The document discusses how to multiply a mixed number by a fraction. It explains that the product will be less than the original mixed number if the fraction is between 0 and 1. It provides a visual example of multiplying 11⁄4 by 1⁄2 to get 5/8. It then outlines the step-by-step process for multiplying a mixed number by a fraction, which involves changing the mixed number to an improper fraction, multiplying the numerators and denominators, and simplifying the final fraction if needed. It concludes by working through some examples.

1. Fractions XV Multiplication of Fractions with Mixed Numbers by Monica Yuskaitis

2. Times You Would Multiply a Mixed Number Times a Fraction In a car race, the track is 2 ¼ miles long. If the car breaks down ½ way through the course, how far did you go? 1/2 of 2 1/4 or 1/2 x 2 1/4

3. Multiplying Fractions Conceptual Understanding When you multiply a positive mixed number by a fraction between 0 and 1 the product is less than the mixed number. 1¼ x ½ = 5/8 Look at the diagram on the next slide to understand why.

4. Multiplying Fractions Conceptual Understanding ¼ ¼ ¼ ¼ 1/8 1¼ x ½ = 5/8 1/8 1/8 1/8 1/8 ¼ ¼ ¼ ¼

5. How to Find a Fraction of a Mixed Number The first thing to remember is “of” means multiply in mathematics. of = x

6. How to Find a Fraction of a Mixed Number Step 1 - When you see a fraction problem you know when you read “of” in the problem you multiply. of x 1 2 4 9 3

7. How to Find a Fraction of a Mixed Number Step 2 – Change the mixed number to an improper fraction. x 1 2 4 9 3 x + 27 27 + 4 31 9

8. How to Find a Fraction of a Mixed Number Step 3 – Multiply the numerators straight across. x 1 2 31 9 31 =

9. How to Find a Fraction of a Mixed Number Step 4 – Multiply the denominators straight across. x 1 2 31 9 31 = 18

10. How to Find a Fraction of a Mixed Number Step 5 – Simplify your answer. In this case change the improper fraction to a mixed number. x 1 2 31 9 31 = 18 18 ) 31 1 18 13 13 18

11. Multiply and Simplify 1 4 = x 4 7 x 35 35 + 4 5 + 39 7 39 28 28 ) 39 1 11 28

12. Multiply and Simplify 4 7 = x 1 9 x 27 27 + 1 3 + 28 9 112 63 63 ) 112 1 49 63 ÷ ÷ 7 7 = 7 9

13. Multiply and Simplify 4 5 = x 3 4 x 24 24 + 3 6 + 27 4 108 20 20 ) 108 5 8 20 ÷ ÷ 4 4 = 2 5

14. Multiply and Simplify 2 5 = x 1 4 x 24 24 + 1 6 + 25 4 50 20 20 ) 50 2 10 20 ÷ ÷ 10 10 = 1 2 You’re shining!

15. Credits Clipart from “Microsoft Clip Gallery” located on the Internet at http://cgl.microsoft.com/ clipgallerylive/default.asp