime factorization of each number. Reduce the common
factors and multiply. (Note: there are 1s next to all the factors
lined out. The six is in the denominator, not the numerator.)
Slide 6
2.3 Multiplying and Dividing Fractions 6 Product and the word
of: To find the product of two fractions, rewrite the fractions in
the same order as presented In the sentence and place a
multiplication sign in between; cross reduce, if possible, then
multiply numerator by numerator and denominator by denominator.
Product translates to multiplication. of translates to
multiplication if a fraction precedes it. Reduce and Multiply. 1 3
Answer Your Turn Problem #5
Slide 7
2.3 Multiplying and Dividing Fractions 7 Word Problems
involving fractions and multiplication. Recall the formula for Area
of a rectangle: A = L W. It doesnt matter if the numbers are
fractions or whole numbers. Example 6. Find the area of a rectangle
if the length is 2 ft. and the width is 1 ft. Solution: Using the
formula, multiply the length and width. Your Turn Problem #6
Answer
Slide 8
2.3 Multiplying and Dividing Fractions 8 Your Turn Problem #7
Four-fifteenths of Loris monthly check goes to rent. If her monthly
check is $3000, how much is her rent? Answer Answer: 8 students
dropped. Reciprocals If the product of two numbers is 1, we say
that they are reciprocals of each other. To find a reciprocal of a
fraction, interchange the numerator and denominator. Examples:
Fraction Reciprocal Note: Zero has no reciprocal.
Slide 9
2.3 Multiplying and Dividing Fractions 9 Division of Fractions
Procedure: Dividing a fraction by another fraction. Step 1. Change
any mixed numbers to improper fractions. Step 2. Rewrite the
problem changing the division sign to a multiplication sign and
inverting any fraction that originally followed a division sign
into its reciprocal. Step 3. Follow the procedures of multiplying
fractions--cross reduce if possible and multiply numerator by
numerator and denominator by denominator. Step 1. No mixed numbers
to change to improper fractions. Step 2. Rewrite the problem.
Change the division sign to a multiplication sign and invert the
second fraction into its reciprocal. Step 3. Reduce and Multiply. 5
72 3 Answer Your Turn Problem #8
Slide 10
2.3 Multiplying and Dividing Fractions 10 Step 1. Change mixed
numbers to improper fractions. Step 2. Rewrite the problem. Change
the division sign to a multiplication sign and invert the second
fraction into its reciprocal. Step 3. Reduce and Multiply. 2 11 2
Answer Your Turn Problem #9
Slide 11
2.3 Multiplying and Dividing Fractions 11 Step 1. Change mixed
numbers to improper fractions. Step 2. Rewrite the problem. Change
the division sign to a multiplication sign and invert the second
fraction into its reciprocal. Step 3. Reduce and Multiply. 3 1
Answer Your Turn Problem #10
Slide 12
2.3 Multiplying and Dividing Fractions 12 Example 11. A certain
size bottle holds exactly 2/3 pints of liquid. How many of these
bottles can be filled from a 12-pint container? Division is an
operation where an amount is being divided into groups. For
example, if you have $20 to divide among 4 people, how much would
each person get? Answer: $20 4 = $5. Note: Division is not
commutative. 20 4 is not the same as 4 20. Unlike multiplication,
order does matter with division. The total must be written 1 st.
Solution: This is a division problem because a quantity is being
separated into groups. Remember to write the total quantity 1 st.
Change to multiplication, reduce and multiply. Answer: 18 bottles A
15 ft pipe must be cut into pieces 1 ft long. How many 1 ft pieces
of pipe can be obtained? Your Turn Problem #11 The End. B.R.
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