Month: September 2017

Math 10- Week 4

This week, my ah-ha moment was while I was working on this question:

((64a)^\frac{1}{3})^\frac{1}{2}

At first, I got the answer to the left. I then checked the answer only to realize that it was wrong but I could not figure out why. A few moments later, I realized that 64 was a coefficient and that \frac{1}{6} also had to be distributed to that as well. So then I redid my work and got the right answer (the work on the right).

Math 10- Week 3

Week 3 was almost like a review of exponents from grade 9 but with a bit more “pizazz” because we learned about negative exponents, which was entirely new to me.

I understood it quickly and got the hang of it after a few examples, however, I did still have some trouble with the assignments. Mainly this one: Simplify. Write the final answer with positive exponents. (5 a^3 b^2)(-2a^-2b)^-3 ÷ (-5a^8b^-9)^-2

At first, I got confused while I was simplifying and ended up with this:

I realized where I went wrong- the exponents inside do not change when you move it “upstairs” or “downstairs.” So then I changed how I did my work and got this:

which was correct. I learned to be extremely careful with negatives because I can be forgetful with the rules.

Week 2- Math 10

This week, we covered more prime factorization and a few square and cube root related questions.

One question I had a bit of trouble with was this one:

The mixed radical \frac{1}{12} \sqrt[3]{128} can be converted to a mixed radical in simplest form a \sqrt[3]{b} . The value of a+b to the nearest tenth is ______. 

At first, I did this:

Then I checked the answer and it wasn’t right. I realized what I did wrong so I redid my math which resulted in this:

And it was the right answer.

Math 10 Week 1

The first week of class we did numbers- more specifically, we did prime numbers, prime factorization, lowest common multiple and greatest common factors (and roots). It was a lot like a review of what we did in grade 9.

One question I had a slightly hard time with was this one:

5. Twin primes are defined to be consecutive odd numbers that are both prime. List the seven other twin primes less than 80.

I counted until 23, which is a prime number, and assumed that it should be on the list paired with 29. However, after a long period of thinking and not seeing 23 in the answer, I realized that 25 was the next odd number but 25 is not a prime number so the next twin pair would be 29 and 31.