Multiplying With Fractions Lesson 5-1

Just Follow These Easy Steps! Multiply the numerators and write down the answer as your new numerator. Multiply the denominators and write down the answer as your new denominator. Simplify.

Example 1 5 3 15 x = 32 8 4 There are no common factors for 15 and 32, so this fraction cannot be simplified.

Example 2 3 2 6 1 x = = 9 36 6 4 This fraction can be reduced. Divide the numerator and denominator by the GCF, which is 6.

A Quick Review: KEY POINT when multiplying fractions: ☼☼ Change a mixed number into an improper fraction, Still simplify your answer.

More on Multiplying Fractions: The word “of” in a problem usually means 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 or 8 x ½ (remember that multiplication is commutative).

Multiplication Continued: What operation will I use for 2/3 of 15? It means 2/3 x 15 It could mean anything. It is helpful if you think of a situation such as: Mike ate 2/3 of 15 cookies. Susie took 2/3 of her 15 marbles to school. The dog ran 2/3 of its 15 laps around the yard.

Multiplying Fractions: Multiplying fractions is easier than adding or subtraction because you don’t need to find common denominators. YAY!!!!!! Just multiply straight across. Multiply numerators together. Then, multiply denominators together.

Multiplying by a Whole Number If you want to multiply a fraction by a whole number, turn your whole number into a fraction by placing a 1 as the denominator. If your answer is improper, divide the bottom into the top. 4 20 80 16 x = = 5 5 1

Another Example 15 1 5 15 x = = 1 6 6 2 15 and 6 have a GCF of 3. Five halves is improper, so we divide the bottom into the top. 2 2 5 4 2 1 2 1

Simplifying Factors Before you multiply, you can make the problem simpler. You can find the GCF of any numerator and denominator. Find a factor that equally divides the top number and bottom number, divide, and rewrite the problem.

Example 1 In the second fraction, 8 and 16 have a GCF of 8. 5 8 1 x 16 2 7 8 ÷ 8 = 1 and 16 ÷ 8 = 2 Now, multiply with the simpler numbers. 5 x 1 = 5 and 7 x 2 = 14. 5 14

Example 2 The top of the first fraction and the bottom of the second fraction have a common factor. The GCF of 2 and 12 is 2. 1 2 5 x 6 12 3 2 ÷ 2 = 1, and 12 ÷ 2 = 6. Now, multiply: 5 18

Multiplying Mixed Numbers Rename the mixed numbers as improper fractions. Multiply the fractions, then simplify. 19 1 4 76 9 1 4 4 9 x 8 x = 1 1 19 9 1 19 2 = x = 9 9

Try some Change any whole or mixed numbers to improper. Multiply straight across. Simplify answers Try some

Answers Change any whole or mixed numbers to improper. Multiply straight across. Simplify answers Answers

Reduce before you multiply Cancelling Reduce before you multiply

Canceling Reducing before mutiplying is called canceling. ICK! Instead think the following in your head.

Canceling on paper Rules: One factor from any numerator cancels with like factor from the denominator.

Try one Say “--- goes into ____ this many times.” As you cross each number out and write what is left after canceling above the number.

Answer Say “--- goes into ____ this many times.” As you cross each number out and write what is left after canceling above the number.

Try one more Make whole and mixed numbers improper Cancel if you can Multiply Numerators and denominators straight across. Simplify

Let’s Practice!