Tip of the Week -- Fractions

A lot of folks are afraid of fractions, but the truth is that we use fractions every day. Every time we use money, measure something, or tell time, we are using fractions.

A fraction is simply this: a part of a whole. The top number is the part and the bottom number is the whole.

A penny is 1/100 of a dollar, because 1 dollar and 100 pennies are the same thing. A quarter is 1/4 of a dollar, because 1 dollar and 4 quarters are the same thing.

And inch is 1/12 of a foot, because 1 foot and 12 inches are the same thing. A foot is 1/3 yard because 1 yard and 3 feet are the same thing.

A minute is 1/60 of an hour, because 1 hour and 60 minutes are the same thing. 15 minutes is 1/4 of an hour because there are four sets of 15 minutes in an hour.

The most common way that fractions are taught is with pizza. Most pizzas are cut into 8 slices, so if we have 8 slices, we have one pizza. Therefore, a slice is 1/8 of a pizza. If two friends share a pizza, and each person eats 4 slices, then each person has eaten 4 slices out of 8, or 4/8, which is the same as 1/2.

Math Tip of the Week -- Subtracting Time

Subtracting time is no different than subtracting other numbers. We know that if all of the digits on the top are bigger than all of the numbers on the bottom, we just subtract straight down. The same goes for time.



But what happens if we have to borrow? When subtracting time, we don't so much borrow as we convert. If we borrow from the hours column, we must add the number of minutes (the equivalent to the hours we borrowed) to the minutes column. It looks like this:

We would use the same process for subtracting units of measure, too. But we would use the equivalent numbers for the measures we're working with. For example, 1 foot = 12 inches, 1 pound = 16 ounces, etc.

Tip of the Week -- Math

A mnemonic device is a little trick to help you remember something.



A good mnemonic to remember the Order of Operations is



Please Excuse My Dear Aunt Sally



Parentheses

Exponents

Multiplication

Division

Addition

Subtraction



Or you could just remember PEMDAS as a fun nonsense word to help you to remember.

Math Tip of Week -- Algebra: Why Are There Letters in Math??

Take a look at the word equation. It has the same root as the word equal. An equation is a situation in which one thing is the same as something else. In math, it means that one number or set of numbers is equal to another number or set of numbers. That's why there is an equal sign (=) in the middle of it.

For example, we know that 2 + 2 is the same thing as 4. We say 2 + 2 = 4. The numbers on both sides of the = mean the same thing.

But what if we only have two numbers in that equation? What if we only have 2 + 2 =
and we don't know what goes on the other side of the =? We substitute the missing information with a letter (usually x, y or z) to represent that we don't know the number yet.

We could write 2 + 2 = x.
To solve for x, we must first isolate x, or get it alone, on one side of the =. In this example, x is already by itself, so we only have to add 2 + 2 to find it.

Simplified, it looks like this: 2 + 2 = x
2 + 2 = 4
x = 4

Let's do another one, and mix it up a little: 2 + x = 4
We need to isolate the x. We know that 2 + something is equal to 4, so 4 - 2 must be equal to that something: 4 - 2 = x. And we have the x right where we want it. Now we just need to solve to find x.

It looks like this: 2 + x = 4
4 - 2 = x
2 = x

Now let's look at a problem like this: 3x = 6
This means that 3 times something is 6 . . . but what is that something?
We follow the same steps: isolate x and solve the problem like this: 3x = 6
x = 6/3
x = 2

Now let's make it a little harder: 3x + 4 = 12
3x = 12 - 4
3x = 9
x = 9/3
x = 3

Math Tip of the Day -- Coordinates on a Grid

The important thing to remember when plotting points on a grid is that the X axis goes east west, and the Y axis goes north and south. When you are writing the coordinates, the X coordinate is always first, just like it comes before Y in the alphabet.

The point where the two axes meet is the center of the graph, and the coordinates are (0,0) because it is at point 0 on both the X and the Y axis.

Another thing that is important to remember is that when we move to the right on the X axis or upward on the Y axis, we are moving in a positive direction. Conversely, when we move to the left on the X axis on downward on the Y axis, we are moving in a negative direction.

The intersection of the two axes creates four quadrants. On one quadrant, all coordinates are positive. In the quadrant that is diagonal to that one, all coordinates are negative.

The other two quadrants contain both positives and negatives. In the lower right quadrant, the first coordinate is positive because the first coordinate is always on the X axis, and we are moving to the right. In the upper left quadrant, the first coordinate is negative because, although we are still on the X axis, we are moving to the left.

Take a look at the grid to the left. We've plotted the coordinates (+3, 0). We've moved three places to the right on the X axis, so our X coordinate is positive. We are still at 0 on the Y axis because we haven't moved upward or downward.

Now take a look at the grid to the right. We've stayed at +3 on the X axis, but we've got downward 2 places on the Y axis. Our coordinates are now (+3, -2)

Math Tip of the Week -- Area and Perimeter

Think of the perimeter as the fence around the yard, and the area as the part you have to mow.

In this example, the perimeter is represented by the border of trees. We find the perimeter by adding the lengths of all of the sides together. In this example, if our yard is 12 feet long by 12 feet wide, we would do this: 12 + 12 + 12 + 12 = 48 ft.

We find the area, or the part in the middle by multiplying the length by the width. Area is represented in square feet. In our example, our yard is 12 feet long by 12 feet wide, we would do this: 12 x 12 = 144 sq. ft.

Math Tip of the Week -- Exponents

Think about how fast word-of-mouth can travel. Whether it's a viral video or a rumor, telling our friends is one of the fasted ways to send information. Why? Because it spreads exponentially.


Let's say you see a funny YouTube video. You send it to two friends. Each of friends sends it to two of their friends. And each of those people send it two more people, and so on.



It would look like this:

Math Tip of the Week - Figuring Out Interest

Did you know that you have to pay a fee to borrow money? It's called "interest," because the person or bank who loans you the money is interested in getting paid back!





How do we figure it out? Easy! Let's say you're buying a car.



Don't be afraid to dream big!!

This car is going to cost $75,000. Hey, I said, "DREAM BIG!!" :)






The rate at which the interest will accrue is 4%.

You will take 5 years to pay off the loan.


We want to find out how much actual interest you will pay on your loan.








First, we must find 4% of $75,000. We know that "of" means "multiply."

.04 x $75,000 = $3,000. This is the interest for 1 year, but we will be paying for 5 years, so we must multiply again by 5.


$3,000 x 5 = $15,000 This is how much total interest we will pay on the loan. That means that we will pay back the $75,000 we borrowed, plus we will pay an extra $15,000 fee (interest).


We can reduce the amount of interest we pay by borrowing a smaller amount, by getting a lower interest rate, or by paying the loan off in less time.

Math Tip of the Week -- Place Values

It can be hard to keep your place when you are working with large numbers. This chart illustrates how place values work. It shows what the number looks like and how we say it and write it out. If you write checks, this is a good thing to know! It also shows how the number breaks down into place values. Just click on the chart to get a closer look!