please explaing reversing the digits. Find the product of 2 two digit numbers and reverse the digits and find the product. The products are the same. Does this happen with any pair of two-digit numbers? Eplain your thinking in solving this problem and include any mathematical work. Thank-you.
xy * wz = (10x + y)(10w+z)
=100xw+10xz+10yw+yz
yx * zw = (10y+x)(10z+w)
=100yz+10yw+10xz+xw
These can be the same but not usually
eg
12*21
Thank-you Damon
To solve this problem, let's break it down step by step:
Step 1: Choose two two-digit numbers
Let's say the first number is xy, where x represents the tens digit and y represents the ones digit. The second number can be represented as uv, with u as the tens digit and v as the ones digit.
Step 2: Find the product of the two numbers
Multiply the two numbers xy and uv together:
xy * uv = xyzv
Step 3: Reverse the digits of the product
To reverse the digits, we need to swap the positions of the ones and thousands digits and the tens and hundreds digits. So the reversed product, let's call it a, would be:
a = zvxy
Step 4: Find the product of the reversed digits
Multiply the reversed digits together:
zv * xy = zvxy
Step 5: Compare the products
If the product (xyzv) and the product of the reversed digits (zvxy) are the same, it means that reversing the digits and finding the product results in the same value.
Now, let's prove whether this happens with any pair of two-digit numbers using an example:
Let's take xy = 34 and uv = 45:
Step 1: Choose two two-digit numbers
xy = 34, uv = 45
Step 2: Find the product of the two numbers
xy * uv = 34 * 45 = 1530
Step 3: Reverse the digits of the product
Reversing the digits gives us: a = 0531
Step 4: Find the product of the reversed digits
zv * xy = 53 * 41 = 2173
Step 5: Compare the products
1530 and 2173 are not the same, so in this case, reversing the digits and finding the product does not result in the same value.
To find out if this happens with any pair of two-digit numbers, we need to test more examples. By trying different combinations, you'll find that there are some cases where the products are the same when you reverse the digits, and there are other cases where they are not the same.
Here's an example where the products are the same:
xy = 12 and uv = 21
12 * 21 = 252
Reversed product: 252
So, the answer to the question "Does this happen with any pair of two-digit numbers?" is no. It only happens in certain cases, as shown in the example above.