Question

1. # Holly Finds That (11M – 13N + 6Mn) – (10M – 7N + 3Mn) = M – 20N + 9Mn. What Error Did Holly Make?

The process of doing math is something that many of us are accustomed to. We may not think twice about it since we’re used to having the answers given to us directly, or using a calculator to assist us. But for some, like Holly here, math can be confusing and errors can easily be made. In this blog post, we will explore the equation Holly came up with and pinpoint the error she made in her work. We’ll go through the steps she took that led to the error, as well as discuss ways to prevent similar mistakes in the future.

## What is the difference between (11M – 13N + 6Mn) and (10M – 7N + 3Mn)?

There are a few things going on in this math problem, so let’s break it down. 11M – 13N + 6Mn is equal to M – N + Mn. This is because 11M and 6Mn cancel each other out, leaving just M – N + Mn. 10M – 7N + 3Mn is also equal to M – N + Mn for the same reason. So, when you subtract one from the other, you’re left with just M – N + Mn on both sides of the equation, which cancels out and leaves you with 0 = 0. Holly made the error of not realizing that 11M and 6Mn cancel each other out, as do 10M and 3Mn.

## How do you solve for M in this equation?

To solve for M in this equation, you need to first simplify the equation. Holly made an error in her equation by not simplifying it first. The correct equation is:

(M – N + Mn) – (M – N + Mn) = M – N + Mn

This can be simplified to:

2(M – N + Mn) = M – N + Mn

And then further simplified to:

2M – 2N + 2Mn = M – N + Mn

From here, you can solve for M by isolating it on one side of the equation. This can be done by adding N to both sides and then subtracting Mn from both sides. This results in the following equation:

2M = 3N

## How do you solve for N in this equation?

In order to solve for N in this equation, one must first understand the distributive property. The distributive property states that for any real numbers a, b, and c, a(b + c) = ab + ac. In other words, the term “a” can be distributed across the terms “b+c”. This is important to note because it is easy to make the mistake of thinking that the entire parentheses can be cancelled out.

For example, in the equation (M – N + Mn) – (M – N + Mn), one might think that because there are two sets of parentheses with identical terms, they cancel each other out and all that is left is M – N + Mn. However, this is not the case. In order to use the distributive property and solve for N, we must first distribute the “-1” across the terms in the second set of parentheses. This gives us:

(M – N + Mn) – (M – N + Mn) = (M – N + Mn) – M + N – Mn

Now we can see that there are three instances of “M-N” which cancel each other out, leaving us with just “Mn”. Therefore, solving for N in this equation simply requires us to divide both sides by “m”, giving us:

N = Mn / m

## What error did Holly make in this equation?

When Holly was solving this equation, she made the error of not distributing the parentheses correctly. She should have distributed the parentheses like this: (M – N + Mn) – (M – N + Mn) = M – N + Mn. By not distributing the parentheses correctly, Holly made the error of getting M – N + Mn on both sides of the equation, which is not equal to M – N + Mn.

## Conclusion

In conclusion, Holly made an error in her calculation by not accounting for the negatives when subtracting two terms. Had she done so, she would have realized that the equation should equal M + 4N + 9Mn instead of M – 20N + 9Mn. That small mistake could have been easily corrected with a bit more attention to detail and an understanding of how negatives interact mathematically with each other. With practice and patience, anyone can become proficient in math!

2. Hey everyone, this is Holly! Today I was working on a math problem and I thought I had it all figured out — until I checked to make sure I got the right answer.

I was trying to solve a problem that went like this:

(11M – 13N + 6Mn) – (10M – 7N + 3Mn) = M – 20N + 9Mn.

I came up with the answer M – 20N + 3Mn, but when I checked it, I found out that I was wrong!

What was the error that I made?

Well, it turns out that I made a simple mistake in the way I distributed the negative sign.

Basically, when I subtracted the second part of the equation from the first part of the equation, I forgot to distribute the negative sign to both the M and the N terms.

So, in the end, my answer should have been M – 20N + 9Mn!

I learned a valuable lesson today: always check your work!