Many of you may have seen the television show, “Are you Smarter than a 5th Grader?” and since my daughter is currently in the 5th grade, I thought it would be the perfect title for my blog post about math.
I have worked for 12 years with individuals preparing for ACE exams and a common fear many of them have is around the math. I sometimes ask myself why individuals are so fearful of math questions.
I personally have taken all four ACE exams and don’t recall them being anything more than addition, subtraction, multiplication or division. To help put any irrational fears to rest, I’ve put together some of the common formulas, as well as some helpful math tips, to prepare you for the big day.
Age Predicted Maximum Heart Rate (MHR)
220 - Age = MHR
MHR x % intensity = Target Heart Rate (THR)
Example: 34 years old at 75% intensity
220 - 34 = 186 x 0.75 = 139.5 bpm
Karvonen Formula - Heart Rate Reserve (HRR)
220 - Age = MHR
MHR - Resting Heart Rate = HRR
(HRR x % intensity) + RHR = THR
Example: 34 year old, resting heart rate = 62 bpm, at 75% intensity
220 - 34 = 186 - 62 = 124 x 0.75 = 93 + 62 = 155 bpm
Body Mass Index (BMI)
Weight (kg) ÷ Height2 (m)
Weight conversion: weight in lb ÷ 2.2 = weight in kg
Height conversion: (height in inches x 2.54) ÷ 100 = height in meters
Example: Height = 5’ 8” Weight = 196 lbs.
(5’ x 12) + 8 = 68” 196 / 2.2 = 89 kg
(68” x 2.54) ÷ 100 = 1.73 m
89 kg ÷ (1.73 m x 1.73 m) = 29.7
Desired Body Weight (DBW)
DBW = LBW ÷ (1 - DBF%)
Step 1: 100 % - Fat % = Lean body %
Step 2: Body weight x Lean body % = LBW
Step 3: 100% - Desired fat % = Desired lean %
Step 4: LBW ÷ Desired lean % = DBW
Example: 200 lbs. individual with 30 % body fat.
How much will he/she weigh at 25 % body fat?
- 100 % - 30 % = 70 %
- 200 lbs. x 0.70 = 140 lbs. LBW
- 100 % - 25 % = 75 %
- 140 lbs. ÷ 0.75 = 187 DBW
Caloric (kcal) Values per Gram (g)
Fat = 9 kcal/g Alcohol = 7 kcal/g
Carbohydrates = 4 kcal/g Protein = 4 kcal/g
Multiplying by a percent
When multiplying by a percent, remember to move the decimal point 2 places to the left in your final answer.
Dividing by a percent
When dividing by a percent, move the decimal point over 2 places to the right before you start long division.
For example: Your client currently weighs 150 lbs. and is 30% body fat. You know her lean body weight is 105 lbs. and her desired percent body fat is 20%. To find her new ideal body weight at 20 % body fat, you must divide 105 lbs. by her new ideal lean body weight percent, which equals 80% or 0.80 in decimal form.
Finding the percent of a whole
When dividing a bigger number into a smaller number, you must add a decimal point and at least 2 zeros at the end of the smaller number. Be sure to extend the decimal point to your answer — writing your answer to the right of the decimal point since it will ultimately be a percent of the whole.
Looking for more practice with these essential calculations? The Fitness Math course will help you to review these critical math skills and formulae in greater depth so that you are confident and ready come exam day!