1. Cross Reducing and Multiplying
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. 3 5
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.
Next, multiply numerator by numerator and denominator by denominator.
Example 1b. 3 4 3 5
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.
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.
Next, multiply numerator by numerator and denominator by denominator.

2. Prime Factorization Method for Multiplying Fractions
Some students prefer the prime factorization method because it is more procedural. You don’t 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 3’s on top with two 3’s on the bottom.
Step 3. Multiply the remaining factors.
Your Turn Problem #1
Multiply the following:
Answer

3. 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 1. Rewrite using the whole number as a fraction.
Step 2. Reduce and multiply using either method.
Your Turn Problem #2
Answer

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. 3 1 5 2
Your Turn Problem #3
Answer

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. 1 1 3 5 9 1 2
Step 1. No mixed numbers to rewrite.
Step 2. Reduce.
8 divides into 8 and 16.
3 divides into 15 and 27.
3 divides into 3 and 9.
5 divides into 5 and 5.
Step 3. Multiply.
Prime Factorization Method:
Find the prime factorization of each number. Reduce the common factors and multiply.
Your Turn Problem #4
Answer
(Note: there are 1’s next to all the factors lined out. The six is in the denominator, not the numerator.)

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. 1 3
Reduce and Multiply.
Your Turn Problem #5
Answer

7. Word Problems involving fractions and multiplication.
Recall the formula for Area of a rectangle: A = L  W.
It doesn’t matter if the numbers are fractions or whole numbers.
Example 6. Find the area of a rectangle if the length is 2 ½ ft. and the width is 1 ¾ ft.
Solution: Using the formula, multiply the length and width.
Your Turn Problem #6
Answer

8. Answer: 8 student’s dropped.
Your Turn Problem #7
Four-fifteenths of Lori’s monthly check goes to rent. If her monthly check is $3000, how much is her rent?
Answer
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.

9. Procedure: Dividing a fraction by another fraction.
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. 2 3 5 7
Step 3. Reduce and Multiply.
Your Turn Problem #8
Answer

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. 1 2 2 1
Step 3. Reduce and Multiply.
Your Turn Problem #9
Answer

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. 3 1
Step 3. Reduce and Multiply.
Your Turn Problem #10
Answer

12. Division is an operation where an amount is being divided into groups
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 1st.
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?
Solution: This is a division problem because a quantity is being separated into groups.
Remember to write the total quantity 1st.
Change to multiplication, reduce and multiply.
Answer: bottles
A 15 ½ ft pipe must be cut into pieces 1 ¾ ft long. How many 1 ¾ ft pieces of pipe can be obtained?
Your Turn Problem #11
The End.
B.R.