My brother used to say he has two sisters; the beautiful one and the smart one. Well, the truth is, that my sister did some photo modelling and I am the one who knows maths. But even my pretty sister found out, she needs maths in her career. What does she do? She's a real estate agent. Calculating mortgages, insurance, working with percentages, formulas...

So what maths can you expect when you love houses and want to be a real estate agent? Have a look at some questions she had to be able to solve when taking the real estate licence test:

**Commision** - how much will I get?

A sales associate, who works for a broker A, obtains a listing for $215,000 at a 6% commission rate. A second sales associate, who works for broker B, finds a buyer for the property. The listing and selling brokers agree to a 50-50 split between the two brokerage firms. The property sells for $200,000. The selling broker keeps 45% of the commission received by their firm. The selling sales associate's commission is...

Well? How much? Would you be able to calculate it?

**Solution:** A bit confusing at the first sight, but we need to focus on the selling price. We know the commission rate is 6%, the quickest way to find out 6% of 200,000 is multiply converted percentages (always by dividing by 100%) -> 200,000 * 0.06 = 12,000. That's the commission rate. If brokers agree to split 50-50, that will give us half of 12,000 which is 6,000. Then we have to split the amount between the selling broker and their associate. If the broker keeps 45%, we'll take away 45% of the commission rate, therefore we'll have only 55% of 6,000, which is (again simple multiplying) 6,000 * 0.55 = 3,300 - which means $3,300 goes to the selling sales associate.

Wow... let's have a look at some another one:

**Converting units and simple geometry** - how big land will I have?

A. Which parcel of land contains exactly 4 acres?

330' x 396' or 330' x 462' or 400' x 4,356' or 528' x 330'

B. Which tract of land has a perimeter of 834.84 linear feet?

100.00' x 834.84' or 100.00' x 417.42' or 200.84' x 215.84' or 208.71' x 208.71'

Multiple choice! How to solve it the most efficient way (as the time matters while taking the test too)?

**Solution A:** First I need to know what is an acre. Acre on its own is a square unit. So we need to convert it into square feet, we must remember this conversion for that type of question, so 1 acre equals 43,560 square feet, therefore 4 acres will be 4 * 43,560 = 174,240.

Now how to find efficiently the solution out of the multiple choice? When thinking about square units, we know in rectangles it's width times length. The third option gives us an interesting (but not satisfying) number considering that 4,356 times only 10 would give us one acre (43,506 as one acre), so we don't have to check how many square feet it is when multiplied by 400, definitely more than we need (for four acres we need 40 times, not 400 times those 4,356 feet).

All the other options use as one of the sides of the rectangle-shaped land length 330 feet, so we can instead of multiplying all three options one after another only divide the answer by one length to get desired another length of the rectangle which represents the land.

So 174,240 / 330 = 528 hence we have our answer - it's the last choice.

**Solution B:** Again, first decide what you need to do - it's about finding a perimeter of a rectangle, which uses the formula 2 * (length + width) (because we go around the land, perimeter is "the length of the fence" - length and width and length and width, four sides - just common sense, not much maths yet =)

So again, how to solve it efficiently? Thinking about the formula, if we take only a half of the area, it will give us the sum of the two sides (width and length), so that will make my calculations quicker: 834.84 / 2 = 417.42 -> that means 417.42 feet is the sum the desired length and width of the land. Which number of the multiple choice will give me sum 417.42? The first two are definitely too big numbers, the last two looks more reasonable. You can either look a think about them (and see that the third one will not give us the answer - it's together slightly less than 417 feet, therefore - just to check - calculate the last one to be sure that yes, that matches), or just calculate both (as you easily got rid of two other choices already, which was the goal, to not to calculate too many numbers to save the time) and will get the correct answer, which is the last one (again, what a coincidence =) as 208.71 + 208.71 = 417.42

You got enough? It's not all what you must face when being a real estate agent - look:

**Rearranging formulas** - how to express whichever I need?

IRV formulas (Income, Rate, Value): I = R x V

You may know the formula, but if you need to express another subject, then you need to rearrange it... What if I know my income and the value of the property, but I want to check if the rate was still the same as we agreed with my broker?

**Solution:** That means I need to express as an subject the rate: in this case the equation is so simple, that all I need to do is divide by value: I / V = R or (even better after changing sides) R = I / V. Now I can always easilly just substitute the income and value and see if the rate I got is not below the agreed percentage (if it's above, you should be happy, right? =)

Rearranging is usually more useful if you need to use the rearranged formula multiple times. Otherwise just substitute everything as it is and check if the left side of the equation matches the right side.

So, considering what you will need to be able to calculate as a real estate agent, I'd say my brother has two smart sisters, because she passed the state licensing test (on her first attempt) - she and one more person out of thirty candidates that day! So my sister belongs to the top 6.7% of her class =)