Multiplication with Arrays and Boxes

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 Split the array at the place value. For example, 17 is split into 10 and 7. Find the product of each new array. (These are much easier problems) 34 4 30 10x4=40 10 x 30 = 300 10 17 7 7x4=28 7 x 30 = 210

Finally, add up the products. 300 210 40 +28 10x4=40 10 x 30 = 300 578 7x4=28 7 x 30 = 210 17 x 34 = 578

How do you solve 26 x 49 using a box 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. Find the product of each new “imaginary” array. (These are much easier problems) 40 49 9 20x9=180 20 x 40 = 800 26 20 6 6x9=54 6 x 40 = 240

Finally, add up the products just like you did with the array. 800 240 180 +54 20x9= 180 20 x 40 = 800 1,274 6x9= 54 6 x 40 = 240 26 x 49 = 1,274

Try these problems for practice 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