Category Archives: Grade 10

Math 10 Week 2 – Exponents and The Scientific Method

Posted by rubym2017 in Math 10 and tagged with

Exponent Law Revision:

  • First, there is the Multiplication Law: If the question is a multiplication question and the bases are the same, you can add the exponents together and keep the base the way it was. Example: 5^6\cdot5^2 = 5^8
  • Then, there was the Division Law: If the question is a division question and the bases are the same, you can subtract the exponents and keep the base the way it was, similar to the multiplication law but instead dealing with subtraction. Example:2^9\div2^4 = 2^3
  • After that, there was the Power of a Power Law: If the question looks like (7^2)^2you can use this law. All you have to do is multiply the exponents and keep the base the way it was. Example: (7^2)^2 = 7^4
  • And last but not least, there is the Exponent of Zero: If the question has an exponent of zero, you automatically know that the answer will equal to one. Example: 3^0 = 1

Negative Exponents:

If you see a number with a negative exponent, we know that you can write the answer as a fraction. If we have {2}^{-3}  and we know the answer to {2}^{3} is equal to 8, then we use the 8 as the denominator and a 1 as the numerator. Example: {2}^{-3} = {2}^{3}

{2}^{3} = 8

{2}^{-3} = \frac{1}{8}

Math 10 Week 1 – Numbers & Factorization

Posted by rubym2017 in Math 10 and tagged with ,

Discovering Prime Factors & Creating Factor Trees:

First, let’s start off with understanding our vocabulary.

  • Prime Number: A prime number is any number that is only divisible by itself and 1. (Example: 2, 3, 5, etc.)
  • Composite Number: A composite number is the opposite of a prime number. Composite numbers are whole numbers that can be divided by numbers other than itself. (Example: 4, 6, 8, etc.)
  • Factors: Factors are numbers that divide into a composite number. (Example: 2 & 5 are factors of 10)

Prime Factorization:

To “factor” a number is to break down that number into smaller parts. To find the prime factorization of a number, you need to break that number down into its prime factors.

In class, we learned different methods to determine the prime factors of a whole number. The method that I thought was the most efficient was the factor tree. Although division tables worked nicely with bigger and more complicated numbers, I felt that the factor trees were easier to understand and faster to complete.

Factor Tree:

Let’s look at an example of a factor tree.

In this example, we see that we are trying the find the prime factors of 24. To start, we need to pick two numbers that can be multiplied to equal 24 (in this case, we have chosen 2 and 12). Then, you use those two numbers and do the same thing to them until you finish with prime numbers. If done correctly, this method will form a tree-like shape.