Explore the Lesson

C. Grid Multiplication

Investigation

Grid multiplication is a strategy that can be used to multiply multi-digit numbers. Consider the following three examples of grid multiplication.

 4 x 37
 

 95 x 36
 

 83 x 961
 


    1. Explain how grid multiplication works.

    2. What is an advantage of grid multiplication?

  2. State the original factors and the final product represented by each of the three grids. (What was multiplied and what was the result?) Use a calculator, if necessary, to check these values.

  3. Use grid multiplication to determine the following products.

    1. 72 × 9



    2. 63 × 81



  4. The following grid shows how the grid multiplication of can be set up.



    1. Complete the grid by filling in the empty cells. State the product.

    2. Multiply using algebra tiles or the distributive property, and show that the result is the same as the result when using grid multiplication.

With grid multiplication, a series of simpler products and sums are used to determine a more complex product. The following grid multiplication shows 36 × 95 = 3 420.

Notice that there are four individual products and the sum of these four products gives the desired product.

This grid multiplication can also be represented as follows.