It's difficult to help with this as there isn't enough information to go on.

Is it that you want to know what  $${\frac{{\mathtt{2}}}{{\mathtt{15}}}}$$ of a minute is?

The question I couldn't get right in your previous challenge was x²+x+6, I still can't work this one out. Can you break this one down for me as it's slightly different to the one in your last post.

The next challenge.

1) x²+7x+6

= (x+1)(x+6)

= x²+6x+x+6

= x²+7x+6

2) x²+10x+21

= (x+3)(x+7)

= x²+7x+3x+21

= x²+10x+21

Without sounding too confident, these were fairly easy. You've still got me beat by your x²+x+6.

If I remember correctly, the questions you have given me are called trinomials, and by simplifying them into two brackets, I have factorised them. Are they then called quadratics once I have two sets of brackets with two terms in each? It makes sense in my head, 3 terms in trinomials and 4 terms in quadratics. Is this correct?

convert .182 to a faction?

I will try to demonstrate the method for this with a simpler number, then go onto your question.

If we take the number 1 and divide it by 2 we get half of 1 which is 0.5      $${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

So we can see that as a fraction and a decimal, and we could have probably guessed the answer.

in this we are saying that 0.5 is a fraction of 1, so could be written like this $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

Sadly $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}}$$ is what we call an improper fraction, in that the top number (Numerator) or bottom number (denominator) are not whole numbers.

To convert $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}}$$ to a proper fraction, where the numerator and denominator are both whole numbers we multiply both terms by 10 until we loose the decimal point.

$${\frac{{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{10}}}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{5}}}{{\mathtt{10}}}}$$  This is now a proper fraction but needs to be reduced or simplified down to it's simplest form by finding a number (their greatest common divisor) that could divide both the numerator and denominator to give us whole numbers for the numerator and denominator.

$${\frac{{\mathtt{5}}}{{\mathtt{10}}}}$$ divided by 5 is simplified to $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ which we know as half of 1.

Now to answer your question; convert .182 to a faction?

We are saying that 0.182 is a fraction of 1 so would be written

$${\frac{{\mathtt{0.182}}}{{\mathtt{1}}}}$$   As in my example, we need to convert this to a proper fraction, so we multiply both the numerator and denominator by 10 until we lose the decimal point.

$${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{1.82}}}{{\mathtt{10}}}}$$ We still have a decimal point to lose so we repeat the process

 $${\frac{\left({\mathtt{1.82}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{18.2}}}{{\mathtt{100}}}}$$  Again, we still have a decimal point to loose so we repeat the process again

$${\frac{\left({\mathtt{18.2}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{100}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$  Finally, we have a proper fraction with no decimal points. 

This is a lengthy way to do it so we have a simpler method. In this process we can see that we had to multiply both the numerator and denominator by 10 3 times, that's 10*10*10. This coincides with the amount of numbers after the decimal point in the original 0.182

So, if we said that for every number after the decimal point, we have to multiply both the numerator and the denominator by 10 we would have

$${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ which is equivalent to $${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}}$$ which equals $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ , much quicker. This is effectively the same as in other math problems where we whish to move the decimal point.

Now all we have to do is simplify $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ to it's simplest form by dividing it by it's greatest common divisor which is 2, $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ divided by 2 equals $${\frac{{\mathtt{91}}}{{\mathtt{500}}}}$$, which is your answer.

$${\frac{{\mathtt{2\,707}}}{{\mathtt{999}}}}$$  Normally we would try to reduce this down to it's simplest form by finding a number (their greatest common divisor) that could divide both the top number (numerator) and bottom number (denominator) to give us whole numbers for the numerator and denominator, this would be called a proper fraction.

e.g. $${\frac{{\mathtt{2}}}{{\mathtt{4}}}}$$ divided by 2 is simplified to $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

$${\frac{{\mathtt{2\,702}}}{{\mathtt{999}}}}$$ does not have a greatest common divisor to reduce or simplify it whilst keeping it as  proper fraction. Therefore, it is called an irreducible fraction and remains as it is.

amount 10000 rate 10% interst?

It is difficult to work this out with the limited information. I have tried to relate it to a few common scenarios.

1) This question could be referring to 10,000.00 of a currency in a savings/bank account and asking how much interest would be earned on it at a rate of 10%? 

2) This question could be referring to a debt of 10,000.00 of a currency on a loan/credit/charge card and asking how much interest would be charged on it at a rate of 10%?

Usually, rates of interest such as these are calculated per annum/year.

I will use the $ (dollar) sign for the currency to try to make it clearer as it's one of the most recognised currency symbols though this can easily be swapped for any other currency.

The calculations for this are the same;

You could start by determining what is 1% of $10,000.00

$${\frac{{\mathtt{10\,000}}}{{\mathtt{100}}}} = {\mathtt{100}}$$   So this shows that 1% of $10,000.00 is $100.00

Now we can easily find 10% 0f $10,000.00 by multiplying 1% ($100.00) by 10

$${\mathtt{100}}{\mathtt{\,\times\,}}{\mathtt{10}} = {\mathtt{1\,000}}$$   This shows that 10% of $10,000.00 is $1,000.00

In the case of example 1 above, this would mean that your $10,000.00 in your savings account would have increased by $1,000.00 to a total of $11,000.00

In the case of example 2 above, this would mean that your debt of $10,000.00 on your loan had increased by $1,000.00 to a total debt of $11,000.00

There are a few other ways you could calculate this;

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{0.1}} = {\mathtt{1\,000}}$$    The 0.1 being the decimal version of 10%, which gives the answer of $1,000.00, to be added to your original $10,000.00

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{1.1}} = {\mathtt{11\,000}}$$    The 1.1 being the decimal version of 110% which is the same as 100% (the original $10,000.00) plus the 10% (the $1,000.00) already added together for us. This being the quickest method as long as you can understand it.

If your calculator has a % button you could use this by typing $${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{10}}\% = {\mathtt{1\,000}}$$  to just find the interest or $${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{110}}\% = {\mathtt{11\,000}}$$ to find the interest with the original amount combined. I would not rely on this method though in case the calculator you were provided with for a test/exam didn't have this feature.

Perimeter is a measurement around something. It doesn't matter what the shape is, as long as you measure all the way around so that you meet back at the same place and the line that you are measuring is in line.

Imagine you are buying a new pair of trousers. To know what waist size you are you would use a tape measure around your waist to measure it's perimeter, where you would have your belt line. If the measuring tape was not in line with where your belt line would be, on your waist, then you would not be measuring the perimeter of your waist.

If you are measuring the perimeter of a circle, it could also be called the circumference.

The word perimiter is often used with fence or wall. You could imagine a perimeter security fence around a prison. Measuring it all the way around the perimiter fence, following any curve or corner, from one point, all the way back to the same point would give the length of the perimeter.

To answer a question on distance, speed or time you need two of these to answer the third.

In this case you have given the time and are asking for the speed, so you will also need to give the distance travelled to enable this.

The formula you require for this is speed = distance/time.

The formula for distance , speed and time calculations is $${\frac{{\mathtt{D}}}{\left({\mathtt{S}}{\mathtt{\,\times\,}}{\mathtt{T}}\right)}}$$ where D=Distance, S=Speed and T=Time. Whichever answer you require, cover it and the remaining is the formula for that answer. So if i wanted to know the distance, you would cover the "D", leaving the formula "S" multiplied by "T". If you wanted to know the speed as in your question, you would cover the "S", leaving "D" divided by "T".

I find it helps me to remember this by the fact that the letters appear in the order they appear in the word "DiSTance", the three letters don't all appear in either "Speed" or "Time".

It is important to ensure that you are using the same units of measure for the distance and speed e.g. Miles for distance and MPH (miles per hour) for speed, or Kilometres for distance and km/h (Kilometres per hour) for speed. It doesn't matter what unit of measure you use, as long as you use it across the whole calculation. If you use any non metric unit of measure you must convert any fraction of a whole unit into a decimal.

You also need to ensure that the time applied to the calculation is expressed in decimal hours e.g. 15 minutes = 0.25 hours, 1 hour 45 minutes = 1.75 hours .etc. Your question gives the time to a to a decimal already. You may then need to convert this back to the conventional hours and minutes if required for your answer?

Assuming that the cat that had the first litter of 3 was the only litter that year? So all calculations will be over the next 7 years? Assuming all other cats born don't have any litters themselves?

We have 4 cats that have 3 litters of 3 kittens, per year, for 7 years, plus the 1 original cat and it's 3 original cats.

(4*3*3*7)+4 = 256

Don't really need the brackets as we should do all multiplication before addition as per order of operations.

Please bear in mind I am just a newbie so there may be more elegant solutions to this and I may be wrong, though I believe I have it correct.

Thanks again Melody.

I'm gaining more confidence to question them.

I've also had a bit of a go at the two factorising questions you set me, not easy!