Using Mathematics in
Savings & Credit,
Cooking, and it is a
Using Mathematics in
Savings & Credit,
Cooking, and it is a
Savings and Credit
You may be surprised to hear that you're just as likely to lose money because of your everyday banking decisions. Many people collect only 1 to 3% interest on money in a savings account while simultaneously paying rates as high as 18 to 20% on credit card balances. Over time, this can mean some pretty heavy losses.
With some math smarts and an understanding of simple and compound interest, you can manage the way your money grows (and ideally keep it from shrinking). The principles of simple and compound interest are the same whether you're calculating your earnings from a savings account or the fees you've accumulated on a credit card. Paying a little attention to these principles could mean big payoffs over time.
Understanding the basics
When you put money in a savings account, the bank pays you interest according to what you deposit. In effect, the bank is paying you for the privilege of "borrowing" your money. The same is true for the interest you pay on a loan you take from the bank or the money you "borrow" from a credit card.
Interest is expressed as a rate, such as 3% or 18%. The dollar amount of the interest you earn on a savings account is figured by multiplying the money you deposit (called the principal) by the rate of interest. If you have $100 in an account that pays only 1% interest, you'll only earn $1 in interest. If you shop around for an account that pays 5% interest, you'll earn five times that amount.
In banking, interest is calculated and added at the end of a certain time period. You might have a savings account that offers a 3% interest rate annually. At the end of each year, the bank multiplies the principal (the amount in the account) by the interest rate of 3% to compute what you have earned in interest.
Interest on interest: Compounding
There are two basic kinds of interest: simple and compound. Simple interest is figured once. If you loaned $300 to a friend for one month and charged her 1% interest ($3) at the end of the month, you'd be dealing with simple interest. Compound interest is a little different. With compound interest, the money you earn in interest becomes part of the principal, and also starts to earn interest. If you loaned that same friend $300 for one month but charged her 1% each day until the end of the month, you'd be using compound interest. At the end of the first day, she would owe you $303. At the end of the second day, she would owe you $306.03. At the end of the third day, she would owe you $309.09, and so on.
Compound interest is what makes credit cards and loans so difficult to pay off. The rules of interest are the same ones that increase your savings over time, only with credit and debt, they're in the bank's favor not in yours. With some rates as high as 21%, collecting interest on credit card loans can be a lucrative business.
What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. How will you know how many rolls of wallpaper to buy if you don't calculate how much wall space you have to cover? Understanding some basic geometry can help you stick to your budget.
The word geometry literally means "to measure the Earth." Geometry is the branch of math that is concerned with studying area, distance, volume, and other properties of shapes and lines. If you need to know the distance between two points, the volume of water in a pool, the angle of a tennis serve, or how much wallpaper it will take to cover a wall, geometry holds the answers.
Figuring area: Squares and rectangles
Imagine you're planning to buy new carpeting for your home. You're going to put down carpeting in the living room, bedroom, and hallway, but not in the bathroom. You could try to guess at how much carpet you might need to cover these rooms, but you're better off figuring out exactly what you need. To determine how much carpet you'll need, you'll use this simple formula:
A = L x W
Or in other words, "area equals length times width." This formula is used to determine the area of a rectangle or square. In the floor plan below, all of the floor space (as well as the walls and ceilings) is made up of squares or rectangles, so this formula will work for figuring the area you need to carpet.
Start by figuring the total area of the floor plan. When you're done, you can deduct the area of the bathroom, since you don't want to carpet that room. To figure out the total area of the floor plan, you'll need to know the total length and width. The total length of the floor plan shown above is 12 feet plus 10 feet, or 22 feet. The total width is 7 feet plus 5 feet, or 12 feet. Plug these numbers into your equation to get the total area of the floor plan:
A = 22 feet x 12 feet
A = 264 square feet
The total area of your floor plan is 264 square feet. Now you need to figure out the area of the bathroom so you can deduct it from the total area. The bathroom is 7 feet long and 5 feet wide, so it has an area of 35 square feet. Deducting the area of the bathroom from the total area (264 minus 35) leaves you with 229 square feet to carpet.
Figuring area: Circles
Calculating how much carpet you'll need is a fairly simple task if your home has only square or rectangular rooms. But what if you have a circular alcove at the end of one room? How do you figure the area of a circle? Geometry comes to the rescue again with a handy formula:
A = (pi) x r2
In English, this formula means "area equals pi times the radius squared." A circle's radius is one half of its diameter, or one half of what you get if you measure all the way across its widest part. "Squaring" something means you multiply it by itself. Pi is a number that roughly equals 3.14159.
If your living room has a semi-circular alcove as shown in the floor plan above, you'll need to use this additional equation to figure out its area. To figure the radius of your alcove, the number you'll need to plug into the equation, you'll divide its diameter in half. Its diameter is the same as the width of the living room: 12 feet. Half of that is its radius: 6 feet.
Let's plug in the numbers:
A = 3.14159 x (6 feet x 6 feet)
A = 113 square feet (rounded to the closest square foot)
If your alcove were a complete circle, it would have an area of 113 square feet. Because it's a half circle, its area is half of that, or 56.5 square feet. Adding 56.5 square feet to the rest of your floor plan's area of 229 square feet gives you the total area you want to carpet: 285.5 square feet. Using geometry, you can buy exactly the amount of carpet you need.
Cooking by Numbers
Not all people are chefs, but we are all eaters. Most of us need to learn how to follow a recipe at some point. To create dishes with good flavor, consistency, and texture, the various ingredients must have a kind of relationship to one another. For instance, to make cookies that both look and taste like cookies, you need to make sure you use the right amount of each ingredient. Add too much flour and your cookies will be solid as rocks. Add too much salt and they'll taste terrible.
Ratios: Relationships between quantities
That ingredients have relationships to each other in a recipe is an important concept in cooking. It's also an important math concept. In math, this relationship between 2 quantities is called a ratio. If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2. In mathematical language, that relationship can be written in two ways:
1/2 or 1:2
Both of these express the ratio of eggs to cups of flour: 1 to 2. If you mistakenly alter that ratio, the results may not be edible.
Working with proportion
All recipes are written to serve a certain number of people or yield a certain amount of food. You might come across a cookie recipe that makes 2 dozen cookies, for example. What if you only want 1 dozen cookies? What if you want 4 dozen cookies? Understanding how to increase or decrease the yield without spoiling the ratio of ingredients is a valuable skill for any cook.
Let's say you have a mouth-watering cookie recipe:
1 cup flour
1/2 tsp. baking soda
1/2 tsp. salt
1/2 cup butter
1/3 cup brown sugar
1/3 cup sugar
1/2 tsp. vanilla
1 cup chocolate chips
This recipe will yield 3 dozen cookies. If you want to make 9 dozen cookies, you'll have to increase the amount of each ingredient listed in the recipe. You'll also need to make sure that the relationship between the ingredients stays the same. To do this, you'll need to understand proportion. A proportion exists when you have 2 equal ratios, such as 2:4 and 4:8. Two unequal ratios, such as 3:16 and 1:3, don't result in a proportion. The ratios must be equal.
Going back to the cookie recipe, how will you calculate how much more of each ingredient you'll need if you want to make 9 dozen cookies instead of 3 dozen? How many cups of flour will you need? How many eggs? You'll need to set up a proportion to make sure you get the ratios right.
Start by figuring out how much flour you will need if you want to make 9 dozen cookies. When you're done, you can calculate the other ingredients. You'll set up the proportion like this:
1 cup flour
X cups flour
You would read this proportion as "1 cup of flour is to 3 dozen as X cups of flour is to 9 dozen." To figure out what X is (or how many cups of flour you'll need in the new recipe), you'll multiply the numbers like this:
X times 3 = 1 times 9
3X = 9
Now all you have to do is find out the value of X. To do that, divide both sides of the equation by 3. The result is X = 3. To extend the recipe to make 9 dozen cookies, you will need 3 cups of flour. What if you had to make 12 dozen cookies? Four dozen? Seven-and-a-half dozen? You'd set up the proportion just as you did above, regardless of how much you wanted to increase the recipe.
The Universal Language
Mathematics is the only language shared by all human beings regardless of culture, religion, or gender. Pi is still 3.14159 regardless of what country you are in. Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, rubles, or yen. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way.
Very few people, if any, are literate in all the world's tongues English, Chinese, Arabic, Bengali, and so on. But virtually all of us possess the ability to be "literate" in the shared language of math. This math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time. It is what links ancient scholars and medieval merchants, astronauts and artists, peasants and presidents.
With this language we can explain the mysteries of the universe or the secrets of DNA. We can understand the forces of planetary motion, discover cures for catastrophic diseases, or calculate the distance from Boston to Bangkok. We can make chocolate chip cookies or save money for retirement. We can build computers and transfer information across the globe. Math is not just for calculus majors. It's for all of us. And it's not just about pondering imaginary numbers or calculating difficult equations. It's about making better daily decisions and, hopefully, leading richer, fuller lives.