**Question:** Use the grid method to work out the following:

𝑎) 433 ×21

𝑏) 223×44

𝑐) 567 ×123

a) To do the grid method, we construct a grid with 400, 30, and 3 across the top and 20 and 1 down the side. Then, we fill in the gaps in the grid by multiplying each component of 433 by each component of 21. This looks like:

Now, we have to add the numbers inside the grid (shown in red) using whichever method you prefer. Adding along the rows, we get

8,000+600+60=8,660

400+30+3=433

Therefore, the final answer is

8,660+433=9,093

b) To do the grid method, we construct a grid with 200, 20, and 3 across the top and 40 and 4 down the side. Then, we fill in the gaps in the grid by multiplying each component of 223 by each component of 44. This looks like:

Now, we have to add the numbers inside the grid (shown in red) using whichever method you prefer. Adding along the rows, we get

8,000+800+120=8,920

800+80+12=892

Therefore, the final answer is

8,920+892=9,812

c) To do the grid method, we construct a grid with 500, 60, and 7 across the top and 100, 20, and 3 down the side. Then, we fill in the gaps in the grid by multiplying each component of 567 by each component of 123. This looks like:

Now, we have to add the numbers inside the grid (shown in red) using whichever method you prefer. Adding along the rows, we get

50,000+6,000+700=56,700

10,000+1200+140=11,340

1,500+180+21=1,701

Therefore, the final answer is

56,700+11,340+1,701=69,741