Math

Question 1

Which way does the decimal move in a decimal to a percentage?

Answer 1

Right by 2 spaces, the number is timed by 100.

Question 2

Which way does the decimal move in a percentage to a decimal?

Answer 2

Left by two spaces, the number is timed by 100.

Question 3

What is the formula for the area of a triangle?

Answer 3

Height times base.

Height times base divided by 2.

Steps:

6’ B x 10’ H = 60 SF / 2 = 30 SF

Question 4

What is the area of a trapezoid?

Answer 4

A+B
——— (times)height
2.
Length times length divided by 2 then timed by height.

8’ Length + 12’ Length = 20’

20’ / 2 = 10’ new Length (after adding the 2 lengths, always divide the answer by 2)

10’ Length x 6’ Height = 60 SF

Example:

What is the area of this trapezoid?

Steps:

12’ Length+ 18’ Length = 30’

30’ / 2 = 15’ new Length (after adding the 2 lengths, always divide the answer by 2)

15’ Length x 10’ Height = 150 SF

Question 5

What is the formula for acres?

Answer 5

1 Acre = 43,560 SF

This is a very important number to remember. It is used in many real estate math calculations.

Formula:

Acres = Total SF / 43,560

T-bar Formula for SF to Acres conversion:

Question 6

If a lot contains 152,460 total SF, how large is the lot in acres?

Answer 6

If a lot contains 152,460 total SF, how large is the lot in acres?

Example #1:

Steps:

152,460 / 43,560 = 3.5 Acres

Question 7

If a man purchases 4 acres of land, how large is the lot in square feet?

Answer 7

Example #2:

If a man purchases 4 acres of land, how large is the lot in square feet?

Steps:

43,560 x 4 = 174,240 Total SF

Question 8

If a man purchases a lot that measured 600’ x 363’ and costs $650 per acre, what was the total cost of the lot?

Answer 8

Steps:

Calculate the size of the lot in acres:

600’ x 363’ = 217,800 SF

Calculate the number of acres in the lot:

217,800 / 43,560 = 5 Acres

Calculate the price of the lot:

$650 per acre x 5 acres = $3,250 total cost of the lot

Question 9

If the EZ Sales car lot is valued at $150,000 and is 300’ wide, how much is it worth per front foot?

Answer 9

Example:

Steps:

$150,000 ÷ 300 = $500 per front foot

Question 10

What is the gross living area?

Answer 10

Gross Living Area, or GLA, the finished square footage of a structure that is measured using the outside dimensions.

When calculating GLA:

Only include areas that are finished
Items excluded from the GLA typically include garages, carports, decks, and patios.
Example:

What is the GLA of this home?

Steps:

Don’t include the garage and the screened porch in the calculation because each is not finished.

Calculate the dimensions of the house: 60’ wide and 40’ deep. Add the depth of the garage, 30’, and the remaining depth of the house, 10’, to get a total of 40’ in depth:

60’ width x 40’ depth = 2,400 SF GLA

Question 11

What is a setback?

Answer 11

Setbacks are the amount of space local zoning regulations require between the property line and any improvements.

The setback line is the boundary line that delineates the setback area.

To calculate the remaining area of the lot that can be built on, subtract the setbacks from the dimensions:

The front yard and back yard setbacks are subtracted from the depth.
The side yard setbacks are subtracted from the width.

Question 12

On a residential lot that measures 70 feet by 100 feet, the side-yard building setbacks are 10 feet, the front-yard setback is 25 feet, and the rear-yard setback is 20 feet. What would the maximum possible area for a one-story structure be for this lot?

Answer 12

Steps:

Subtract the front yard and back yard setbacks from the depth: 100’ – 25’ – 20’ = 55’ new depth
Subtract the side yard setbacks from the width: 70’ – 10’ – 10’ = 50’ new width
Multiply new depth by new width: 55’ depth x 50’ width = 2,750 SF maximum possible area

Question 13

What is The Rectangular/Government Survey?

Answer 13

The Rectangular/Government Survey is a type of legal description that describes a parcel of land using a set of fractions and the corresponding section, township and range numbers. While legal descriptions will be covered in detail in the National Appraisal chapter, students must learn how to calculate the size of the parcel described using this method.

A section is a square tract of land used in the Rectangular/Government Survey method.

Question 14

How many acres are there in the S ½ of the SE ¼ of the SW ¼ of section 24, township 32 north, range 18 east?

Answer 14

Steps:

Ignore the text “section 24, township 32 north, range 18 east.” It doesn’t affect the answer.
Multiply all denominators together (the bottom number of the fraction), 2 x 4 x 4 = 32.
Divide 640 by that answer, 640 ÷ 32 = 20 acres.

Question 15

What is A section?

Answer 15

A section is a square tract of land used in the Rectangular/Government Survey method.

A section:

Is 1 mile wide and 1 mile deep.
Contains 640 Acres

Question 16

What is volume?

Answer 16

Volume is the amount of something that a container can hold. For example, the amount of water required to fill a swimming pool is the volume of water that the swimming pool can hold.

Question 17

What is volume’s measurement and formula?

Answer 17

Volume is expressed in CUBIC feet (not in square feet like area).

Volume = Height (or Depth) x Width x Length

Question 18

If a homeowner wishes to fill in an old, outdated swimming pool that measures 20’ in length, 10’ in width and is 6’ in depth with dirt, how much dirt will he need to buy in cubic feet?

Answer 18

Steps:

H (or D) x W X L
6’ x 10’ x 20’ = 1,200 Cu/Ft

Question 19

Andre owned a 1/4 acre lot. He wanted to construct a 120’ x 80’ tennis court on the lot. How many square feet will remain uncovered after he builds the tennis court?

Answer 19

1,290 SF remaining

Question 20

What is 75% converted to a decimal?

Answer 20

.75

Question 21

A developer wants to develop a 20-acre subdivision. He figures that the streets and common area will take up about 25% of this overall area. If the minimum lot size is to be 10,000 SF, how many lots can the developer have on this property?

Answer 21

20 acres ÷ 4 = 5 acres, 20 acres - 5 acres = 15 acres, 15 acres x 43,560 SF= 653,400 SF, 653,400 SF ÷ 10,000 SF= 65 lots

Question 22

An investor just purchased a rectangular 1-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?

Answer 22

$100,000 ÷ $250 = 400’, 1 acre = 43,560 s/f, 43,560 s/f ÷ 400’ = 109

Question 23

Terry bought a home that home that had an attached one-car garage and a screened porch that spanned the length of the home. If the garage measured 16’ in depth which was half the depth of the house and the screened porch was 64’ in width, what is the GLA of the house?

Answer 23

16 X 2 = 32 X 64 = 2, 048

Question 24

If a rectangular house is 50 feet wide and contains 2,500 sq/ft, what is its depth?

Answer 24

2500/50= 50

Question 25

If an investor wants to combine a 3/4 acre parcel with a 1.6 acre parcel, how big will the parcel be, expressed as a decimal?

Answer 25

.75 plus 1.6 = 2.35

Question 26

A commercial builder has a downtown lot with 250 frontage feet on Broadway. The lot is 200’ deep. By code, the builder must allow for a 15’ setback on Broadway, and 10’ on both sides of the lot. How many square feet does the builder have left to build on?

Answer 26

250 Front Feet - 20 feet = 230 front feet; 200 - 15 setback = 185 feet; 230 X 185 = 42,550

Question 27

Calculate how many acres are in the Southwestern 1/4 of the Northern 1/2 of the Eastern 1/2 of Section 14.

Answer 27

1 section = 640 acres, 4 x 2 x 2 = 16; 640 ÷ 16 which equals 40 acres

Question 28

John bought an odd-shaped lot that was 100 feet deep, but the front footage was 160 feet and the length of the back side of the lot was 80 feet. What is the square footage of his lot?

Answer 28

160’ + 80’ = 240’; 240’ ÷ 2 = 120’ new length; 120’ L x 100’ D = 12,000 SF

Question 29

If a salesperson sells 3/4 of an acre for $80,000, what was the price per square foot rounded to two decimal spaces?

Answer 29

43560 times .75 then 80,000 divided by 32670 equals 2.45

Question 30

Adjusting Comparables

Rules:

Never adjust the subject!
If the comparable is superior to the subject, subtract value from the comparable.
If the comparable is inferior to the subject, add value to the comparable.

Answer 30

The subject has a $10,000 pool and no porch. A comparable that sold for $250,000 has a porch ($5,000), an extra bathroom ($6,000), and no pool.

Adjustments to comp: $250,000 (+10,000 - 5,000 - 6,000) = $249,000 indicated value of subject

A comparable has 3 bedrooms and the subject has 4.

The appraiser estimates the value contribution of a bedroom to be $10,000.
Adjust the comparable by entering +$10,000 in the CMA.