Category Archives: Math 9

What I Have Learned About Grade 9 Exponents

Posted by rubym2017 in Math 9, Uncategorized and tagged with

What is an exponent? What does it tell you to do?

  • The exponent of a number says how many times to use a number in multiplication or how many copies are being made of a number.
  • An example is 5^3 = 5\cdot5\cdot5 = 125.
  • A common mistake made, is that people assume that 5^3 = 5\cdot3
  • We need to remember that the exponent is the number of copies being made of the base and not the multiplication of the two numbers.

Evaluating Exponents. How do brackets affect evaluating a power? 

  • Exponents are lazy!
  • If you have (-3^2) = (-3)(-3) = 9

In this case, the exponent 2 sees the negative three in the brackets and copies the whole equation twice.

  • However, if you have the equation -3^2, the exponent will only copy the 3 (not the negative sign).

-(3)(3) = -9

  • Brackets indicate what the exponent should use. So if you would like for the exponent to see a negative base, remember to place the number inside a pair of brackets.

Multiplication Law of exponents. 

The multiplication law is simple.

  • If the bases are the same number, all you have to do is add the exponents together and the base will stay the way it was.
  • Example: 5^9\cdot5^2 = 5^{9+2} = 5^{11}
  • If the bases are different numbers, the question does not fall into the multiplication law category and instead is thought of as a BEDMAS question.

Division Law of exponents. 

  • The division law is similar to the multiplication law, but with different rules.
  • Just like the multiplication law, only if the bases are same number, will this rule be successful.
  • But instead of adding the exponents together, we subtract the exponents while using the division law.
  • Example: 8^{12}\div8^6 = 8^{12-6} = 8^6
  • If the bases are different numbers, this rule will not fall into the division law category and instead will also be thought of as a BEDMAS question.

Power of a Power Law.

  • When you see a question that looks like this (4^2)^4, you can use the power of a power law.
  • All you have to do, is to multiply the two exponents (the exponent on the inside of the brackets and the exponent on the outside of the brackets).
  • Example: (4^2)^4 = 4^{2\cdot4} = 4^8

BEDMAS – When is an exponent question really a BEDMAS question?

  • We use the BEDMAS technique when we are adding exponents and subtracting exponents, no matter what the base is. We also use BEDMAS when we are multiplying and dividing exponents, but only when the bases are different numbers. 
  • Before we evaluate a BEDMAS question, we always need to remember the order of operations.

  • In a question including brackets, we always do the work that is inside the brackets first. Example: (2^3\cdot2^5)+2

2^3\cdot2^5 = 2^{3+5} = 2^8 + 2^1

= 256 + 2 = 258

With any question using addition, subtraction, division or multiplication, that does not include brackets in the question, you always do the exponent work first and then evaluate the existing numbers using the symbol that is requested. Example: 4^2\cdot2^3

= 16\cdot8 = 128

What I Have Learned About Grade 9 Fractions -Updated Version

Posted by rubym2017 in Math 9

What is a Rational Number?

  • A rational number is any number that can be written as a fraction or a quotient. Example: \frac{1}{2} = A rational number

What I know about Number Lines

  • You can place fractions on a number line between whole numbers. In order to do this you have to make them have a common denominator. For example you can place 8\frac{2}{3} and 8\frac{5}{6} between the numbers 8 and 9 on the number line. But before you can do that you have to find a common denominator, which would change them to 8\frac{4}{6} and 8\frac{5}{6} . You can then plot them on the number line.

What I know about Comparing Fractions

  • How can you tell if a rational number is greater than another? You can create a common denominator to find out which one is greater than the other.
  • For example: Which fraction is greater? \frac{1}{3} or \frac{2}{4}
  • Find the common denominator and change it to \frac{4}{12} and \frac{6}{12}
  • Now you can see that \frac{6}{12} is greater than \frac{4}{12} because 6 parts out of 12 is greater than 4 parts out of 12.

 

What I know about Adding and Subtraction Fractions

  • For both adding and subtracting fractions you have to find a common denominator
  • For example: \frac{-2}{3} + \frac{1}{5} you would need to change it to \frac{-10}{15} + \frac{3}{15}
  • Next, you would add the numerators and keep the denominator the same which would equal to \frac{-7}{15}
  • The same rules apply for subtracting fractions

What I know about Multiplying Fractions

  • You don’t need a common denominator when multiplying fractions. Like Ms. Burton says it’s a “Just do it question.”
  • For example: \frac{2}{3}\times\frac{1}{5} is equal to \frac{2}{15}
  • If your answer is a fraction that is not in its’ simplest form, you would simplify it.
  • To simplify a fraction you would divide both the top and bottom of the fraction by the greatest common factor. For example in \frac{8}{12} the largest number that would go exactly into both 8 and 12 would be the number 4. You would divide both the top and bottom by 4 and you would get the simplified fraction of \frac{2}{3}

What I know about Dividing Fractions

  • Let’s look at the equation \frac{1}{2}\div\frac{1}{6}
  • You would need to change the second fraction in the division equation upside down. It becomes a reciprocal. For example \frac{1}{6} would become \frac{6}{1}
  • Next you would change it from a division question to a multiplication question \frac{1}{2}\times\frac{6}{1} = \frac{6}{2} = 3

 

Digital Footprint- Ruby Maher

This is a presentation on Digital Footprints and how to keep them safe.

  1. How might your digital footprint affect your future opportunities? Give at least two examples.

Answer: Your digital footprint can affect your future if you use social media and other online sources inappropriately. Future post secondary schools may look in to your online presence as part of their admission process. If you plan to go to college or university after graduation, consider the fact that they might be checking out your digital footprint. Also, future employers will most likely check in to your online presence when they are looking to hire you. If they something inappropriate, they probably won’t hire you.

2. Describe at least three strategies that you can use to keep your digital footprint appropriate and safe.

Answer: The first strategy that you can use is to keep your social media accounts private and do not allow anyone one to follow you if you do not know them. The second strategy you can use is apply the THINK method before posting anything online ( Is it true, is it helpful, is it inspiring, is it necessary and is it kind). The third strategy you can use is to remember how this could possibly affect you in the future before posting.

3. What information did you learn that you would pass on to other students? How would you go about telling them?

Answer: I learned from the video that up to 70% of employers will look into your online presence before they hire you. They suggested that you really filter what you put online. They say to be protective and selective about what you put out there. They also recommended to be very vigilant about your privacy settings. They strongly urge everyone to research themselves to see what is out there for the public to see.