1. STRUCTURES IThursday, 11/8/2012Methods of MultiplicationView this presentation as a slide show so you hear the narration as well.You will need to click to advance the slides. On some slides, you will need to click to bring up parts of the presentation on that slide. 2. Remember The Array ModelUse an array model to multiply 17X5350 3 The product is the sum of the pieces 10 500 500+350+30+21 30 850+30+21 880+21 901 735021 3. Traditional MethodMultiply 17 X 53 using the traditional method. 53 17 371 7X3=21, 7X5=35, 35+2=37 530 10X53=530 901 4. Connecting the Traditional Method to the Array ModelNote the sum of the rows. 503 10500 30 530 7 350 21 371 5. Try It AgainDo Both Array and Traditional Before Clicking Forward 19X28 Traditional20828 X19 Sum of25210 Rows28020080 532 2809252 18072 6. Partial ProductsMultiply 17 X 53 using the partial productsmethod. 53x17500 10x50 30 10x3350 7x50 21 7x3901Note: It is the array method without the array! 7. Using the Partial Products MethodTry 19x28 using the partial products method.Click to see the process when you have finished.28X 192008018072532 8. Partial Product Connections Note that the partial product method is anextension of the distributive property! 17x53=(10+7)x(50+3)=10x50+10x3+7x50+7x3 19x28=(10+9)x(20+8)=10x20+10x8+9x20+9x8 9. Lattice MethodNamed for the lattice look to the model17x531. Draw an array based on the number of digits in the numbers (2 by 2 in this case)2. Draw diagonal lines to create the lattice3. Multiply the digits putting the tens above the line and the units below the line4. Add down the diagonals5. The answer is read from top left to bottom right5 35 3 0 0 1 1 0 1 5 3 7 3 2 7 9 5 1 0 1 10. Using LatticeTry 19x28 using the lattice method. Click to see the process when you havefinished. 2 8 0 0 2 01 28 1 79 5 82 3 2 11. Try The Following Using Array, PartialProduct and Lattice. Check using yournormal method.1. 24 x 252. 46 x 843. 55 x 98 12. A Discovery Activity Use your calculator to complete the tableNumber 1 Number 2Product of the Two Numbers245126 3087024.5 1.2630.87024.5 12.6308.702.45 1.263.0870.245 126 30.87024.5 .1263.0870 What do you notice about the digits in theanswers? 13. Placing the Decimal We probably all remember what we were taught;count the total number of decimal places andensure that number of places are in the answer.But why does it work? Start with 245x126=30870. 2.45x1.26 moveseach number two places to the left, so move fourplaces to the left in the answer. 24.5x1.26 movesone place in 245 and two places in 126, so movethree places in the answer. Looking at it mathematically, 2.45=245x10-2 and1.26=126x10-2. 245x10-2x126x10-2=30870x10-4. 14. Placing the Decimal by Estimation Compare the Estimate and Where the Decimalis Placed Number 1 Number 2 EstimateProduct 24512630870 24.5 1.26 24x1=24 30.870 24.5 12.6 25x12=300 308.70 2.45 1.26 2x1=2 3.0870 .245 126.2x100=20 30.870 24.5 .126 24x.1=2.4 3.0870 15. Practice Given the information, place the decimal byestimation. If 12x55=660, what estimation would you use toplace the decimal for 1.2x5.5. If 26x37=962, what estimation would you use toplace the decimal for 26x3.7. If 87x932=81084, what estimations would youuse for 8.7x93.2 8.7x9.32 .87x93.2 16. Using the Array for MultiplyingFractions 2 3 Consider 3 4Start with a 1x1 rectangleDivide one side into thirdsDivide the other side into fourthsTake two-thirds and three-quarters and surround them with a rectangleThe rectangle has 6 pieces out of a total of twelve, 6/12 or .1 1 1 14 4 4 4131313 17. Practice Use an array to illustrate the followingproducts2 32 35 55 82 3 4 33 5 5 8 Looking at your arrays and the answers, what rule could you give so you dont need to draw arrays all the time. 18. A Exploration Complete each and look for a relationship 2 3 3 2 5 8 5 8 2 33 2 3 53 5 4 33 4 5 85 8What relationship do you see?How might it help you? 19. Multiplying Fractions The arrays should have illustrated that the totalnumber of pieces is the product of the denominatorsand the number in the rectangle is the product of thenumerators. So, to multiply fractions, you multiply thenumerators and multiply the denominators. In the exploration, you should have seen that thenumerators (or the denominators) could be switchedand still yield the same result. Therefore, you might beable to use this concept to simplify the problem beforemultiplying. For example, seeing 2/3x3/5 was thesame as 3/3x2/5 makes it 1x2/5 or 2/5. 20. Using an Array to Multiply Mixed Numbers Consider 8 25 5 4382/5Answer=48 3/10 5 402 3/4 6 3/10 21. Practice Use an array to find the following products:342 95 3 2379 69 1312 6 15 8