Math Help - Help with basic explanation

1. Help with basic explanation

Hey guys, I'm really bad at maths and have to take this bridging course as I need to do one subject for my degree for the maths aspect of it. Was just wondering if anyone can help me or show me where I can get some help..

I know the answers the these, I just can't articulate it and provide proper examples, so frustrating! Here they are...

Explain in your own words why brackets need to have the highest precedence amongst all mathematical operators

Explain in your own words using everyday examples and diagrams:
a. Why adding a negative number is the same as subtracting a positive number of the same size.
b. Why subtracting a negative number is the same as adding a positive number of the same size.
c. Why multiplying a negative number by a positive number gives you a positive answer.
d. Why multiplying a negative number by a negative number gives a positive answer.
e. Why it is not possible to take the square root of a negative number.

2. Originally Posted by mathsilliterate
e. Why it is not possible to take the square root of a negative number.
Well consider $\sqrt{36} = -6$ and $6$

Why? because $-6\times -6 = 36$ and $6\times 6 = 36$ . As you need to find a number that multiplies by itself to make $36$

So for $\sqrt{-36}$ We need two numbers that are the same that multiply to give $-36$ . But because $-36$ is negative we can never find this number, as two numbers that mulitply to get a negative answer, one must be positive and the other neagtive, therefore never the same.

3. Originally Posted by pickslides
post
Awesome man! Thanks a lot and that actually makes sense to me. This is what I got for the others:

Explain in your own words why brackets need to have the highest precedence amongst all mathematical operators.

According to the BIDMAS rule, brackets must be done first in the instance that a certain combination of numbers need to be calculated before others - in order to get the desired answer. For example:

5 + 3 x 8 = 29

Brackets are not needed on that occasion. But when an answer needs to be calculated against this:

8 x (3 + 5) = 64

Numbers are being calculated in different orders to get the "desired" answer.

Do you guys think that's an ok answer?

4. Originally Posted by mathsilliterate
Explain in your own words why brackets need to have the highest precedence amongst all mathematical operators
Hmm, how would you explain this in words? To avoid confusion, perhaps? The PEMDAS order of operations is more of a convention than anything else, it is just a way to ensure that when faced with some sort of arithmetical computation, everyone will work it out the same way and get to the same answer. Brackets indicate what should be computed first, and so that takes precedence.

d. Why multiplying a negative number by a negative number gives a positive answer.
Based on the way the questions are phrased, it doesn't seem like rigorous proofs are required. Maybe example proofs can work though. So you can provide an example and give your reasoning in one shot. For example, for the above problem, see: Multiplying integers

They show that negative * negative = positive by using an example, -2 * -5 = 10.

A similar technique can be used to answer part (c)

5. Originally Posted by mathsilliterate
Awesome man! Thanks a lot and that actually makes sense to me. This is what I got for the others:

Explain in your own words why brackets need to have the highest precedence amongst all mathematical operators.

According to the BIDMAS rule, brackets must be done first in the instance that a certain combination of numbers need to be calculated before others - in order to get the desired answer. For example:

5 + 3 x 8 = 29

Brackets are not needed on that occasion. But when an answer needs to be calculated against this:

8 x (3 + 5) = 64

Numbers are being calculated in different orders to get the "desired" answer.

Do you guys think that's an ok answer?
it seems to be an ok answer here.

6. Originally Posted by mathsilliterate
Explain in your own words using everyday examples and diagrams:
a. Why adding a negative number is the same as subtracting a positive number of the same size.
b. Why subtracting a negative number is the same as adding a positive number of the same size.
for these, along with examples, i think you can use the number line to help you explain. remember, we think of adding positive numbers as moving to the right on the number line, subtracting positive numbers amounts to moving to the left.