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Multiplying Fractions and Mixed Numbers Unit 5.8 Pages 254-257 Warm Up Problems Write each fraction in simplest form. 1. 1 3 1 2 x = 1/6 2. 4 5 3 8 3/10 3. 3 11 x 2 = 6/11 4. 3 8 5 8 x = x = 15/64 Solving for Multiplication using Mixed Numbers Objective: Students will be able to multiply mixed numbers together by changing them into improper fractions, finding their product, and then convert it back to a mixed number. CHALLENGE! I will hand each partner pair 2 whole circles and ¼ of a circle. Your challenge is to find ½ of the total circles given to you. How did you find the answer? Write down each step you used to find the answer and model the steps you wrote using the circles. We can paper fold to find how to Multiply mixed numbers: The reason our answer is less To find 1/2 x 1 ½ fold two sheets in than the beginning half vertically to show 1 Mixed ½. number is the because to show ½ of 1 ½ wewe foldare both sheets in half horizontally. multiplying that number by another number is justthat a if we label each foldthat we make, of¾a total whole. showspiece we have squares. We multiply Mixed Numbers together by getting rid of the whole first, multiplying the numbers together, and then putting them all back together again. Marie and Matt are sharing a large Pizza. Marie cuts the pizza in half. Matt knows he can’t eat his half of the pizza, so he cuts it into fourths and eats one piece. What is the fraction of the whole pizza that Matt did not eat? Write and equation and solve for this question: 7/8 of the pizza Find the Product, and simplify it. Change mixed numbers to improper fractions Now find the product Reduce or change from improper to proper fractions. 1 x 3 1 x 3 1 1 2 1 12 1 2 1 x 3 = 3 3 2 6 1 x 3 = 3 3 2 6 (1 x 3) (2 x 3) 1 2 Find the Product, and simplify it. Change mixed numbers to improper fractions Simplify 1st (if possible) and find the product Reduce or change from improper to proper fractions. 1 x 2 15 3 1 x 2 15 3 6 x 2 = 5 3 4 = 5 4 5 1 x 14 Find the Product, and simplify it. NOW YOU TRY 1 13 Change mixed numbers to improper fractions 1 x 14 1 13 Simplify 1st (if possible) and find the product x = Reduce or change from improper to proper fractions. = 1 2 3 1 x 4 Find the Product, and simplify it. NOW YOU TRY Change mixed numbers to improper fractions Simplify 1st (if possible) and find the product Reduce or change from improper to proper fractions. 1 x 4 x = 1 13 1 13 = 1 3 12 x 13 Find the Product, and simplify it. NOW YOU TRY Change mixed numbers to improper fractions Simplify 1st (if possible) and find the product Reduce or change from improper to proper fractions. 12 x 13 2 x = = 5 226 3 28 3 8 When we have a number that multiplies a mixed number by a whole, we can use the Distributive Property. That means you can multiply each separate addend and still get the same number. x 5 3 2 11 Find the Product, and simplify it. Use the Distributive Property to solve. Separate into parts and wholes by adding brackets. Use the distributive property Add the wholes and parts back together, then reduce. x 5 x 5 3 5 3 15 x 2 11 10 = + 11 2 3 11 2 11 5 x 3 = 15 5 x 2 = 10 1 11 11 10 15 11 Find the Product, and simplify it. Use the Distributive Property to solve. Separate into parts and wholes by adding brackets. Use the distributive property Add the wholes and parts back together, then reduce. x 5 x 5 4 5 4 20 x 7 10 7 4 10 7 10 5 x 4 = 20 5 x 7 = 35 1 10 10 35 = + 10 4 85 Find the Product, and simplify it. Use the Distributive Property to solve. Separate into parts and wholes by adding brackets. Use the distributive property Add the wholes and parts back together, then reduce. x 2 2 1 2 1 3 x x 3 5 6 = + 5 3 15 3 5 2x1=3 2x 3= 6 1 5 5 1 45 Find the Product, and simplify it. Use the Distributive Property to solve. Separate into parts and wholes by adding brackets. Use the distributive property Add the wholes and parts back together, then reduce. x + 3 x x 3 2 __ = 2 23 2 3 8 A patient was given 3 ½ tablets of medicine. If each tablet contains 1/20 grains each of medicine, how much grains of medicine did the patient receive? = 1/20 g = 1/20 g = 1/20 g = ½ of 1/20 g 7/40 grains of medicine Homework 5.8 page 256 Due: Friday 13-24 42 (14 questions)