Draw conclusions for the following statements. 44 x 5 = 55 x 4 77 x 3 = 33 x 7 2...

Questions

September 2022 1 2 Report

Draw conclusions for the following statements.
44 x 5 = 55 x 4
77 x 3 = 33 x 7
22 x 9 = 99 x 2
66 x 8 = 88 x 6
______ = _______
______ = _______

Answers & Comments

shaheendandy

Answer:

110 × 16 = 176 × 10
11 × 11 = 121 × 1

Before I jump to the explanation, I just want to say that this is very hard to crack. My answer might be overdue to be valid or wrong but here is the explanation. I hope this helps you.

Explanation:

So what I noticed at first is that the expression, say 44 × 5, will be reversed and the multiplicand will be doubled and the multiplier will be deducted by one digit. And it goes on and on. Seems pretty easy to solve right?

Until you realized what numbers are you going to put on the blanks.

But I noticed something. If you take a closer look at the expressions on the left of the equal signs, you'll see that each expression when subtracted in a way that > - < (big number - small number), the difference will be the number on the top-right of the previous expression. This also applies to the expressions on the right of the equal sign, but in reverse (I'll talk about that later). To show you what I mean:

77 x 3 = 33 x 7

22 x 9 = 99 x 2

Did you notice? Removing one digit of 99 is 9 which will be 9 - 2 = 7. The same goes to the opposite side.

Also, numbers on the left of the the expressions are always multiplied by 11. When it comes to the expressions on the right, reverse the equation and deduct one digit to the big number and multipy the number on the left of the expression by 11. When you do the math, the expressions on the left of the equal sign need to have the same product as the expression on it's right side. I hope you get what I mean. To illustrate:

77 x 3 = 33 x 7 (The 7 on the left expression and the 3 on the right expression is multipied by 11 as they are on the left of their respective expressions)
The expression on the left: 77 x 3 = 231
The expression on the left: 33 x 77 = 231

So now, what I did is I find two numbers that when subtracted it becomes six. But I also kept in mind that I can't use the same numbers given and that's why for this reason I chose 10 and 16, 11 and 1. To conclude: