# Math Formulas All Grown Ups Should Know

TR Smith is a product designer and former teacher who uses math in her work every day.

Most adults know how to calculate tips, balance an account, work out their monthly expenses, and all the other mundane math you learn in school. But there are more unconventional applications of math they don't teach you in school that will serve you well in life.

Impress your friends by learning how to calculate the day of the week from any date, estimate the day of ovulation, keeps score by hand in a game of bowling, calculate the number of calories you need per day, and figure how many decades it takes to pay off a credit card balance if you only make the minimum monthly payment.

## How to Find the Day of the Week of Any Date

Was your birthday on a Monday or a Wednesday in 1996? Did you first meet your spouse on a Thrusday or Friday?

For the date in question, past or future, call the date number D and the year Y, where 1 ≤ D ≤ 31 and 1600 ≤ Y. (Historical note: By 1600, most of Europe had already adopted the Gregorian Calendar, which is the calendar system this formula is based on. The Julian Calendar was in use earlier.)

The month number M ranges from 3 to 14 and must be counted in a special way. If the month is March through December, then March = 3, April = 4, ... December = 12 and Y equals the year. But if the month is January, you count it as the 13th month of the previous year; if the month is February, you count it as the 14th month of the previous year. Thus, if the month is January or February then M = 13 or 14 and you subtract 1 from the year number. It's very important not to forget to subtract 1 if the month is January or February!

Once you have the values of D, Y, and M you can plug them into this formula:

D + 2M + ⌊(3M+3)/5⌋ + Y + ⌊Y/4⌋ - ⌊Y/100⌋ + ⌊Y/400⌋

where the ⌊ ⌋ symbol is the floor function, or "decimal point ignoring" function. You simply consider the integer value of the quantity and disregard any fractional or decimal amounts. Divide the number you obtain from this formula by 7 and look at the remainder, which ranges from 0 to 6. The remainder tells you the day of the week:

0 = Monday, 1 = Tuesday, 2 = Wednesday, 3 = Thursday,
4 = Friday, 5 = Saturday, 6 = Sunday.

Example: Consider the date February 23, 1996. Here we have D = 23, M = 14, and Y = 1995. Plugging these values into the formula gives us 2538. Dividing 2538 by 7 gives us 362 with a remainder of 4. According to the formula, 4 = Friday. Thus, the date February 23, 1996 occurred on a Friday.

## How to Estimate Ovulation Date

Knowing the date range when you or your partner is ovulating is a key when trying to conceive -- or trying to avoid conception. Ovulation is when an egg is released from a follicle in an ovary and it occurs some time in the middle of the menstrual cycle. The menstrual cycle is the time between onset dates of your periods.

The span of time after ovulation and before the onset of the next menses (period) is called the luteal phase, and lasts between 12 and 16 days. To estimate when you are ovulating, you need to know the length of your shortest and longest menstrual cycles in the past several months. Say the length of your shortest is S and the length of the longest cycle is L. Calculate two numbers A and B with the formulas

A = S - 16
B = L - 12

Your ovulation date is some time between A days and B days after the start of your next period.

Example. Your shortest menstrual cycle was 26 days and your longest was 31 days. So you have S = 26 and L = 31. Now you calculate

A = 26 - 16 = 10
B = 31 - 12 = 19

This means you will ovulate between 10 and 19 days after the start of your next period. As you can see, the date range can be wide. A more accurate way to predict when you're ovulating is to chart your temperature and cervical mucous consistency over many menstrual cycles. During ovulation, your temperature is slightly elevated and your cervical mucus has a different texture. Recognizing these signs will give you a more precise window.

## How to Keep Score in a Bowling Game

Sure, you can let the bowling alley computer keep score for you, but what if the machines are down, or you're playing an informal game in the garage with empty beer bottles and a mannequin head? Knowing how to keep score in bowling will impress your date and ensure a fair game of mannequin head beer bottle bowling.

The key rules you need to remember are:

• The base number of points you earn for a frame is the the total number of pins you knock over in the two rolls allotted per frame.
• If you make a spare (knock over all 10 pins with two rolls) your base score for that frame is increased by the number of pins you knock over on your next roll. Note that it's only for the next roll, not the next entire frame. The number of pins you knock over on your next roll are also counted for that frame, so that roll is double counted.
• If you make a strike (knock over all 10 pins on your first roll), your base score for that frame is increased by the number of pins you knock over on your next two rolls. Again, note that it's for the next two rolls, not the next two frames. Your next two rolls are also counted for the frame(s) they occur in, so they're counted doubly or triply.

As you can see from these scoring rules, if you roll a spare or a strike you can't immediately record your score for that frame because you're getting bonus points from your next turn.

A game of bowling consists of 10 frames. If you score a spare on your last frame, you get another roll to obtain your bonus points. If you happen to knock all 10 pins over, you don't get a strike bonus.

If you score a strike on your last frame, you also get two more rolls to score your bonus points.

## The Number of Calories You Need Per Day

The number of calories you need per day is a function of your basal metabolic rate and your activity level. Your basal metabolic rate depends on your gender, age, height, and weight. The Harris-Benedict formulas to estimate BMR for men and women are

Women: BMR = 9.247W + 3.098H - 4.33A + 447.593

Men: BMR = 13.397W + 4.799H - 5.677A + 88.362

where W is your weight in kilograms, H is your height in centimeters, and A is your age in years. Yes, these equations are in metric units. For convenience, 1 pound = 0.4536 kg and 1 inch = 2.54 cm.

To find your daily calorie needs, you multiply your BMR by an activity level factor that ranges from 1.2 to 1.9. This scale will help you estimate your factor:

sedentary lifestyle: 1.2
exercise 3-5 times a week: 1.55
vigorous daily exercise: 1.9

Example: You are a 35-year-old male, 175 cm tall and weighing 73 kg. Your basal metabolic rate is 13.397*73 + 4.799*175 - 5.677*35 + 88.362 = 1707.473 calories. You estimate your activity level factor to be 1.4. Therefore, the number of calories you need to consume per day is 1.4*1707.473 ≈ 2390. This is equivalent to eating about 3/4 of a large 14" pan pizza from Pizza Hut.

## Length of Time to Pay Off Credit Card Debt

Most people know if they pay only the minimum monthly amount on their credit card balance it will take ages to pay it off. Ever wonder just how long it will take? Use this formula to find the number of months it will take to get your credit card balance to zero:

months = [ Log(M) - Log(M - BR/1200) ] / Log(1 + R/1200)

Where \$M is the minimum amount you are required to pay every month, \$B is the current credit card balance, and R is the annual percentage rate. When you plug these three variables into the formula you get the number of months it will take to pay off your credit card, assuming you don't make any more charges. In the formula, the percentage R is divided by 1200 to convert it into a monthly rate as a decimal.

For example, suppose your card has an interest rate of 21.99% and your current balance is \$950. If the minimum monthly payment they require is \$19, then you plug the values R = 21.99, B = 950, and M = 19 into the formula. This gives you 136 months, or about 11 years to pay off the balance on your credit card while making only the bare minimum monthly payment.

Here's a tip: If M - BR/1200 is less than zero, you'll never be able to pay off the balance making only the minimum payment.

Images courtesy of Pixabay public domain images.

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