Adding and subtracting negative numbers is a pretty tricky thing to learn (trust me, I know!), but if you go through it slowly and use a couple tricks, you can figure it out.
Here's our equation:
The first two numbers we are going to deal with are
So the easiest way to learn how to do this type of problem is make a number line like this:
Obviously, this number line doesn't go far enough, but you could draw it to go all the way to
( If you need extra explanation: You moved 9 spaces to the right because that is that direction positive numbers are. Since 9 is positive, you will get closer to 0, not further away.)
Okay! So now we have:
Put your finger back on the
You should now be at
As the last two digits in
but factors of
Hence prime factors of
Note : This method of factorization, in which we first find identifiable factors and then proceed until all prime factors are known is called tree method. This is graphically described below.
Do long division ..
You can continue for as many decimal places as you wish.
Or simply use a calculator if you need the answer immediately.
This is a metric prefix problem. Some of the metric prefixes are:
In this case, you have:
We see that the largest is
See the construction tips in the explanation.
Draw a number line ( A to B) of some easily divisible length. Perhaps 15 lots of
Draw the line BG of some length that is easily divided into 5 equal parts. The angle does not matter as long as it is sensible.
Draw the line GA. Then the parallel lines from F,E,D and C
This has provided a full set of
In the same way as in Step 1 divide AH into 3 parts
In the same way divide AB into
In order to compare, we need to convert all four speeds to a common unit. Let's convert them all to feet per hour:
A teacher will expect the prime number method. Just for the hell of it this is a different approach!
We have two numbers ; 24 and 7
I am going to count the 24's. However lets look at this value.
24 can be 'split' into a sum of 7's with a remainder. So each 24 consists of:
If we sum columns of these we will get the 3 summing to a value into which 7 will divide exactly. When this happens we have found our least common multiple.
REMEMBER WE ARE COUNTING THE 24's
We have a count of 7 so the value is
Let's use a number line and start at
Now since the temperature rose by 8, we know that it is going to move to the right towards the positive numbers. It is always the same on a number line:
Put your finger on the
You should be on the
So the temperature is now
Write each number as the product of its prime factors.
Then you see what are made up of and what they have in common: