BurtonMath10

Target- find a cylinder with a volume between 770-790 cm3

Measurement has definitley been the hardest unit for me so far. Once provided with a formula sheet, you can figure out lots of different solutions like a recipe. Something I found interesting was how 2 cones fit exactly into a sphere with the same dimensions. This means that a hemisphere is equal to 1 cone. We also found out that 3 cones fit exactly into a cylinder, and 3 pyramids fit exactly into a box of the same dimensions. As shown below.

The measurement unit is especially hard for me. Something I found fascinating is how a cone is always exactly 1/3 of a box it could be in. Shown below, I demonstrate how to find the volume of a cone.

In order to simplify rational/fractioned exponents, we use FLOWER POWER. This means that the root is always on the bottom, so we take the denominator and put it in the index, as shown above.

In order to solve a value with a negative exponent, we need to flip the reciprocal to turn the negative values into happy ones; as shown above.

This week we ended our numbers unit. I learned a lot, but one of the useful tools was converting entire and mixed square roots.

Entire to Mixed:

Divide the radicand into 2 parts.

Find the square root of one of the 2 new radicands.

Take the square root and put it in front of the other root.

Mixed to Entire:

Find the root of the whole number in front.

Multiply the two root.

This week in math I learned an easy was to find the prime factors of a number, division tables.

Division tables are quite easy once you get the hang of it. Basically you can take any number, and divide it by the smallest prime. Here’s how:

We always want to start with dividing the number by 2, because it is the smallest prime and will chop the number in half making it signifigantly smaller. Of course, we can only divide by 2 on an even number.

If your given number is not divisible by 2, you will want to try and divide it by 3. Add up all of the digits to see if that final number is divisible by 3.

Eg: 45 = 4 + 5.

4+ 5= 9

9 is divisible by 3, therefore 45 is also.

When we can’t divide the number by 3 anymore, we will want to move on to 5. We can tell if the number can be divided by 5 if the last digit is 5 or 0.

After 5 we can try 7, then 11.

Once you reach the bottom of your division table, you should end up with a prime number that you can divide by itself.

You can easily gather the prime factors of a number by looking at the amount of primes you put on the left of the table, shown in the video example above.

Division tables are over all a very effecient way of finding prime factors.

pythagoreans theorem