My brother used to say he has two sisters: the beautiful one and the smart one. Well, the truth is, my sister did some photo modeling, and I'm 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:

Commission - How much will I get?

A sales associate, who works for 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 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 to multiply by the converted percentage (always by dividing by 100%):

$200,000 * 0.06 = $12,000. That's the total commission.

If brokers agree to split 50-50, that will give us half of $12,000, which is $6,000. Then we have to split this amount between the selling broker and their associate. If the broker keeps 45%, we'll take away 45% of the commission, therefore we'll have only 55% of $6,000, which is (again, simple multiplying):

$6,000 * 0.55 = $3,300.

This means $3,300 goes to the selling sales associate.

Wow, we did it! Let's have a look at another one:

Converting units and simple geometry: How big a land will I have?

Question 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'

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

Solution A: First, I need to know what an acre is. An 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: 1 acre equals 43,560 square feet. Therefore, 4 acres will be:

4 * 43,560 = 174,240 square feet.

Now, how to efficiently find the solution out of the multiple choice options? When thinking about square units, we know in rectangles it's width times length. The third option (400' x 4,356') gives us an interesting (but not satisfying) number, considering that 4,356 times only 10 would give us one acre (43,560 square feet). So, we don't have to check how many square feet it is when multiplied by 400; it's definitely more than we need (for four acres, we need 40 times 4,356, not 400 times).

All the other options use 330 feet as one of the sides of the rectangle-shaped land. So, instead of multiplying all three options one after another, we can simply divide the target area by one given length to get the desired other length of the rectangle that represents the land.

174,240 / 330 = 528.

Hence, we have our answer – it's the last choice (528' x 330').

Question 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'

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 half of the perimeter, it will give us the sum of the two sides (width and length), which will make my calculations quicker:

834.84 / 2 = 417.42.

This means 417.42 feet is the sum of the desired length and width of the land. Which numbers from the multiple choice options will give me a sum of 417.42? The first two are definitely too big. The last two look more reasonable. You can either look and 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, not calculate too many numbers and save time) and you will get the correct answer, which is the last one (208.71' x 208.71') as 208.71 + 208.71 = 417.42, half the perimeter, which is what we were checking.

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

Rearranging formulas - How to express whichever variable 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 is still the same as we agreed with my broker?

Solution: That means I need to express the rate as the subject: in this case, the equation is so simple that all I need to do is divide by the V value: I / V = R or (even better after changing sides) R = I / V. Now I can always just easily 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 our sister passed the state licensing test (on her first attempt) – her and one more person out of thirty candidates that day! So my sister belongs to the top 6.7% of her class!