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Multiplication with Arrays and Boxes – A Visual Model How do you solve 17x34 using an array? The goal is to make easier problems that can be solved without a calculator. 34 17 Split the array at the place value. For example, 17 and 34 are split into 10 and 7 and 30 and 4. 30 10 34 4 10 x 30 = 300 10x4=40 7 x 30 = 210 7x4=28 17 7 Find the product of each new array. (These are much easier problems) Finally, add up the products. 10 x 30 = 300 7 x 30 = 210 10x4=40 7x4=28 300 210 40 +28 578 17 x 34 = 578 How do you solve 26 x 49 using a box? (that would be too many dots to draw) First, draw a rectangular box. Treat this box like a 26 x 49 array. 26 rows, 49 in each row. Split those numbers at the place value. 49 40 9 20 20 x 40 = 800 20x9=180 6 6 x 40 = 240 6x9=54 26 Find the product of each new “imaginary” array. (These are much easier problems) Finally, add up the products just like you did with the array. 800 240 20 x 40 = 800 180 20x9= 180 +54 6 x 40 = 240 1,274 6x9= 54 26 x 49 = 1,274 Try these problems for practice. If you need help, look back at the previous slides. • • • • • • • 17 x 25 28 x 31 39 x 23 47 x 72 56 x 17 49 x 85 99 x 99